Trò chơi con trăn nhảy 2

trò chơi c++ 2d, trò chơi c++ sdl, trò chơi 2d c++ sdl, trò chơi c++, trò chơi c++ sdl 2. 0, học làm trò chơi với c++, hướng dẫn học lập trình trò chơi c++ 1 phút đọc

Hello, chào mừng các bạn đã đến với chủ đề học lập trình game c++ phần 2

Bài số 6 này chúng ta sẽ cùng tìm hiểu một kỹ thuật tiếp theo trong chương trình game c++

Đó là. Kỹ thuật nhảy, [nhảy ] cho game nhân vật1. Lý thuyết cơ bản

Trong bài trước, chúng ta đã xử lý việc tải game nhân vật, di chuyển trên màn hình bên trái phải

Về cơ bản trạng thái di chuyển của trò chơi nhân vật được quản lý và lưu trữ bởi biến input_tyle. with full status as

Đưa ra một mảng arr[] trong đó mỗi phần tử biểu thị số bước tối đa có thể được thực hiện từ chỉ mục đó. Nhiệm vụ là tìm số bước nhảy ít nhất để đi đến cuối mảng bắt đầu từ chỉ số 0. Nếu không thể truy cập đến cuối, hãy trả về -1

ví dụ.  

Đầu vào. mảng[] = {1, 3, 5, 8, 9, 2, 6, 7, 6, 8, 9}
Đầu ra. 3 [1-> 3 -> 9 -> 9]
Giải thích. Nhảy từ phần tử thứ nhất sang phần tử thứ 2 vì chỉ có 1 bước.
Bây giờ có ba tùy chọn 5, 8 hoặc 9. Tôi
f 8 hoặc 9 được chọn thì có thể đến nút cuối 9. Vì vậy, 3 bước nhảy được thực hiện.

Đầu vào. mảng[] = {1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}
Đầu ra. 10
Giải thích. Trong mỗi bước cần có một lần nhảy nên số lần nhảy là 10.

Đề nghị thực hành

trò chơi nhảy

Thử nó

Số lần nhảy tối thiểu để đến đích bằng cách sử dụng Đệ quy.  

Bắt đầu từ phần tử đầu tiên và gọi đệ quy tất cả các phần tử có thể truy cập được từ phần tử đầu tiên. Số lần nhảy tối thiểu để kết thúc từ lần đầu tiên có thể được tính bằng cách sử dụng giá trị tối thiểu từ các cuộc gọi đệ quy.  

minJumps[start, end] = Min [ minJumps[k, end] ] cho tất cả k có thể truy cập từ đầu

Thực hiện theo các bước được đề cập dưới đây để thực hiện ý tưởng

• Tạo một hàm đệ quy
• Trong mỗi cuộc gọi đệ quy, nhận tất cả các nút có thể truy cập từ chỉ mục đó
  • Đối với mỗi chỉ mục, hãy gọi hàm đệ quy
  • Tìm số lần nhảy tối thiểu để đi đến cuối từ chỉ mục hiện tại
• Trả về số lần nhảy tối thiểu từ lời gọi đệ quy

Dưới đây là việc thực hiện phương pháp trên

C++

Minimum number of jumps to reach end is 3

568

Minimum number of jumps to reach end is 3

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Minimum number of jumps to reach end is 3

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Minimum number of jumps to reach end is 3

574

Minimum number of jumps to reach end is 3

0

Minimum number of jumps to reach end is 3

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Minimum number of jumps to reach end is 3

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Minimum number of jumps to reach end is 3

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Minimum number of jumps to reach end is 3

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Minimum number of jumps to reach end is 3

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Minimum number of jumps to reach end is 3

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Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

9

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

1

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

3

Minimum number of jumps to reach end is 3

4

Minimum number of jumps to reach end is 3

5

Minimum number of jumps to reach end is 3

6

Minimum number of jumps to reach end is 3

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Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

9

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Minimum number of jumps to reach end is 3

5685

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

5687

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

1

Minimum number of jumps to reach end is 3

5690

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

5692

Minimum number of jumps to reach end is 3

5693

Minimum number of jumps to reach end is 3

1

Minimum number of jumps to reach end is 3

5695

Minimum number of jumps to reach end is 3

5

Minimum number of jumps to reach end is 3

3

Minimum number of jumps to reach end is 3

5698

Minimum number of jumps to reach end is 3

5699

Minimum number of jumps to reach end is 3

1

Minimum number of jumps to reach end is 3

5701

Minimum number of jumps to reach end is 3

5699

Minimum number of jumps to reach end is 3

3

Minimum number of jumps to reach end is 3

5704

Minimum number of jumps to reach end is 3

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Minimum number of jumps to reach end is 3

5706

Minimum number of jumps to reach end is 3

5____15708

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Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

6

Minimum number of jumps to reach end is 3

5713

Minimum number of jumps to reach end is 3

5708

 

Minimum number of jumps to reach end is 3

5715

Minimum number of jumps to reach end is 3

1

Minimum number of jumps to reach end is 3

5717

Minimum number of jumps to reach end is 3

7

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

1

Minimum number of jumps to reach end is 3

5721

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

1

Minimum number of jumps to reach end is 3

5724

Minimum number of jumps to reach end is 3

5725

Minimum number of jumps to reach end is 3

5726

Minimum number of jumps to reach end is 3

5725

Minimum number of jumps to reach end is 3

5728

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

5730

Minimum number of jumps to reach end is 3

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Minimum number of jumps to reach end is 3

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Minimum number of jumps to reach end is 3

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Minimum number of jumps to reach end is 3

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Minimum number of jumps to reach end is 3

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Minimum number of jumps to reach end is 3

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Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

6

Minimum number of jumps to reach end is 3

7

Minimum number of jumps to reach end is 3

5708

 

Minimum number of jumps to reach end is 3

5741

Minimum number of jumps to reach end is 3

5742

C

Minimum number of jumps to reach end is 3

5743

Minimum number of jumps to reach end is 3

569

Minimum number of jumps to reach end is 3

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Minimum number of jumps to reach end is 3

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Minimum number of jumps to reach end is 3

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Minimum number of jumps to reach end is 3

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Minimum number of jumps to reach end is 3

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Minimum number of jumps to reach end is 3

1

Minimum number of jumps to reach end is 3

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Minimum number of jumps to reach end is 3

1

Minimum number of jumps to reach end is 3

04

Minimum number of jumps to reach end is 3

1

Minimum number of jumps to reach end is 3

06

Minimum number of jumps to reach end is 3

7

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

09

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

3

Minimum number of jumps to reach end is 3

12

Minimum number of jumps to reach end is 3

5

Minimum number of jumps to reach end is 3

6

Minimum number of jumps to reach end is 3

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Minimum number of jumps to reach end is 3

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Minimum number of jumps to reach end is 3

17

Minimum number of jumps to reach end is 3

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Minimum number of jumps to reach end is 3

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Minimum number of jumps to reach end is 3

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Minimum number of jumps to reach end is 3

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Minimum number of jumps to reach end is 3

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Minimum number of jumps to reach end is 3

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Minimum number of jumps to reach end is 3

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Minimum number of jumps to reach end is 3

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Minimum number of jumps to reach end is 3

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Minimum number of jumps to reach end is 3

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Minimum number of jumps to reach end is 3

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Minimum number of jumps to reach end is 3

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Minimum number of jumps to reach end is 3

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Minimum number of jumps to reach end is 3

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Minimum number of jumps to reach end is 3

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Minimum number of jumps to reach end is 3

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Minimum number of jumps to reach end is 3

1

Minimum number of jumps to reach end is 3

36

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

5692

Minimum number of jumps to reach end is 3

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Minimum number of jumps to reach end is 3

1

Minimum number of jumps to reach end is 3

41

Minimum number of jumps to reach end is 3

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Minimum number of jumps to reach end is 3

1

Minimum number of jumps to reach end is 3

44

Minimum number of jumps to reach end is 3

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Minimum number of jumps to reach end is 3

3

Minimum number of jumps to reach end is 3

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Minimum number of jumps to reach end is 3

5699

Minimum number of jumps to reach end is 3

49

_______08____15708

 

Minimum number of jumps to reach end is 3

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Minimum number of jumps to reach end is 3

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Minimum number of jumps to reach end is 3

54

Minimum number of jumps to reach end is 3

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Minimum number of jumps to reach end is 3

56

Minimum number of jumps to reach end is 3

1

Minimum number of jumps to reach end is 3

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Minimum number of jumps to reach end is 3

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Minimum number of jumps to reach end is 3

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Minimum number of jumps to reach end is 3

1

Minimum number of jumps to reach end is 3

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Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

1

Minimum number of jumps to reach end is 3

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Minimum number of jumps to reach end is 3

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Minimum number of jumps to reach end is 3

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Minimum number of jumps to reach end is 3

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Minimum number of jumps to reach end is 3

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_______08

Minimum number of jumps to reach end is 3

71____15693

Minimum number of jumps to reach end is 3

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Minimum number of jumps to reach end is 3

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Minimum number of jumps to reach end is 3

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Minimum number of jumps to reach end is 3

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Minimum number of jumps to reach end is 3

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Minimum number of jumps to reach end is 3

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Minimum number of jumps to reach end is 3

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Minimum number of jumps to reach end is 3

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Java

Minimum number of jumps to reach end is 3

81

Minimum number of jumps to reach end is 3

569

________ 083 ________ 084

Minimum number of jumps to reach end is 3

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Minimum number of jumps to reach end is 3

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Minimum number of jumps to reach end is 3

94

Minimum number of jumps to reach end is 3

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Minimum number of jumps to reach end is 3

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Minimum number of jumps to reach end is 3

1

Minimum number of jumps to reach end is 3

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Minimum number of jumps to reach end is 3

1

Minimum number of jumps to reach end is 3

04

Minimum number of jumps to reach end is 3

1

Minimum number of jumps to reach end is 3

06

Minimum number of jumps to reach end is 3

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Minimum number of jumps to reach end is 3

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Minimum number of jumps to reach end is 3

5

Minimum number of jumps to reach end is 3

06

Minimum number of jumps to reach end is 3

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Minimum number of jumps to reach end is 3

08

Minimum number of jumps to reach end is 3

5

Minimum number of jumps to reach end is 3

3

Minimum number of jumps to reach end is 3

12

Minimum number of jumps to reach end is 3

5699

Minimum number of jumps to reach end is 3

6

Minimum number of jumps to reach end is 3

14

Minimum number of jumps to reach end is 3

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Minimum number of jumps to reach end is 3

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Minimum number of jumps to reach end is 3

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Minimum number of jumps to reach end is 3

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Minimum number of jumps to reach end is 3

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Minimum number of jumps to reach end is 3

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Minimum number of jumps to reach end is 3

3

Minimum number of jumps to reach end is 3

22

Minimum number of jumps to reach end is 3

14

Minimum number of jumps to reach end is 3

24

Minimum number of jumps to reach end is 3

5699

Minimum number of jumps to reach end is 3

6

Minimum number of jumps to reach end is 3

27

 

Minimum number of jumps to reach end is 3

5

Minimum number of jumps to reach end is 3

9

Minimum number of jumps to reach end is 3

5

Minimum number of jumps to reach end is 3

27

Minimum number of jumps to reach end is 3

5

Minimum number of jumps to reach end is 3

29

Minimum number of jumps to reach end is 3

5

Minimum number of jumps to reach end is 3

31

Minimum number of jumps to reach end is 3

5

Minimum number of jumps to reach end is 3

33

Minimum number of jumps to reach end is 3

5

Minimum number of jumps to reach end is 3

1

Minimum number of jumps to reach end is 3

40

Minimum number of jumps to reach end is 3

5

Minimum number of jumps to reach end is 3

5692

Minimum number of jumps to reach end is 3

5693

Minimum number of jumps to reach end is 3

1

Minimum number of jumps to reach end is 3

45

Minimum number of jumps to reach end is 3

46

Minimum number of jumps to reach end is 3

47

Minimum number of jumps to reach end is 3

48

Minimum number of jumps to reach end is 3

49

Minimum number of jumps to reach end is 3

5699

Minimum number of jumps to reach end is 3

1

Minimum number of jumps to reach end is 3

44

Minimum number of jumps to reach end is 3

5699

Minimum number of jumps to reach end is 3

3

Minimum number of jumps to reach end is 3

55

Minimum number of jumps to reach end is 3

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Minimum number of jumps to reach end is 3

57____046

Minimum number of jumps to reach end is 3

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Minimum number of jumps to reach end is 3

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Minimum number of jumps to reach end is 3

61

Minimum number of jumps to reach end is 3

46

Minimum number of jumps to reach end is 3

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Minimum number of jumps to reach end is 3

5____15708

Minimum number of jumps to reach end is 3

5

Minimum number of jumps to reach end is 3

6

Minimum number of jumps to reach end is 3

54

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Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

72

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

74

Minimum number of jumps to reach end is 3

94

Minimum number of jumps to reach end is 3

76

Minimum number of jumps to reach end is 3

77

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

7

Minimum number of jumps to reach end is 3

5

Minimum number of jumps to reach end is 3

1

Minimum number of jumps to reach end is 3

82

Minimum number of jumps to reach end is 3

46

Minimum number of jumps to reach end is 3

74

Minimum number of jumps to reach end is 3

85

Minimum number of jumps to reach end is 3

74

Minimum number of jumps to reach end is 3

87

Minimum number of jumps to reach end is 3

74

Minimum number of jumps to reach end is 3

89

Minimum number of jumps to reach end is 3

74

Minimum number of jumps to reach end is 3

91

Minimum number of jumps to reach end is 3

74

Minimum number of jumps to reach end is 3

93

Minimum number of jumps to reach end is 3

74

Minimum number of jumps to reach end is 3

95

Minimum number of jumps to reach end is 3

74

Minimum number of jumps to reach end is 3

97

Minimum number of jumps to reach end is 3

74

Minimum number of jumps to reach end is 3

95

Minimum number of jumps to reach end is 3

74

Minimum number of jumps to reach end is 3

89

Minimum number of jumps to reach end is 3

74

Minimum number of jumps to reach end is 3

91

Minimum number of jumps to reach end is 3

56804

Minimum number of jumps to reach end is 3

5

Minimum number of jumps to reach end is 3

1

Minimum number of jumps to reach end is 3

56807

Minimum number of jumps to reach end is 3

5____156809

Minimum number of jumps to reach end is 3

5699

Minimum number of jumps to reach end is 3

56811

Minimum number of jumps to reach end is 3

5699

Minimum number of jumps to reach end is 3

56813

Minimum number of jumps to reach end is 3

14

Minimum number of jumps to reach end is 3

56815

Minimum number of jumps to reach end is 3

46

Minimum number of jumps to reach end is 3

56817

_______08____15708

Minimum number of jumps to reach end is 3

5708

 

Minimum number of jumps to reach end is 3

56821

Python3

Minimum number of jumps to reach end is 3

56822

Minimum number of jumps to reach end is 3

56823

 

Minimum number of jumps to reach end is 3

56824

Minimum number of jumps to reach end is 3

56825

 

 

Minimum number of jumps to reach end is 3

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Minimum number of jumps to reach end is 3

56827

 

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Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

3

Minimum number of jumps to reach end is 3

56834

Minimum number of jumps to reach end is 3

56835

Minimum number of jumps to reach end is 3

56835

Minimum number of jumps to reach end is 3

56837

Minimum number of jumps to reach end is 3

5

Minimum number of jumps to reach end is 3

6

Minimum number of jumps to reach end is 3

14

 

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Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

3

Minimum number of jumps to reach end is 3

56847

Minimum number of jumps to reach end is 3

56835

Minimum number of jumps to reach end is 3

56835

Minimum number of jumps to reach end is 3

14

Minimum number of jumps to reach end is 3

56851

Minimum number of jumps to reach end is 3

5

Minimum number of jumps to reach end is 3

6

Minimum number of jumps to reach end is 3

56854

Minimum number of jumps to reach end is 3

5693

Minimum number of jumps to reach end is 3

56856

Minimum number of jumps to reach end is 3

24

 

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

56859

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Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

56863

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

56865

_______08____156867

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

56869

Minimum number of jumps to reach end is 3

56835

Minimum number of jumps to reach end is 3

56854

Minimum number of jumps to reach end is 3

5693

Minimum number of jumps to reach end is 3

56856

Minimum number of jumps to reach end is 3

24

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

5692

Minimum number of jumps to reach end is 3

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Minimum number of jumps to reach end is 3

56878

Minimum number of jumps to reach end is 3

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Minimum number of jumps to reach end is 3

56880

Minimum number of jumps to reach end is 3

56881

Minimum number of jumps to reach end is 3

46

Minimum number of jumps to reach end is 3

56883

Minimum number of jumps to reach end is 3

56881

Minimum number of jumps to reach end is 3

46

Minimum number of jumps to reach end is 3

56851

Minimum number of jumps to reach end is 3

5

Minimum number of jumps to reach end is 3

3

Minimum number of jumps to reach end is 3

56889

Minimum number of jumps to reach end is 3

56881

Minimum number of jumps to reach end is 3

56891

Minimum number of jumps to reach end is 3

56881

Minimum number of jumps to reach end is 3

46

Minimum number of jumps to reach end is 3

56851

Minimum number of jumps to reach end is 3

5699

Minimum number of jumps to reach end is 3

56896

Minimum number of jumps to reach end is 3

56835

Minimum number of jumps to reach end is 3

56898

Minimum number of jumps to reach end is 3

5699

Minimum number of jumps to reach end is 3

3

Minimum number of jumps to reach end is 3

56901

Minimum number of jumps to reach end is 3

56835

Minimum number of jumps to reach end is 3

56854

Minimum number of jumps to reach end is 3

5693

Minimum number of jumps to reach end is 3

56856

Minimum number of jumps to reach end is 3

24

Minimum number of jumps to reach end is 3

56907

Minimum number of jumps to reach end is 3

56908

Minimum number of jumps to reach end is 3

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Minimum number of jumps to reach end is 3

56881

Minimum number of jumps to reach end is 3

46

Minimum number of jumps to reach end is 3

56912____156869

Minimum number of jumps to reach end is 3

56851

Minimum number of jumps to reach end is 3

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Minimum number of jumps to reach end is 3

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Minimum number of jumps to reach end is 3

56835

Minimum number of jumps to reach end is 3

56896

Minimum number of jumps to reach end is 3

56881

Minimum number of jumps to reach end is 3

46

 

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

6

Minimum number of jumps to reach end is 3

56869

 

 

Minimum number of jumps to reach end is 3

56924

Minimum number of jumps to reach end is 3

56925

Minimum number of jumps to reach end is 3

56835

Minimum number of jumps to reach end is 3

56927

Minimum number of jumps to reach end is 3

46

Minimum number of jumps to reach end is 3

74

Minimum number of jumps to reach end is 3

85

Minimum number of jumps to reach end is 3

74

Minimum number of jumps to reach end is 3

87

Minimum number of jumps to reach end is 3

74

Minimum number of jumps to reach end is 3

89

Minimum number of jumps to reach end is 3

74

Minimum number of jumps to reach end is 3

91

Minimum number of jumps to reach end is 3

74

Minimum number of jumps to reach end is 3

93

Minimum number of jumps to reach end is 3

74

Minimum number of jumps to reach end is 3

95

Minimum number of jumps to reach end is 3

74

Minimum number of jumps to reach end is 3

97

Minimum number of jumps to reach end is 3

74

Minimum number of jumps to reach end is 3

95

Minimum number of jumps to reach end is 3

74

Minimum number of jumps to reach end is 3

89

Minimum number of jumps to reach end is 3

74__156___1

Minimum number of jumps to reach end is 3

56950

Minimum number of jumps to reach end is 3

56835

Minimum number of jumps to reach end is 3

56952

Minimum number of jumps to reach end is 3

56953

Minimum number of jumps to reach end is 3

56954

Minimum number of jumps to reach end is 3

5693____156956

Minimum number of jumps to reach end is 3

74

Minimum number of jumps to reach end is 3

56958

Minimum number of jumps to reach end is 3

56959

Minimum number of jumps to reach end is 3

56960

Minimum number of jumps to reach end is 3

14

Minimum number of jumps to reach end is 3

56962

Minimum number of jumps to reach end is 3

56963

Minimum number of jumps to reach end is 3

46

Minimum number of jumps to reach end is 3

56965

 

Minimum number of jumps to reach end is 3

56966

C#

Minimum number of jumps to reach end is 3

56967

Minimum number of jumps to reach end is 3

569

Minimum number of jumps to reach end is 3

571

Minimum number of jumps to reach end is 3

56970

 

Minimum number of jumps to reach end is 3

87

Minimum number of jumps to reach end is 3

88

_______08____15747

_______08____15748

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

94

Minimum number of jumps to reach end is 3

1

Minimum number of jumps to reach end is 3

2

Minimum number of jumps to reach end is 3

1

Minimum number of jumps to reach end is 3

56982

Minimum number of jumps to reach end is 3

1

Minimum number of jumps to reach end is 3

04

Minimum number of jumps to reach end is 3

1

Minimum number of jumps to reach end is 3

06

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

7

Minimum number of jumps to reach end is 3

5

Minimum number of jumps to reach end is 3

06

Minimum number of jumps to reach end is 3

5

Minimum number of jumps to reach end is 3

08

Minimum number of jumps to reach end is 3

5

Minimum number of jumps to reach end is 3

3

Minimum number of jumps to reach end is 3

12

Minimum number of jumps to reach end is 3

5699

Minimum number of jumps to reach end is 3

6

Minimum number of jumps to reach end is 3

7

 

Minimum number of jumps to reach end is 3

5

Minimum number of jumps to reach end is 3

17

Minimum number of jumps to reach end is 3

5

Minimum number of jumps to reach end is 3

19

Minimum number of jumps to reach end is 3

5

Minimum number of jumps to reach end is 3

3

Minimum number of jumps to reach end is 3

20

Minimum number of jumps to reach end is 3

5699

Minimum number of jumps to reach end is 3

6

Minimum number of jumps to reach end is 3

1____157009

 

Minimum number of jumps to reach end is 3

5

Minimum number of jumps to reach end is 3

9

Minimum number of jumps to reach end is 3

5

Minimum number of jumps to reach end is 3

27

Minimum number of jumps to reach end is 3

5

Minimum number of jumps to reach end is 3

29

Minimum number of jumps to reach end is 3

5

Minimum number of jumps to reach end is 3

31

Minimum number of jumps to reach end is 3

5

Minimum number of jumps to reach end is 3

33

Minimum number of jumps to reach end is 3

5

Minimum number of jumps to reach end is 3

1

Minimum number of jumps to reach end is 3

57022____01

Minimum number of jumps to reach end is 3

57009

Minimum number of jumps to reach end is 3

5

Minimum number of jumps to reach end is 3

5692

Minimum number of jumps to reach end is 3

5693

Minimum number of jumps to reach end is 3

1

Minimum number of jumps to reach end is 3

57029

Minimum number of jumps to reach end is 3

48

Minimum number of jumps to reach end is 3

49

Minimum number of jumps to reach end is 3

5699

Minimum number of jumps to reach end is 3

1

Minimum number of jumps to reach end is 3

44

Minimum number of jumps to reach end is 3

5699

Minimum number of jumps to reach end is 3

3

Minimum number of jumps to reach end is 3

57037

Minimum number of jumps to reach end is 3

1

Minimum number of jumps to reach end is 3

57039

Minimum number of jumps to reach end is 3

5705

Minimum number of jumps to reach end is 3

49

Minimum number of jumps to reach end is 3

5____15708

Minimum number of jumps to reach end is 3

5

Minimum number of jumps to reach end is 3

6

Minimum number of jumps to reach end is 3

54

_______08____15708

 

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

72

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

74

Minimum number of jumps to reach end is 3

94

Minimum number of jumps to reach end is 3

76

Minimum number of jumps to reach end is 3

57055

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

7

Minimum number of jumps to reach end is 3

5

Minimum number of jumps to reach end is 3

1

Minimum number of jumps to reach end is 3

57060

Minimum number of jumps to reach end is 3

5

Minimum number of jumps to reach end is 3

1

Minimum number of jumps to reach end is 3

57063

_______05____157065

Minimum number of jumps to reach end is 3

5699

Minimum number of jumps to reach end is 3

56811

Minimum number of jumps to reach end is 3

5699

Minimum number of jumps to reach end is 3

57069

_______08____15708

Minimum number of jumps to reach end is 3

5708

 

Minimum number of jumps to reach end is 3

57073

PHP

Minimum number of jumps to reach end is 3

57074

Minimum number of jumps to reach end is 3

57075

Minimum number of jumps to reach end is 3

569

 

Minimum number of jumps to reach end is 3

57077

Minimum number of jumps to reach end is 3

57078

Minimum number of jumps to reach end is 3

57079

Minimum number of jumps to reach end is 3

2____157081

Minimum number of jumps to reach end is 3

74

Minimum number of jumps to reach end is 3

57083

Minimum number of jumps to reach end is 3

74

Minimum number of jumps to reach end is 3

57085

Minimum number of jumps to reach end is 3

24

Minimum number of jumps to reach end is 3

7

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

9

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

1

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

3

Minimum number of jumps to reach end is 3

5693____157085

Minimum number of jumps to reach end is 3

57097

Minimum number of jumps to reach end is 3

57083

Minimum number of jumps to reach end is 3

24

Minimum number of jumps to reach end is 3

5

Minimum number of jumps to reach end is 3

6

Minimum number of jumps to reach end is 3

7

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

17

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

19

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

3

Minimum number of jumps to reach end is 3

5693____157081

Minimum number of jumps to reach end is 3

56927

Minimum number of jumps to reach end is 3

57083

Minimum number of jumps to reach end is 3

57114

Minimum number of jumps to reach end is 3

5

Minimum number of jumps to reach end is 3

6

Minimum number of jumps to reach end is 3

57085____157118

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

9

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

27

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

29

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

31

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

33

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

57131

Minimum number of jumps to reach end is 3

57132

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

5692

Minimum number of jumps to reach end is 3

5693

Minimum number of jumps to reach end is 3

57137

Minimum number of jumps to reach end is 3

56835

Minimum number of jumps to reach end is 3

57083

Minimum number of jumps to reach end is 3

57118

Minimum number of jumps to reach end is 3

57137

Minimum number of jumps to reach end is 3

57142

Minimum number of jumps to reach end is 3

57085

Minimum number of jumps to reach end is 3

57144

Minimum number of jumps to reach end is 3

48

Minimum number of jumps to reach end is 3

57137

Minimum number of jumps to reach end is 3

57142

Minimum number of jumps to reach end is 3

57083

Minimum number of jumps to reach end is 3

56881

Minimum number of jumps to reach end is 3

57081

Minimum number of jumps to reach end is 3

56927

Minimum number of jumps to reach end is 3

57083

Minimum number of jumps to reach end is 3

57153

Minimum number of jumps to reach end is 3

57137

Minimum number of jumps to reach end is 3

57155

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

7

Minimum number of jumps to reach end is 3

5

Minimum number of jumps to reach end is 3

57159

Minimum number of jumps to reach end is 3

57160

Minimum number of jumps to reach end is 3

57081

Minimum number of jumps to reach end is 3

74

Minimum number of jumps to reach end is 3

57137

Minimum number of jumps to reach end is 3

74

Minimum number of jumps to reach end is 3

57085

Minimum number of jumps to reach end is 3

57166

Minimum number of jumps to reach end is 3

5

Minimum number of jumps to reach end is 3

5

Minimum number of jumps to reach end is 3

3____15693

Minimum number of jumps to reach end is 3

57159

Minimum number of jumps to reach end is 3

57172

Minimum number of jumps to reach end is 3

57173

Minimum number of jumps to reach end is 3

57159

Minimum number of jumps to reach end is 3

57175

Minimum number of jumps to reach end is 3

57131

Minimum number of jumps to reach end is 3

24

Minimum number of jumps to reach end is 3

5699

Minimum number of jumps to reach end is 3

57131

Minimum number of jumps to reach end is 3

56835

Minimum number of jumps to reach end is 3

57159

Minimum number of jumps to reach end is 3

57182

_______08____15708

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

6

Minimum number of jumps to reach end is 3

57131

Minimum number of jumps to reach end is 3

5732

Minimum number of jumps to reach end is 3

5708

 

Minimum number of jumps to reach end is 3

56

Minimum number of jumps to reach end is 3

57081

Minimum number of jumps to reach end is 3

56835____157194

Minimum number of jumps to reach end is 3

57195

Minimum number of jumps to reach end is 3

57196

Minimum number of jumps to reach end is 3

56835

Minimum number of jumps to reach end is 3

57198

Minimum number of jumps to reach end is 3

5693

Minimum number of jumps to reach end is 3

57081

Minimum number of jumps to reach end is 3

57166

 

Minimum number of jumps to reach end is 3

57202

Minimum number of jumps to reach end is 3

57203

Minimum number of jumps to reach end is 3

57204

Minimum number of jumps to reach end is 3

57205

Minimum number of jumps to reach end is 3

57206

Minimum number of jumps to reach end is 3

57207

Minimum number of jumps to reach end is 3

57081

Minimum number of jumps to reach end is 3

57209

Minimum number of jumps to reach end is 3

57196

Minimum number of jumps to reach end is 3

57211

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

57073

Minimum number of jumps to reach end is 3

57214

Javascript

Minimum number of jumps to reach end is 3

57215

 

Minimum number of jumps to reach end is 3

57216

Minimum number of jumps to reach end is 3

569

 

Minimum number of jumps to reach end is 3

574

Minimum number of jumps to reach end is 3

0

Minimum number of jumps to reach end is 3

57079

Minimum number of jumps to reach end is 3

57221

Minimum number of jumps to reach end is 3

7

 

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

9

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

1

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

3

Minimum number of jumps to reach end is 3

4

Minimum number of jumps to reach end is 3

5

Minimum number of jumps to reach end is 3

6

Minimum number of jumps to reach end is 3

7

 

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

9

_______08____15681

_______08____15683

_______08

Minimum number of jumps to reach end is 3

5685

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

5687

_______08____157244

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

5692

Minimum number of jumps to reach end is 3

57247

Minimum number of jumps to reach end is 3

5

Minimum number of jumps to reach end is 3

3

Minimum number of jumps to reach end is 3

5698

Minimum number of jumps to reach end is 3

5699

Minimum number of jumps to reach end is 3

57252

Minimum number of jumps to reach end is 3

5699

Minimum number of jumps to reach end is 3

3

Minimum number of jumps to reach end is 3

57255

Minimum number of jumps to reach end is 3

5705

Minimum number of jumps to reach end is 3

57257

Minimum number of jumps to reach end is 3

5____15708

_______08____15708

 

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

6

Minimum number of jumps to reach end is 3

5713

Minimum number of jumps to reach end is 3

5708

 

 

Minimum number of jumps to reach end is 3

5715

 

_______08____157268

_______08____157270

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

57272

Minimum number of jumps to reach end is 3

5731

Minimum number of jumps to reach end is 3

57166

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

57272

Minimum number of jumps to reach end is 3

57277

Minimum number of jumps to reach end is 3

57278

 

Minimum number of jumps to reach end is 3

57279

Đầu ra

Minimum number of jumps to reach end is 3

47

Độ phức tạp về thời gian. O[nNn].  

• Có tối đa n cách di chuyển từ một phần tử.  
• Vì vậy, số bước tối đa có thể là nn, do đó O[nn]

Không gian phụ trợ. Trên]. Đối với ngăn xếp cuộc gọi đệ quy.  

Số lần nhảy tối thiểu để kết thúc bằng Lập trình động từ trái sang phải

Có thể quan sát thấy rằng sẽ có các bài toán con trùng nhau.  

Ví dụ: trong mảng, arr[] = {1, 3, 5, 8, 9, 2, 6, 7, 6, 8, 9} minJumps[3, 9] sẽ được gọi hai lần khi arr[3] có thể truy cập được . Như vậy bài toán này có cả hai tính chất [cấu trúc con tối ưu và các bài toán con chồng lấp] của Quy hoạch động

Thực hiện theo các bước dưới đây để thực hiện ý tưởng

• Tạo mảng jumps[] từ trái sang phải sao cho jumps[i] cho biết số bước nhảy tối thiểu cần thiết để đạt được mảng[i] từ mảng[0]
• Để lấp đầy mảng nhảy, hãy chạy bộ đếm vòng lặp bên trong vòng lặp lồng nhau là j và số vòng lặp bên ngoài là i
  • Vòng ngoài từ 1 đến n-1 và vòng trong từ 0 đến i
  • Nếu i nhỏ hơn j + arr[j] thì đặt jumps[i] ở mức tối thiểu của jumps[i] và jumps[j] + 1. ban đầu đặt jump[i] thành INT MAX
• Nhảy trở lại [n-1]

Dưới đây là việc thực hiện các phương pháp trên

C++

Minimum number of jumps to reach end is 3

57280

Minimum number of jumps to reach end is 3

57281

Minimum number of jumps to reach end is 3

570

________ 1571 ________ 1572 ________ 1573

 

Minimum number of jumps to reach end is 3

1

Minimum number of jumps to reach end is 3

57287

Minimum number of jumps to reach end is 3

1

Minimum number of jumps to reach end is 3

57289

Minimum number of jumps to reach end is 3

1

Minimum number of jumps to reach end is 3

57291

Minimum number of jumps to reach end is 3

6

Minimum number of jumps to reach end is 3

57293

 

Minimum number of jumps to reach end is 3

57077

Minimum number of jumps to reach end is 3

57295

Minimum number of jumps to reach end is 3

1

Minimum number of jumps to reach end is 3

2

Minimum number of jumps to reach end is 3

1

Minimum number of jumps to reach end is 3

4

Minimum number of jumps to reach end is 3

1

Minimum number of jumps to reach end is 3

6

Minimum number of jumps to reach end is 3

7

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

57304

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

1

Minimum number of jumps to reach end is 3

57307

Minimum number of jumps to reach end is 3

57308

Minimum number of jumps to reach end is 3

1

Minimum number of jumps to reach end is 3

57310

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

1

Minimum number of jumps to reach end is 3

57313

 

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

3

Minimum number of jumps to reach end is 3

57316

Minimum number of jumps to reach end is 3

5

Minimum number of jumps to reach end is 3

6

Minimum number of jumps to reach end is 3

23

 

_______08____157321

 

_______08____157323

_______08

Minimum number of jumps to reach end is 3

57325

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

5692

Minimum number of jumps to reach end is 3

57328

Minimum number of jumps to reach end is 3

5____157330

Minimum number of jumps to reach end is 3

5

Minimum number of jumps to reach end is 3

5692

Minimum number of jumps to reach end is 3

57333

Minimum number of jumps to reach end is 3

5699

Minimum number of jumps to reach end is 3

3

Minimum number of jumps to reach end is 3

57336

Minimum number of jumps to reach end is 3

5705

Minimum number of jumps to reach end is 3

57338

Minimum number of jumps to reach end is 3

5705

Minimum number of jumps to reach end is 3

57340

Minimum number of jumps to reach end is 3

5732

Minimum number of jumps to reach end is 3

5699

Minimum number of jumps to reach end is 3

5708

Minimum number of jumps to reach end is 3

5____15708

_______08____15708

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

6

Minimum number of jumps to reach end is 3

57350

Minimum number of jumps to reach end is 3

5708

 

Minimum number of jumps to reach end is 3

72

Minimum number of jumps to reach end is 3

1

Minimum number of jumps to reach end is 3

5717

Minimum number of jumps to reach end is 3

7

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

1

Minimum number of jumps to reach end is 3

5721

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

1

Minimum number of jumps to reach end is 3

57361

Minimum number of jumps to reach end is 3

5725

Minimum number of jumps to reach end is 3

5726

Minimum number of jumps to reach end is 3

5725

Minimum number of jumps to reach end is 3

5693

Minimum number of jumps to reach end is 3

1

Minimum number of jumps to reach end is 3

57166

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

5730

Minimum number of jumps to reach end is 3

56811

Minimum number of jumps to reach end is 3

57371____157372

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

6

Minimum number of jumps to reach end is 3

7

Minimum number of jumps to reach end is 3

5708

 

Minimum number of jumps to reach end is 3

57377

C

Minimum number of jumps to reach end is 3

57378

Minimum number of jumps to reach end is 3

57281

Minimum number of jumps to reach end is 3

5745

Minimum number of jumps to reach end is 3

5746

 

Minimum number of jumps to reach end is 3

1

Minimum number of jumps to reach end is 3

57287

Minimum number of jumps to reach end is 3

1

Minimum number of jumps to reach end is 3

57289

Minimum number of jumps to reach end is 3

1

Minimum number of jumps to reach end is 3

57291

Minimum number of jumps to reach end is 3

6

Minimum number of jumps to reach end is 3

57293

 

Minimum number of jumps to reach end is 3

5747

Minimum number of jumps to reach end is 3

57391

Minimum number of jumps to reach end is 3

1

Minimum number of jumps to reach end is 3

2

Minimum number of jumps to reach end is 3

1

Minimum number of jumps to reach end is 3

4

Minimum number of jumps to reach end is 3

1

Minimum number of jumps to reach end is 3

6

Minimum number of jumps to reach end is 3

7

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

57304

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

1

Minimum number of jumps to reach end is 3

57403

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

1

Minimum number of jumps to reach end is 3

57313

 

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

3

Minimum number of jumps to reach end is 3

57316

Minimum number of jumps to reach end is 3

5

Minimum number of jumps to reach end is 3

6

Minimum number of jumps to reach end is 3

23

 

_______08____157321

 

_______08____157416

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

57418

_______08____157420

_______08____157422

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

5692

Minimum number of jumps to reach end is 3

57328

Minimum number of jumps to reach end is 3

5____157330

Minimum number of jumps to reach end is 3

5

Minimum number of jumps to reach end is 3

5692

Minimum number of jumps to reach end is 3

57333

Minimum number of jumps to reach end is 3

5699

Minimum number of jumps to reach end is 3

3

Minimum number of jumps to reach end is 3

57336

Minimum number of jumps to reach end is 3

5705

Minimum number of jumps to reach end is 3

57338

Minimum number of jumps to reach end is 3

5705

Minimum number of jumps to reach end is 3

57340

Minimum number of jumps to reach end is 3

5732

Minimum number of jumps to reach end is 3

5699

Minimum number of jumps to reach end is 3

5708

Minimum number of jumps to reach end is 3

5____15708

_______08____15708

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

6

Minimum number of jumps to reach end is 3

57350

Minimum number of jumps to reach end is 3

5708

 

Minimum number of jumps to reach end is 3

56

Minimum number of jumps to reach end is 3

1

Minimum number of jumps to reach end is 3

5717

Minimum number of jumps to reach end is 3

7

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

1

Minimum number of jumps to reach end is 3

5721

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

1

Minimum number of jumps to reach end is 3

57361

Minimum number of jumps to reach end is 3

5725

Minimum number of jumps to reach end is 3

5726

Minimum number of jumps to reach end is 3

5725

Minimum number of jumps to reach end is 3

5693

Minimum number of jumps to reach end is 3

1

Minimum number of jumps to reach end is 3

57166

_______08

Minimum number of jumps to reach end is 3

71____15693

Minimum number of jumps to reach end is 3

73

Minimum number of jumps to reach end is 3

74

Minimum number of jumps to reach end is 3

75

Minimum number of jumps to reach end is 3

57471

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

6

Minimum number of jumps to reach end is 3

7

Minimum number of jumps to reach end is 3

5708

Java

Minimum number of jumps to reach end is 3

57476

Minimum number of jumps to reach end is 3

57281

 

________ 083 ________ 084

 

Minimum number of jumps to reach end is 3

87

Minimum number of jumps to reach end is 3

88

 

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

57483

Minimum number of jumps to reach end is 3

94

Minimum number of jumps to reach end is 3

1

Minimum number of jumps to reach end is 3

2

Minimum number of jumps to reach end is 3

1

Minimum number of jumps to reach end is 3

56982

Minimum number of jumps to reach end is 3

1

Minimum number of jumps to reach end is 3

6

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

7

Minimum number of jumps to reach end is 3

5____157494

Minimum number of jumps to reach end is 3

5

Minimum number of jumps to reach end is 3

1

Minimum number of jumps to reach end is 3

57497

Minimum number of jumps to reach end is 3

57308

Minimum number of jumps to reach end is 3

1

Minimum number of jumps to reach end is 3

57310

_______05____0002

Minimum number of jumps to reach end is 3

5

Minimum number of jumps to reach end is 3

1

Minimum number of jumps to reach end is 3

57313

 

_______05____0007

Minimum number of jumps to reach end is 3

5

Minimum number of jumps to reach end is 3

3

Minimum number of jumps to reach end is 3

010

Minimum number of jumps to reach end is 3

14

Minimum number of jumps to reach end is 3

012

Minimum number of jumps to reach end is 3

14

Minimum number of jumps to reach end is 3

014

Minimum number of jumps to reach end is 3

14

Minimum number of jumps to reach end is 3

24

Minimum number of jumps to reach end is 3

5699

Minimum number of jumps to reach end is 3

6

Minimum number of jumps to reach end is 3

27

_______05____0021

 

Minimum number of jumps to reach end is 3

5

Minimum number of jumps to reach end is 3

023

Minimum number of jumps to reach end is 3

14

Minimum number of jumps to reach end is 3

025

Minimum number of jumps to reach end is 3

14

Minimum number of jumps to reach end is 3

5732

 

Minimum number of jumps to reach end is 3

5

Minimum number of jumps to reach end is 3

57323

Minimum number of jumps to reach end is 3

5

Minimum number of jumps to reach end is 3

57325

Minimum number of jumps to reach end is 3

5

Minimum number of jumps to reach end is 3

5692

Minimum number of jumps to reach end is 3

034

Minimum number of jumps to reach end is 3

46

Minimum number of jumps to reach end is 3

036

Minimum number of jumps to reach end is 3

5699____0038

Minimum number of jumps to reach end is 3

5699

Minimum number of jumps to reach end is 3

5692

Minimum number of jumps to reach end is 3

041

Minimum number of jumps to reach end is 3

14

Minimum number of jumps to reach end is 3

043

Minimum number of jumps to reach end is 3

5705

Minimum number of jumps to reach end is 3

3

Minimum number of jumps to reach end is 3

046

Minimum number of jumps to reach end is 3

56908____0048

Minimum number of jumps to reach end is 3

56908

Minimum number of jumps to reach end is 3

050

_______0051____0052____046

Minimum number of jumps to reach end is 3

57166

Minimum number of jumps to reach end is 3

56908

Minimum number of jumps to reach end is 3

57340

Minimum number of jumps to reach end is 3

5732

Minimum number of jumps to reach end is 3

5705

Minimum number of jumps to reach end is 3

5708

Minimum number of jumps to reach end is 3

5699

Minimum number of jumps to reach end is 3

5708

Minimum number of jumps to reach end is 3

5____15708

Minimum number of jumps to reach end is 3

5

Minimum number of jumps to reach end is 3

6

Minimum number of jumps to reach end is 3

066____046

Minimum number of jumps to reach end is 3

57153

_______08____15708

 

_______08____0072

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

74

Minimum number of jumps to reach end is 3

94

Minimum number of jumps to reach end is 3

76

Minimum number of jumps to reach end is 3

077

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

7

Minimum number of jumps to reach end is 3

5

Minimum number of jumps to reach end is 3

1

Minimum number of jumps to reach end is 3

82

Minimum number of jumps to reach end is 3

46

Minimum number of jumps to reach end is 3

74

Minimum number of jumps to reach end is 3

85

Minimum number of jumps to reach end is 3

74

Minimum number of jumps to reach end is 3

87

Minimum number of jumps to reach end is 3

74

Minimum number of jumps to reach end is 3

89

Minimum number of jumps to reach end is 3

74

Minimum number of jumps to reach end is 3

91

Minimum number of jumps to reach end is 3

74

Minimum number of jumps to reach end is 3

93

Minimum number of jumps to reach end is 3

74

Minimum number of jumps to reach end is 3

95

Minimum number of jumps to reach end is 3

74

Minimum number of jumps to reach end is 3

97

Minimum number of jumps to reach end is 3

74

Minimum number of jumps to reach end is 3

95

Minimum number of jumps to reach end is 3

74

Minimum number of jumps to reach end is 3

89

Minimum number of jumps to reach end is 3

74

Minimum number of jumps to reach end is 3

91

Minimum number of jumps to reach end is 3

56804

 

_______05____0106

Minimum number of jumps to reach end is 3

5699____0108

_______15699____0110

_______08____15708

Minimum number of jumps to reach end is 3

5708

 

Minimum number of jumps to reach end is 3

114

Python3

Minimum number of jumps to reach end is 3

56822

Minimum number of jumps to reach end is 3

56823

 

Minimum number of jumps to reach end is 3

56824

Minimum number of jumps to reach end is 3

118

 

 

Minimum number of jumps to reach end is 3

56826

Minimum number of jumps to reach end is 3

120

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

56896

Minimum number of jumps to reach end is 3

56835

Minimum number of jumps to reach end is 3

56927

Minimum number of jumps to reach end is 3

14

Minimum number of jumps to reach end is 3

5692

Minimum number of jumps to reach end is 3

56877

Minimum number of jumps to reach end is 3

56878

Minimum number of jumps to reach end is 3

56879

Minimum number of jumps to reach end is 3

130

 

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

3

Minimum number of jumps to reach end is 3

133

Minimum number of jumps to reach end is 3

56835

Minimum number of jumps to reach end is 3

56835

Minimum number of jumps to reach end is 3

14

Minimum number of jumps to reach end is 3

24

Minimum number of jumps to reach end is 3

138

Minimum number of jumps to reach end is 3

139

Minimum number of jumps to reach end is 3

14

Minimum number of jumps to reach end is 3

56949

Minimum number of jumps to reach end is 3

56835

Minimum number of jumps to reach end is 3

56835

Minimum number of jumps to reach end is 3

14

Minimum number of jumps to reach end is 3

56851

Minimum number of jumps to reach end is 3

5

Minimum number of jumps to reach end is 3

6

Minimum number of jumps to reach end is 3

56854

Minimum number of jumps to reach end is 3

5693

Minimum number of jumps to reach end is 3

56856

Minimum number of jumps to reach end is 3

24

 

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

023____014

Minimum number of jumps to reach end is 3

56949

Minimum number of jumps to reach end is 3

56835

Minimum number of jumps to reach end is 3

14

 

_______08____0159

_______08____0161

_______08____0163

_______08____0165

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

5692

Minimum number of jumps to reach end is 3

56877

Minimum number of jumps to reach end is 3

56878

Minimum number of jumps to reach end is 3

56879

Minimum number of jumps to reach end is 3

5693

Minimum number of jumps to reach end is 3

46

Minimum number of jumps to reach end is 3

173

Minimum number of jumps to reach end is 3

5

Minimum number of jumps to reach end is 3

050____156835

Minimum number of jumps to reach end is 3

56854

Minimum number of jumps to reach end is 3

5693

Minimum number of jumps to reach end is 3

56856

Minimum number of jumps to reach end is 3

24

Minimum number of jumps to reach end is 3

5

Minimum number of jumps to reach end is 3

5692

Minimum number of jumps to reach end is 3

183

Minimum number of jumps to reach end is 3

56878

Minimum number of jumps to reach end is 3

56879

Minimum number of jumps to reach end is 3

186

Minimum number of jumps to reach end is 3

5699

Minimum number of jumps to reach end is 3

3

Minimum number of jumps to reach end is 3

189

Minimum number of jumps to reach end is 3

56835

Minimum number of jumps to reach end is 3

183

Minimum number of jumps to reach end is 3

56881

Minimum number of jumps to reach end is 3

193

Minimum number of jumps to reach end is 3

56907

Minimum number of jumps to reach end is 3

195

Minimum number of jumps to reach end is 3

56835

Minimum number of jumps to reach end is 3

56854

Minimum number of jumps to reach end is 3

5693

Minimum number of jumps to reach end is 3

56856

Minimum number of jumps to reach end is 3

200

Minimum number of jumps to reach end is 3

5705

Minimum number of jumps to reach end is 3

050

Minimum number of jumps to reach end is 3

56835

Minimum number of jumps to reach end is 3

56869

Minimum number of jumps to reach end is 3

205____156881

Minimum number of jumps to reach end is 3

46

Minimum number of jumps to reach end is 3

24

Minimum number of jumps to reach end is 3

5705

Minimum number of jumps to reach end is 3

57340

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

6

Minimum number of jumps to reach end is 3

213____156963

Minimum number of jumps to reach end is 3

46

Minimum number of jumps to reach end is 3

56949

 

 

Minimum number of jumps to reach end is 3

217

Minimum number of jumps to reach end is 3

56925

Minimum number of jumps to reach end is 3

56835

Minimum number of jumps to reach end is 3

56927

Minimum number of jumps to reach end is 3

46

Minimum number of jumps to reach end is 3

74

Minimum number of jumps to reach end is 3

85

Minimum number of jumps to reach end is 3

74

Minimum number of jumps to reach end is 3

87

Minimum number of jumps to reach end is 3

74

Minimum number of jumps to reach end is 3

89

Minimum number of jumps to reach end is 3

74

Minimum number of jumps to reach end is 3

91

Minimum number of jumps to reach end is 3

74

Minimum number of jumps to reach end is 3

93

Minimum number of jumps to reach end is 3

74

Minimum number of jumps to reach end is 3

95

Minimum number of jumps to reach end is 3

74

Minimum number of jumps to reach end is 3

97

Minimum number of jumps to reach end is 3

74

Minimum number of jumps to reach end is 3

95

Minimum number of jumps to reach end is 3

74

Minimum number of jumps to reach end is 3

89

Minimum number of jumps to reach end is 3

74__156___1

Minimum number of jumps to reach end is 3

243

Minimum number of jumps to reach end is 3

56835

Minimum number of jumps to reach end is 3

56952

Minimum number of jumps to reach end is 3

56953

Minimum number of jumps to reach end is 3

56954

Minimum number of jumps to reach end is 3

5693____156956

Minimum number of jumps to reach end is 3

74

Minimum number of jumps to reach end is 3

56958____156959____0253

 

Minimum number of jumps to reach end is 3

56966

C#

Minimum number of jumps to reach end is 3

255

Minimum number of jumps to reach end is 3

571

Minimum number of jumps to reach end is 3

56970

 

Minimum number of jumps to reach end is 3

87

Minimum number of jumps to reach end is 3

88

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

94

Minimum number of jumps to reach end is 3

1

Minimum number of jumps to reach end is 3

2

Minimum number of jumps to reach end is 3

1

Minimum number of jumps to reach end is 3

56982

Minimum number of jumps to reach end is 3

1

Minimum number of jumps to reach end is 3

6

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

7

Minimum number of jumps to reach end is 3

5____157494

_______05____0002

Minimum number of jumps to reach end is 3

5

Minimum number of jumps to reach end is 3

1

Minimum number of jumps to reach end is 3

276

Minimum number of jumps to reach end is 3

57308

Minimum number of jumps to reach end is 3

1

Minimum number of jumps to reach end is 3

57310

 

_______05____0007

Minimum number of jumps to reach end is 3

5

Minimum number of jumps to reach end is 3

3

Minimum number of jumps to reach end is 3

57316

 

Minimum number of jumps to reach end is 3

5699____0021

Minimum number of jumps to reach end is 3

5699

Minimum number of jumps to reach end is 3

6

Minimum number of jumps to reach end is 3

1____157009

 

Minimum number of jumps to reach end is 3

5____157321

 

Minimum number of jumps to reach end is 3

5

Minimum number of jumps to reach end is 3

57416

Minimum number of jumps to reach end is 3

5

Minimum number of jumps to reach end is 3

57418

_______05____0298

_______05____0300

Minimum number of jumps to reach end is 3

5

Minimum number of jumps to reach end is 3

5692

Minimum number of jumps to reach end is 3

5693

Minimum number of jumps to reach end is 3

1

Minimum number of jumps to reach end is 3

305

_______15699____0307____01

Minimum number of jumps to reach end is 3

57009

Minimum number of jumps to reach end is 3

5699

Minimum number of jumps to reach end is 3

5692

Minimum number of jumps to reach end is 3

5693

Minimum number of jumps to reach end is 3

1

Minimum number of jumps to reach end is 3

314

Minimum number of jumps to reach end is 3

5705

Minimum number of jumps to reach end is 3

3

Minimum number of jumps to reach end is 3

046

_______156908____0319____01

Minimum number of jumps to reach end is 3

321

Minimum number of jumps to reach end is 3

56908

Minimum number of jumps to reach end is 3

050

_______0051____0325

Minimum number of jumps to reach end is 3

56908

Minimum number of jumps to reach end is 3

57340

Minimum number of jumps to reach end is 3

5732

Minimum number of jumps to reach end is 3

5705

Minimum number of jumps to reach end is 3

5708

Minimum number of jumps to reach end is 3

5699

Minimum number of jumps to reach end is 3

5708

Minimum number of jumps to reach end is 3

5____15708

Minimum number of jumps to reach end is 3

5

Minimum number of jumps to reach end is 3

6

Minimum number of jumps to reach end is 3

57350

_______08____15708

 

_______08____0341

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

74

Minimum number of jumps to reach end is 3

94

Minimum number of jumps to reach end is 3

76

Minimum number of jumps to reach end is 3

57055

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

7

Minimum number of jumps to reach end is 3

5

Minimum number of jumps to reach end is 3

1

Minimum number of jumps to reach end is 3

57060

_______05____157065

Minimum number of jumps to reach end is 3

5699____0108

Minimum number of jumps to reach end is 3

5699____0357

_______08____15708

Minimum number of jumps to reach end is 3

5708

 

Minimum number of jumps to reach end is 3

57073

PHP

Minimum number of jumps to reach end is 3

57074

Minimum number of jumps to reach end is 3

363

Minimum number of jumps to reach end is 3

364

 

Minimum number of jumps to reach end is 3

57077

Minimum number of jumps to reach end is 3

57295

Minimum number of jumps to reach end is 3

57079

Minimum number of jumps to reach end is 3

2____157081____074

Minimum number of jumps to reach end is 3

57196

Minimum number of jumps to reach end is 3

24

Minimum number of jumps to reach end is 3

7

_______08____0375

_______08____0377

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

57159

Minimum number of jumps to reach end is 3

56835

Minimum number of jumps to reach end is 3

57194

Minimum number of jumps to reach end is 3

5693____157196

Minimum number of jumps to reach end is 3

57166

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

3

Minimum number of jumps to reach end is 3

5693____157196

Minimum number of jumps to reach end is 3

390

Minimum number of jumps to reach end is 3

57081

Minimum number of jumps to reach end is 3

392

Minimum number of jumps to reach end is 3

5

Minimum number of jumps to reach end is 3

6

Minimum number of jumps to reach end is 3

395

 

_______08____157159____0398

 

_______08____157416

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

57418

_______08____0298

_______08____0300

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

5692

Minimum number of jumps to reach end is 3

5693

Minimum number of jumps to reach end is 3

57137

Minimum number of jumps to reach end is 3

411

Minimum number of jumps to reach end is 3

57137

Minimum number of jumps to reach end is 3

56912

Minimum number of jumps to reach end is 3

57196

Minimum number of jumps to reach end is 3

5732

Minimum number of jumps to reach end is 3

57137

Minimum number of jumps to reach end is 3

57155

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

7

_______157159____156927

Minimum number of jumps to reach end is 3

57137

Minimum number of jumps to reach end is 3

424

Minimum number of jumps to reach end is 3

5

Minimum number of jumps to reach end is 3

5692

Minimum number of jumps to reach end is 3

5693

Minimum number of jumps to reach end is 3

428

Minimum number of jumps to reach end is 3

429

Minimum number of jumps to reach end is 3

428

Minimum number of jumps to reach end is 3

56912

Minimum number of jumps to reach end is 3

57137

Minimum number of jumps to reach end is 3

5732

Minimum number of jumps to reach end is 3

428

Minimum number of jumps to reach end is 3

57155

Minimum number of jumps to reach end is 3

5

Minimum number of jumps to reach end is 3

7

Minimum number of jumps to reach end is 3

5699

Minimum number of jumps to reach end is 3

3

Minimum number of jumps to reach end is 3

5693

Minimum number of jumps to reach end is 3

57137

Minimum number of jumps to reach end is 3

57142

Minimum number of jumps to reach end is 3

428

Minimum number of jumps to reach end is 3

56881

Minimum number of jumps to reach end is 3

57081

Minimum number of jumps to reach end is 3

56927

Minimum number of jumps to reach end is 3

428

Minimum number of jumps to reach end is 3

448

Minimum number of jumps to reach end is 3

5705

Minimum number of jumps to reach end is 3

57159

Minimum number of jumps to reach end is 3

56927

Minimum number of jumps to reach end is 3

428

Minimum number of jumps to reach end is 3

453

Minimum number of jumps to reach end is 3

5699

Minimum number of jumps to reach end is 3

7

Minimum number of jumps to reach end is 3

5705

Minimum number of jumps to reach end is 3

57159

Minimum number of jumps to reach end is 3

56927

Minimum number of jumps to reach end is 3

57137

Minimum number of jumps to reach end is 3

460

Minimum number of jumps to reach end is 3

57159

Minimum number of jumps to reach end is 3

56927

Minimum number of jumps to reach end is 3

57137

Minimum number of jumps to reach end is 3

464

Minimum number of jumps to reach end is 3

465

Minimum number of jumps to reach end is 3

57159

Minimum number of jumps to reach end is 3

56927

Minimum number of jumps to reach end is 3

428

Minimum number of jumps to reach end is 3

469

Minimum number of jumps to reach end is 3

5705

Minimum number of jumps to reach end is 3

57340

Minimum number of jumps to reach end is 3

5732

Minimum number of jumps to reach end is 3

5699

Minimum number of jumps to reach end is 3

5708

Minimum number of jumps to reach end is 3

5____15708

_______08____15708

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

6

Minimum number of jumps to reach end is 3

57159____156927

Minimum number of jumps to reach end is 3

57196

Minimum number of jumps to reach end is 3

484

Minimum number of jumps to reach end is 3

5708

 

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

5715

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

57081

Minimum number of jumps to reach end is 3

56835

Minimum number of jumps to reach end is 3

57194

Minimum number of jumps to reach end is 3

57195

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

494

Minimum number of jumps to reach end is 3

56835

Minimum number of jumps to reach end is 3

57198

Minimum number of jumps to reach end is 3

5693

Minimum number of jumps to reach end is 3

57081

Minimum number of jumps to reach end is 3

57166

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

57202

Minimum number of jumps to reach end is 3

56811

Minimum number of jumps to reach end is 3

57205

Minimum number of jumps to reach end is 3

465

Minimum number of jumps to reach end is 3

2____157081

Minimum number of jumps to reach end is 3

74

Minimum number of jumps to reach end is 3

494

Minimum number of jumps to reach end is 3

57166

Minimum number of jumps to reach end is 3

465

Minimum number of jumps to reach end is 3

57073

Minimum number of jumps to reach end is 3

57214

Javascript

Minimum number of jumps to reach end is 3

57215

 

Minimum number of jumps to reach end is 3

514

Minimum number of jumps to reach end is 3

515

Minimum number of jumps to reach end is 3

57079

Minimum number of jumps to reach end is 3

517

 

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

7

Minimum number of jumps to reach end is 3

5____157494

Minimum number of jumps to reach end is 3

5

Minimum number of jumps to reach end is 3

523

Minimum number of jumps to reach end is 3

524

_______05____0002

Minimum number of jumps to reach end is 3

5

Minimum number of jumps to reach end is 3

523

Minimum number of jumps to reach end is 3

57313

 

_______05____0007

Minimum number of jumps to reach end is 3

5

Minimum number of jumps to reach end is 3

3

Minimum number of jumps to reach end is 3

57316

Minimum number of jumps to reach end is 3

5699

Minimum number of jumps to reach end is 3

6

Minimum number of jumps to reach end is 3

537

_______05____0021

 

Minimum number of jumps to reach end is 3

5____157321

 

Minimum number of jumps to reach end is 3

5

Minimum number of jumps to reach end is 3

57323

Minimum number of jumps to reach end is 3

5

Minimum number of jumps to reach end is 3

57325

Minimum number of jumps to reach end is 3

5

Minimum number of jumps to reach end is 3

5692

Minimum number of jumps to reach end is 3

57328

Minimum number of jumps to reach end is 3

5699____0550

Minimum number of jumps to reach end is 3

5699

Minimum number of jumps to reach end is 3

5692

Minimum number of jumps to reach end is 3

57333

Minimum number of jumps to reach end is 3

5705

Minimum number of jumps to reach end is 3

3

Minimum number of jumps to reach end is 3

046

Minimum number of jumps to reach end is 3

56908

Minimum number of jumps to reach end is 3

558

_______0559____0560

Minimum number of jumps to reach end is 3

56908

Minimum number of jumps to reach end is 3

562

Minimum number of jumps to reach end is 3

56908

Minimum number of jumps to reach end is 3

57340

Minimum number of jumps to reach end is 3

5732

Minimum number of jumps to reach end is 3

5705

Minimum number of jumps to reach end is 3

5708

Minimum number of jumps to reach end is 3

5699

Minimum number of jumps to reach end is 3

5708

Minimum number of jumps to reach end is 3

5____15708

Minimum number of jumps to reach end is 3

5

Minimum number of jumps to reach end is 3

6

Minimum number of jumps to reach end is 3

57350

_______08____15708

 

Minimum number of jumps to reach end is 3

072

Minimum number of jumps to reach end is 3

523

Minimum number of jumps to reach end is 3

579

 

Minimum number of jumps to reach end is 3

57272____0108

_______0582____0110

 

Minimum number of jumps to reach end is 3

584

 

Minimum number of jumps to reach end is 3

57279

Đầu ra

Minimum number of jumps to reach end is 3

Cảm ơn para đã đề xuất phương pháp này.  

Độ phức tạp về thời gian. O[n2] 
Không gian phụ. O[n], vì đã chiếm thêm n dung lượng.

Một triển khai khác sử dụng Lập trình động

Xây dựng mảng jumps[] từ phải sang trái sao cho jumps[i] cho biết số bước nhảy tối thiểu cần thiết để đạt được mảng[n-1] từ mảng[i]. Cuối cùng, chúng tôi quay lại jumps[0]. Sử dụng Lập trình động theo cách tương tự của phương pháp trên

Dưới đây là việc thực hiện phương pháp trên

C++

Minimum number of jumps to reach end is 3

586

Minimum number of jumps to reach end is 3

570

________ 1571 ________ 1572 ________ 1573

 

Minimum number of jumps to reach end is 3

591

Minimum number of jumps to reach end is 3

1

Minimum number of jumps to reach end is 3

2

Minimum number of jumps to reach end is 3

1

Minimum number of jumps to reach end is 3

4

Minimum number of jumps to reach end is 3

1

Minimum number of jumps to reach end is 3

6

Minimum number of jumps to reach end is 3

7

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

600

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

1

Minimum number of jumps to reach end is 3

57307

Minimum number of jumps to reach end is 3

57308

Minimum number of jumps to reach end is 3

1

Minimum number of jumps to reach end is 3

57310

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

1

Minimum number of jumps to reach end is 3

54

 

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

611

_______08____0613

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

615

 

_______08____0617

_______08____0619

_______08____0621

_______08____0623

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

5692

Minimum number of jumps to reach end is 3

5693

Minimum number of jumps to reach end is 3

1

Minimum number of jumps to reach end is 3

5695

_______05____0630

_______05____0632

Minimum number of jumps to reach end is 3

5

Minimum number of jumps to reach end is 3

3

Minimum number of jumps to reach end is 3

635

Minimum number of jumps to reach end is 3

5699

Minimum number of jumps to reach end is 3

57330

 

_______05____0639

_______05____0641

Minimum number of jumps to reach end is 3

5

Minimum number of jumps to reach end is 3

643

Minimum number of jumps to reach end is 3

3

Minimum number of jumps to reach end is 3

645

Minimum number of jumps to reach end is 3

5699____0647

 

_______05____0649

Minimum number of jumps to reach end is 3

5

Minimum number of jumps to reach end is 3

651

_______05____0653

_______05____0655

Minimum number of jumps to reach end is 3

5

Minimum number of jumps to reach end is 3

643

Minimum number of jumps to reach end is 3

7

Minimum number of jumps to reach end is 3

5699____0660

Minimum number of jumps to reach end is 3

5699

Minimum number of jumps to reach end is 3

36

 

Minimum number of jumps to reach end is 3

5699____0664

Minimum number of jumps to reach end is 3

5699____0666

Minimum number of jumps to reach end is 3

5699

Minimum number of jumps to reach end is 3

5692

Minimum number of jumps to reach end is 3

5693

Minimum number of jumps to reach end is 3

1

Minimum number of jumps to reach end is 3

671

_______0672____0673

Minimum number of jumps to reach end is 3

5705

Minimum number of jumps to reach end is 3

3

Minimum number of jumps to reach end is 3

676

Minimum number of jumps to reach end is 3

56908

Minimum number of jumps to reach end is 3

678

Minimum number of jumps to reach end is 3

5699

Minimum number of jumps to reach end is 3

5708

 

Minimum number of jumps to reach end is 3

5699____0682

________ 15699 ________ 03 ________ 0685

_______15705____0687

Minimum number of jumps to reach end is 3

5699____0643

________ 15705 ________ 0691 ________ 0692

Minimum number of jumps to reach end is 3

5____15708

_______08____15708

 

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

6

Minimum number of jumps to reach end is 3

699

Minimum number of jumps to reach end is 3

5708

 

Minimum number of jumps to reach end is 3

56

Minimum number of jumps to reach end is 3

1

Minimum number of jumps to reach end is 3

5717

Minimum number of jumps to reach end is 3

7

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

1

Minimum number of jumps to reach end is 3

5721

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

1

Minimum number of jumps to reach end is 3

57361

Minimum number of jumps to reach end is 3

5725

Minimum number of jumps to reach end is 3

5726

Minimum number of jumps to reach end is 3

5725

Minimum number of jumps to reach end is 3

5693

Minimum number of jumps to reach end is 3

1

Minimum number of jumps to reach end is 3

57166

_______08____15730____0719

Minimum number of jumps to reach end is 3

57371____0721____0722

Minimum number of jumps to reach end is 3

57372

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

6

Minimum number of jumps to reach end is 3

7

Minimum number of jumps to reach end is 3

5708

 

Minimum number of jumps to reach end is 3

728

C

Minimum number of jumps to reach end is 3

729

Minimum number of jumps to reach end is 3

5745

Minimum number of jumps to reach end is 3

5746

 

Minimum number of jumps to reach end is 3

591

Minimum number of jumps to reach end is 3

1

Minimum number of jumps to reach end is 3

2

Minimum number of jumps to reach end is 3

1

Minimum number of jumps to reach end is 3

4

Minimum number of jumps to reach end is 3

1

Minimum number of jumps to reach end is 3

6

Minimum number of jumps to reach end is 3

7

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

600

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

1

Minimum number of jumps to reach end is 3

57403

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

1

Minimum number of jumps to reach end is 3

54

 

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

611

_______08____0613

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

615

 

_______08____0617

_______08____0619

_______08____0621

_______08____0623

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

5692

Minimum number of jumps to reach end is 3

5693

Minimum number of jumps to reach end is 3

1

Minimum number of jumps to reach end is 3

5695

_______05____0630

_______05____0632

Minimum number of jumps to reach end is 3

5

Minimum number of jumps to reach end is 3

3

Minimum number of jumps to reach end is 3

635

Minimum number of jumps to reach end is 3

5699

Minimum number of jumps to reach end is 3

57330

 

_______05____0639

_______05____0641

Minimum number of jumps to reach end is 3

5

Minimum number of jumps to reach end is 3

643

Minimum number of jumps to reach end is 3

3

Minimum number of jumps to reach end is 3

645

Minimum number of jumps to reach end is 3

5699____0647

 

_______05____0649

Minimum number of jumps to reach end is 3

5

Minimum number of jumps to reach end is 3

651

_______05____0653

_______05____0655

Minimum number of jumps to reach end is 3

5

Minimum number of jumps to reach end is 3

643

Minimum number of jumps to reach end is 3

7

Minimum number of jumps to reach end is 3

5699____0660

Minimum number of jumps to reach end is 3

5699

Minimum number of jumps to reach end is 3

36

 

Minimum number of jumps to reach end is 3

5699____0664

Minimum number of jumps to reach end is 3

5699____0666

Minimum number of jumps to reach end is 3

5699

Minimum number of jumps to reach end is 3

5692

Minimum number of jumps to reach end is 3

5693

Minimum number of jumps to reach end is 3

1

Minimum number of jumps to reach end is 3

671

_______0672____0673

Minimum number of jumps to reach end is 3

5705

Minimum number of jumps to reach end is 3

3

Minimum number of jumps to reach end is 3

676

Minimum number of jumps to reach end is 3

56908

Minimum number of jumps to reach end is 3

678

Minimum number of jumps to reach end is 3

5699

Minimum number of jumps to reach end is 3

5708

 

Minimum number of jumps to reach end is 3

5699____0682

________ 15699 ________ 03 ________ 0685

_______15705____0687

Minimum number of jumps to reach end is 3

5699____0643

________ 15705 ________ 0691 ________ 0692

Minimum number of jumps to reach end is 3

5____15708

_______08____15708

 

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

6

Minimum number of jumps to reach end is 3

699

Minimum number of jumps to reach end is 3

5708

 

Minimum number of jumps to reach end is 3

56

Minimum number of jumps to reach end is 3

1

Minimum number of jumps to reach end is 3

5717

Minimum number of jumps to reach end is 3

7

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

1

Minimum number of jumps to reach end is 3

5721

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

1

Minimum number of jumps to reach end is 3

57361

Minimum number of jumps to reach end is 3

5725

Minimum number of jumps to reach end is 3

5726

Minimum number of jumps to reach end is 3

5725

Minimum number of jumps to reach end is 3

5693

Minimum number of jumps to reach end is 3

1

Minimum number of jumps to reach end is 3

57166

_______08

Minimum number of jumps to reach end is 3

71____15693

Minimum number of jumps to reach end is 3

73

Minimum number of jumps to reach end is 3

74

Minimum number of jumps to reach end is 3

75

Minimum number of jumps to reach end is 3

57471

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

6

Minimum number of jumps to reach end is 3

7

Minimum number of jumps to reach end is 3

5708

 

Minimum number of jumps to reach end is 3

728

Java

Minimum number of jumps to reach end is 3

867

 

Minimum number of jumps to reach end is 3

87

Minimum number of jumps to reach end is 3

88

_______08____0591

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

94

Minimum number of jumps to reach end is 3

1

Minimum number of jumps to reach end is 3

2

Minimum number of jumps to reach end is 3

1

Minimum number of jumps to reach end is 3

4

Minimum number of jumps to reach end is 3

1

Minimum number of jumps to reach end is 3

6

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

7

Minimum number of jumps to reach end is 3

5

Minimum number of jumps to reach end is 3

600

Minimum number of jumps to reach end is 3

5

Minimum number of jumps to reach end is 3

1

Minimum number of jumps to reach end is 3

276

Minimum number of jumps to reach end is 3

57308

Minimum number of jumps to reach end is 3

1

Minimum number of jumps to reach end is 3

57310

Minimum number of jumps to reach end is 3

5

Minimum number of jumps to reach end is 3

1

Minimum number of jumps to reach end is 3

54

 

_______05____0894

_______05____0896

Minimum number of jumps to reach end is 3

5

Minimum number of jumps to reach end is 3

066

Minimum number of jumps to reach end is 3

46

Minimum number of jumps to reach end is 3

025

Minimum number of jumps to reach end is 3

14

Minimum number of jumps to reach end is 3

5732

 

_______05____0617

_______05____0906

Minimum number of jumps to reach end is 3

5____0908

Minimum number of jumps to reach end is 3

5

Minimum number of jumps to reach end is 3

910

Minimum number of jumps to reach end is 3

5

Minimum number of jumps to reach end is 3

5692

Minimum number of jumps to reach end is 3

5693

Minimum number of jumps to reach end is 3

1

Minimum number of jumps to reach end is 3

915

Minimum number of jumps to reach end is 3

93____0917

Minimum number of jumps to reach end is 3

14

Minimum number of jumps to reach end is 3

919

Minimum number of jumps to reach end is 3

5699____0630

Minimum number of jumps to reach end is 3

5699____0632

Minimum number of jumps to reach end is 3

5699

Minimum number of jumps to reach end is 3

3

Minimum number of jumps to reach end is 3

926

Minimum number of jumps to reach end is 3

14

Minimum number of jumps to reach end is 3

24

Minimum number of jumps to reach end is 3

5705

Minimum number of jumps to reach end is 3

038

 

Minimum number of jumps to reach end is 3

5699____0932

Minimum number of jumps to reach end is 3

5699____0934

Minimum number of jumps to reach end is 3

5699

Minimum number of jumps to reach end is 3

643

Minimum number of jumps to reach end is 3

3

Minimum number of jumps to reach end is 3

938

Minimum number of jumps to reach end is 3

46

Minimum number of jumps to reach end is 3

24

Minimum number of jumps to reach end is 3

5705

Minimum number of jumps to reach end is 3

307

Minimum number of jumps to reach end is 3

46

Minimum number of jumps to reach end is 3

5732

 

Minimum number of jumps to reach end is 3

5699____0649

Minimum number of jumps to reach end is 3

5699____0651

Minimum number of jumps to reach end is 3

5699____0950

Minimum number of jumps to reach end is 3

5699____0952

Minimum number of jumps to reach end is 3

5699

Minimum number of jumps to reach end is 3

643

Minimum number of jumps to reach end is 3

7

Minimum number of jumps to reach end is 3

5705

Minimum number of jumps to reach end is 3

660

Minimum number of jumps to reach end is 3

5705

Minimum number of jumps to reach end is 3

40

 

Minimum number of jumps to reach end is 3

5705

Minimum number of jumps to reach end is 3

664

Minimum number of jumps to reach end is 3

5705____0666

Minimum number of jumps to reach end is 3

5705

Minimum number of jumps to reach end is 3

5692

Minimum number of jumps to reach end is 3

5693

Minimum number of jumps to reach end is 3

1

Minimum number of jumps to reach end is 3

968

Minimum number of jumps to reach end is 3

46

Minimum number of jumps to reach end is 3

5732

Minimum number of jumps to reach end is 3

57173____0972

Minimum number of jumps to reach end is 3

56908

Minimum number of jumps to reach end is 3

3

Minimum number of jumps to reach end is 3

676

_______0051____0678

Minimum number of jumps to reach end is 3

5705

Minimum number of jumps to reach end is 3

5708

 

Minimum number of jumps to reach end is 3

5705____0682

Minimum number of jumps to reach end is 3

5705

Minimum number of jumps to reach end is 3

3

Minimum number of jumps to reach end is 3

984

Minimum number of jumps to reach end is 3

56908

Minimum number of jumps to reach end is 3

986

Minimum number of jumps to reach end is 3

46

Minimum number of jumps to reach end is 3

5732

_______15705____0643

Minimum number of jumps to reach end is 3

56908____0691____0993

Minimum number of jumps to reach end is 3

5699

Minimum number of jumps to reach end is 3

5708

Minimum number of jumps to reach end is 3

5____15708

 

Minimum number of jumps to reach end is 3

5

Minimum number of jumps to reach end is 3

6

Minimum number of jumps to reach end is 3

023____014

Minimum number of jumps to reach end is 3

57153

_______08____15708

 

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

5715

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

74

Minimum number of jumps to reach end is 3

94

Minimum number of jumps to reach end is 3

76

Minimum number of jumps to reach end is 3

077

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

7

Minimum number of jumps to reach end is 3

5

Minimum number of jumps to reach end is 3

1

Minimum number of jumps to reach end is 3

016

Minimum number of jumps to reach end is 3

46

Minimum number of jumps to reach end is 3

74

Minimum number of jumps to reach end is 3

85

Minimum number of jumps to reach end is 3

74

Minimum number of jumps to reach end is 3

87

Minimum number of jumps to reach end is 3

74

Minimum number of jumps to reach end is 3

89

Minimum number of jumps to reach end is 3

74

Minimum number of jumps to reach end is 3

91

Minimum number of jumps to reach end is 3

74

Minimum number of jumps to reach end is 3

93

Minimum number of jumps to reach end is 3

74

Minimum number of jumps to reach end is 3

95

Minimum number of jumps to reach end is 3

74

Minimum number of jumps to reach end is 3

97

Minimum number of jumps to reach end is 3

74

Minimum number of jumps to reach end is 3

95

Minimum number of jumps to reach end is 3

74

Minimum number of jumps to reach end is 3

89

Minimum number of jumps to reach end is 3

74

Minimum number of jumps to reach end is 3

91

Minimum number of jumps to reach end is 3

56804

Minimum number of jumps to reach end is 3

5

Minimum number of jumps to reach end is 3

1

Minimum number of jumps to reach end is 3

041

_______05____0106

Minimum number of jumps to reach end is 3

5699

Minimum number of jumps to reach end is 3

56811

Minimum number of jumps to reach end is 3

5699____0047

_______08____15708

Minimum number of jumps to reach end is 3

5708

 

Minimum number of jumps to reach end is 3

728

Python3

Minimum number of jumps to reach end is 3

56822

Minimum number of jumps to reach end is 3

56823

 

Minimum number of jumps to reach end is 3

054

Minimum number of jumps to reach end is 3

055

 

 

Minimum number of jumps to reach end is 3

56826

Minimum number of jumps to reach end is 3

120

 

_______08____0059

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

56896

Minimum number of jumps to reach end is 3

56835

Minimum number of jumps to reach end is 3

56927

Minimum number of jumps to reach end is 3

14

Minimum number of jumps to reach end is 3

5692

Minimum number of jumps to reach end is 3

56877

Minimum number of jumps to reach end is 3

56878

Minimum number of jumps to reach end is 3

56879

Minimum number of jumps to reach end is 3

130

 

_______08____0071

_______08____0073

_______08____0075

_______08____0077

 

_______08____0079

_______08____0081

_______08____0083

_______08____0085

_______08____0087

_______08____0089

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

5692

Minimum number of jumps to reach end is 3

56877

Minimum number of jumps to reach end is 3

56878

Minimum number of jumps to reach end is 3

56879

Minimum number of jumps to reach end is 3

133

Minimum number of jumps to reach end is 3

56963

Minimum number of jumps to reach end is 3

93

Minimum number of jumps to reach end is 3

74

Minimum number of jumps to reach end is 3

56963

Minimum number of jumps to reach end is 3

46

Minimum number of jumps to reach end is 3

74

Minimum number of jumps to reach end is 3

56963

Minimum number of jumps to reach end is 3

46

Minimum number of jumps to reach end is 3

56851

 

_______05____0106

Minimum number of jumps to reach end is 3

5

Minimum number of jumps to reach end is 3

108

Minimum number of jumps to reach end is 3

5

Minimum number of jumps to reach end is 3

3

Minimum number of jumps to reach end is 3

111

Minimum number of jumps to reach end is 3

56835

Minimum number of jumps to reach end is 3

56835

Minimum number of jumps to reach end is 3

14

Minimum number of jumps to reach end is 3

56851

Minimum number of jumps to reach end is 3

5699

Minimum number of jumps to reach end is 3

050

Minimum number of jumps to reach end is 3

56835

Minimum number of jumps to reach end is 3

56854

Minimum number of jumps to reach end is 3

5693

Minimum number of jumps to reach end is 3

56856

Minimum number of jumps to reach end is 3

24

 

_______05____0124

_______05____0126

_______05____0128

Minimum number of jumps to reach end is 3

5

Minimum number of jumps to reach end is 3

130

Minimum number of jumps to reach end is 3

131

Minimum number of jumps to reach end is 3

56835

Minimum number of jumps to reach end is 3

56950

Minimum number of jumps to reach end is 3

56963

Minimum number of jumps to reach end is 3

56877

Minimum number of jumps to reach end is 3

56963

Minimum number of jumps to reach end is 3

46

Minimum number of jumps to reach end is 3

56851

Minimum number of jumps to reach end is 3

5699

Minimum number of jumps to reach end is 3

050____156835

Minimum number of jumps to reach end is 3

46

 

_______05____0144

_______05____0146

_______05____0148

_______05____0150

_______05____0152

_______05____0154

Minimum number of jumps to reach end is 3

5

Minimum number of jumps to reach end is 3

643

Minimum number of jumps to reach end is 3

157

Minimum number of jumps to reach end is 3

5699____0159

Minimum number of jumps to reach end is 3

5699

Minimum number of jumps to reach end is 3

56869

Minimum number of jumps to reach end is 3

56835

Minimum number of jumps to reach end is 3

56854

Minimum number of jumps to reach end is 3

5693

Minimum number of jumps to reach end is 3

56856

Minimum number of jumps to reach end is 3

24

 

Minimum number of jumps to reach end is 3

5699____0168

_______15699____0170

_______15699____0172

Minimum number of jumps to reach end is 3

5699

Minimum number of jumps to reach end is 3

5692

Minimum number of jumps to reach end is 3

183

Minimum number of jumps to reach end is 3

56878

Minimum number of jumps to reach end is 3

56879

Minimum number of jumps to reach end is 3

178

Minimum number of jumps to reach end is 3

56881

Minimum number of jumps to reach end is 3

46

Minimum number of jumps to reach end is 3

173

Minimum number of jumps to reach end is 3

5705

Minimum number of jumps to reach end is 3

3

Minimum number of jumps to reach end is 3

184

Minimum number of jumps to reach end is 3

56835

Minimum number of jumps to reach end is 3

186

Minimum number of jumps to reach end is 3

56881

Minimum number of jumps to reach end is 3

188

Minimum number of jumps to reach end is 3

56908

Minimum number of jumps to reach end is 3

3

Minimum number of jumps to reach end is 3

5693

Minimum number of jumps to reach end is 3

56869

Minimum number of jumps to reach end is 3

193

Minimum number of jumps to reach end is 3

051

Minimum number of jumps to reach end is 3

56869

Minimum number of jumps to reach end is 3

56835

Minimum number of jumps to reach end is 3

197

 

Minimum number of jumps to reach end is 3

5699

Minimum number of jumps to reach end is 3

199

Minimum number of jumps to reach end is 3

5699

Minimum number of jumps to reach end is 3

3

Minimum number of jumps to reach end is 3

5693

Minimum number of jumps to reach end is 3

56869

Minimum number of jumps to reach end is 3

204

Minimum number of jumps to reach end is 3

56835

Minimum number of jumps to reach end is 3

56854

Minimum number of jumps to reach end is 3

5693

Minimum number of jumps to reach end is 3

56856

Minimum number of jumps to reach end is 3

200

Minimum number of jumps to reach end is 3

5705

Minimum number of jumps to reach end is 3

050

Minimum number of jumps to reach end is 3

56835

Minimum number of jumps to reach end is 3

56869

Minimum number of jumps to reach end is 3

56881

Minimum number of jumps to reach end is 3

46

Minimum number of jumps to reach end is 3

5699____0643

Minimum number of jumps to reach end is 3

157

Minimum number of jumps to reach end is 3

5705

Minimum number of jumps to reach end is 3

220

Minimum number of jumps to reach end is 3

5705

Minimum number of jumps to reach end is 3

050____156835

Minimum number of jumps to reach end is 3

56869

 

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

6

Minimum number of jumps to reach end is 3

023____014

Minimum number of jumps to reach end is 3

56949

 

 

Minimum number of jumps to reach end is 3

56924

Minimum number of jumps to reach end is 3

56925

Minimum number of jumps to reach end is 3

56835

Minimum number of jumps to reach end is 3

56927

Minimum number of jumps to reach end is 3

46

Minimum number of jumps to reach end is 3

74

Minimum number of jumps to reach end is 3

85

Minimum number of jumps to reach end is 3

74

Minimum number of jumps to reach end is 3

87

Minimum number of jumps to reach end is 3

74

Minimum number of jumps to reach end is 3

89

Minimum number of jumps to reach end is 3

74

Minimum number of jumps to reach end is 3

91

Minimum number of jumps to reach end is 3

74

Minimum number of jumps to reach end is 3

93

Minimum number of jumps to reach end is 3

74

Minimum number of jumps to reach end is 3

95

Minimum number of jumps to reach end is 3

74

Minimum number of jumps to reach end is 3

97

Minimum number of jumps to reach end is 3

74

Minimum number of jumps to reach end is 3

95

Minimum number of jumps to reach end is 3

74

Minimum number of jumps to reach end is 3

89

Minimum number of jumps to reach end is 3

74__156___1

Minimum number of jumps to reach end is 3

56950

Minimum number of jumps to reach end is 3

56835

Minimum number of jumps to reach end is 3

56952

Minimum number of jumps to reach end is 3

56953

Minimum number of jumps to reach end is 3

56954

Minimum number of jumps to reach end is 3

5693____156956

Minimum number of jumps to reach end is 3

74

Minimum number of jumps to reach end is 3

56958

Minimum number of jumps to reach end is 3

56959

Minimum number of jumps to reach end is 3

266

Minimum number of jumps to reach end is 3

56963

Minimum number of jumps to reach end is 3

46

Minimum number of jumps to reach end is 3

56965

 

Minimum number of jumps to reach end is 3

56966

C#

Minimum number of jumps to reach end is 3

56967

Minimum number of jumps to reach end is 3

569

Minimum number of jumps to reach end is 3

571

Minimum number of jumps to reach end is 3

56970

 

Minimum number of jumps to reach end is 3

87

Minimum number of jumps to reach end is 3

88

_______08____0278

_______08____157281

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

74

Minimum number of jumps to reach end is 3

94

Minimum number of jumps to reach end is 3

1

Minimum number of jumps to reach end is 3

2

Minimum number of jumps to reach end is 3

1

Minimum number of jumps to reach end is 3

56982

Minimum number of jumps to reach end is 3

1

Minimum number of jumps to reach end is 3

6

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

7

_______05____0293

_______05____0377

Minimum number of jumps to reach end is 3

5

Minimum number of jumps to reach end is 3

1

Minimum number of jumps to reach end is 3

276

Minimum number of jumps to reach end is 3

57308

Minimum number of jumps to reach end is 3

1

Minimum number of jumps to reach end is 3

57310

Minimum number of jumps to reach end is 3

5

Minimum number of jumps to reach end is 3

1

Minimum number of jumps to reach end is 3

54

 

Minimum number of jumps to reach end is 3

5

Minimum number of jumps to reach end is 3

306

_______05____0308

_______05____0310

Minimum number of jumps to reach end is 3

5

Minimum number of jumps to reach end is 3

615

 

_______05____0314

_______05____0316

_______05____0318

_______05____0320

_______05____0623

Minimum number of jumps to reach end is 3

5

Minimum number of jumps to reach end is 3

5692

Minimum number of jumps to reach end is 3

5693

Minimum number of jumps to reach end is 3

1

Minimum number of jumps to reach end is 3

5695

Minimum number of jumps to reach end is 3

5699____0329

Minimum number of jumps to reach end is 3

5699____0331

Minimum number of jumps to reach end is 3

5699

Minimum number of jumps to reach end is 3

3

Minimum number of jumps to reach end is 3

334

Minimum number of jumps to reach end is 3

5705

Minimum number of jumps to reach end is 3

307

Minimum number of jumps to reach end is 3

1

Minimum number of jumps to reach end is 3

57009

Minimum number of jumps to reach end is 3

5699

Minimum number of jumps to reach end is 3

5708

 

Minimum number of jumps to reach end is 3

5699____0342

Minimum number of jumps to reach end is 3

5699____0344

Minimum number of jumps to reach end is 3

5699____0643

Minimum number of jumps to reach end is 3

3

Minimum number of jumps to reach end is 3

348

_______15705____0647

Minimum number of jumps to reach end is 3

5699

Minimum number of jumps to reach end is 3

5708

 

_______15699____0354

_______15699____0356

Minimum number of jumps to reach end is 3

5699____0358

Minimum number of jumps to reach end is 3

5699____0360

Minimum number of jumps to reach end is 3

5699____0952

Minimum number of jumps to reach end is 3

5699

Minimum number of jumps to reach end is 3

643

Minimum number of jumps to reach end is 3

7

Minimum number of jumps to reach end is 3

5705

Minimum number of jumps to reach end is 3

660

Minimum number of jumps to reach end is 3

5705

Minimum number of jumps to reach end is 3

57022____01

Minimum number of jumps to reach end is 3

57009

 

Minimum number of jumps to reach end is 3

5705

Minimum number of jumps to reach end is 3

373

Minimum number of jumps to reach end is 3

5705____0375

Minimum number of jumps to reach end is 3

5705

Minimum number of jumps to reach end is 3

5692

Minimum number of jumps to reach end is 3

5693

Minimum number of jumps to reach end is 3

1

Minimum number of jumps to reach end is 3

380

Minimum number of jumps to reach end is 3

57173____0972

Minimum number of jumps to reach end is 3

56908

Minimum number of jumps to reach end is 3

3

Minimum number of jumps to reach end is 3

385

_______0051____0678

Minimum number of jumps to reach end is 3

56908

Minimum number of jumps to reach end is 3

5708

Minimum number of jumps to reach end is 3

5705

Minimum number of jumps to reach end is 3

5708

 

Minimum number of jumps to reach end is 3

5705____0682

Minimum number of jumps to reach end is 3

5705

Minimum number of jumps to reach end is 3

3

Minimum number of jumps to reach end is 3

396

Minimum number of jumps to reach end is 3

1

Minimum number of jumps to reach end is 3

321

Minimum number of jumps to reach end is 3

56908

Minimum number of jumps to reach end is 3

687

Minimum number of jumps to reach end is 3

5705

Minimum number of jumps to reach end is 3

5708

Minimum number of jumps to reach end is 3

5705

Minimum number of jumps to reach end is 3

643

Minimum number of jumps to reach end is 3

7

Minimum number of jumps to reach end is 3

56908____0691____0993

Minimum number of jumps to reach end is 3

5705

Minimum number of jumps to reach end is 3

5708

Minimum number of jumps to reach end is 3

5699

Minimum number of jumps to reach end is 3

5708

Minimum number of jumps to reach end is 3

5____15708

 

Minimum number of jumps to reach end is 3

5

Minimum number of jumps to reach end is 3

6

Minimum number of jumps to reach end is 3

699

_______08____15708

 

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

5715

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

74

Minimum number of jumps to reach end is 3

94

Minimum number of jumps to reach end is 3

76

Minimum number of jumps to reach end is 3

426

Minimum number of jumps to reach end is 3

427

Minimum number of jumps to reach end is 3

428

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

7

Minimum number of jumps to reach end is 3

5

Minimum number of jumps to reach end is 3

1

Minimum number of jumps to reach end is 3

433

Minimum number of jumps to reach end is 3

5699

Minimum number of jumps to reach end is 3

56835____157308

Minimum number of jumps to reach end is 3

1

Minimum number of jumps to reach end is 3

438

Minimum number of jumps to reach end is 3

5

Minimum number of jumps to reach end is 3

1

Minimum number of jumps to reach end is 3

441

Minimum number of jumps to reach end is 3

5

Minimum number of jumps to reach end is 3

443____0444

________ 0445 ________ 156881 ________ 0447

Minimum number of jumps to reach end is 3

445____0047

_______08____15708

Minimum number of jumps to reach end is 3

5708

 

Minimum number of jumps to reach end is 3

453

PHP

Minimum number of jumps to reach end is 3

57074

Minimum number of jumps to reach end is 3

455

Minimum number of jumps to reach end is 3

569

 

Minimum number of jumps to reach end is 3

457

Minimum number of jumps to reach end is 3

458

Minimum number of jumps to reach end is 3

57079

Minimum number of jumps to reach end is 3

2____157081____074

Minimum number of jumps to reach end is 3

57196

Minimum number of jumps to reach end is 3

24

Minimum number of jumps to reach end is 3

7

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

600

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

57159

Minimum number of jumps to reach end is 3

56927

Minimum number of jumps to reach end is 3

57196

Minimum number of jumps to reach end is 3

025

Minimum number of jumps to reach end is 3

57194

Minimum number of jumps to reach end is 3

474

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

57131

Minimum number of jumps to reach end is 3

5732

 

_______08____0479

_______08____0481

_______08____0483

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

57159____156927

Minimum number of jumps to reach end is 3

57196

Minimum number of jumps to reach end is 3

488

Minimum number of jumps to reach end is 3

57194

Minimum number of jumps to reach end is 3

490

 

_______08____0492

_______08____0494

_______08____0496

_______08____0498

_______08____0500

_______08____0623

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

5692

Minimum number of jumps to reach end is 3

5693

Minimum number of jumps to reach end is 3

57137

Minimum number of jumps to reach end is 3

56835

Minimum number of jumps to reach end is 3

57196

Minimum number of jumps to reach end is 3

509

Minimum number of jumps to reach end is 3

57137

Minimum number of jumps to reach end is 3

511

Minimum number of jumps to reach end is 3

57137

Minimum number of jumps to reach end is 3

513

Minimum number of jumps to reach end is 3

8

Minimum number of jumps to reach end is 3

7

_______05____0329

_______05____0331

Minimum number of jumps to reach end is 3

5

Minimum number of jumps to reach end is 3

3

Minimum number of jumps to reach end is 3

5693____157081

Minimum number of jumps to reach end is 3

56927

Minimum number of jumps to reach end is 3

57137

Minimum number of jumps to reach end is 3

57114

Minimum number of jumps to reach end is 3

5699

Minimum number of jumps to reach end is 3

57159

Minimum number of jumps to reach end is 3

56927

Minimum number of jumps to reach end is 3

57137

Minimum number of jumps to reach end is 3

531

 

_______05____0533

_______05____0535

_______05____0537

Minimum number of jumps to reach end is 3

5

Minimum number of jumps to reach end is 3

643

Minimum number of jumps to reach end is 3

3

Minimum number of jumps to reach end is 3

5693

Minimum number of jumps to reach end is 3

57081

Minimum number of jumps to reach end is 3

56927

Minimum number of jumps to reach end is 3

57137

Minimum number of jumps to reach end is 3

545

Minimum number of jumps to reach end is 3

57196

Minimum number of jumps to reach end is 3

56963

Minimum number of jumps to reach end is 3

57137

Minimum number of jumps to reach end is 3

549

Minimum number of jumps to reach end is 3

5699

Minimum number of jumps to reach end is 3

57159

Minimum number of jumps to reach end is 3

56927

Minimum number of jumps to reach end is 3

57137

Minimum number of jumps to reach end is 3

554

 

_______05____0354

_______05____0356

_______05____0358

_______05____0562

_______05____0564

_______05____0643

Minimum number of jumps to reach end is 3

5

Minimum number of jumps to reach end is 3

7

Minimum number of jumps to reach end is 3

5699____0660

Minimum number of jumps to reach end is 3

5699

Minimum number of jumps to reach end is 3

57131

Minimum number of jumps to reach end is 3

573

 

Minimum number of jumps to reach end is 3

5699____0373

Minimum number of jumps to reach end is 3

5699____0577

Minimum number of jumps to reach end is 3

5699____0579

Minimum number of jumps to reach end is 3

5699

Minimum number of jumps to reach end is 3

5692

Minimum number of jumps to reach end is 3

5693

Minimum number of jumps to reach end is 3

428

Minimum number of jumps to reach end is 3

56835

Minimum number of jumps to reach end is 3

57137

Minimum number of jumps to reach end is 3

57182

Minimum number of jumps to reach end is 3

428

Minimum number of jumps to reach end is 3

56912

Minimum number of jumps to reach end is 3

57196

Minimum number of jumps to reach end is 3

57144

Minimum number of jumps to reach end is 3

672

Minimum number of jumps to reach end is 3

428

Minimum number of jumps to reach end is 3

57142

Minimum number of jumps to reach end is 3

57081

Minimum number of jumps to reach end is 3

56927

Minimum number of jumps to reach end is 3

57137

Minimum number of jumps to reach end is 3

597

Minimum number of jumps to reach end is 3

57137

Minimum number of jumps to reach end is 3

5732

Minimum number of jumps to reach end is 3

428

Minimum number of jumps to reach end is 3

57155

Minimum number of jumps to reach end is 3

5699

Minimum number of jumps to reach end is 3

7

Minimum number of jumps to reach end is 3

5705

Minimum number of jumps to reach end is 3

3

Minimum number of jumps to reach end is 3

5693

Minimum number of jumps to reach end is 3

57131

Minimum number of jumps to reach end is 3

608

Minimum number of jumps to reach end is 3

57159

Minimum number of jumps to reach end is 3

56927

Minimum number of jumps to reach end is 3

428

Minimum number of jumps to reach end is 3

612