Hướng dẫn heap dictionary python - heap từ điển python

Prerequisites:

  • Cấu trúc dữ liệu nặng nhị phân
  • Mô -đun Heapq trong Python
  • Từ điển trong Python.

Từ điển có thể được duy trì trong đống dựa trên khóa hoặc dựa trên giá trị. Các quy ước được duy trì được liệt kê dưới đây:

  • Cặp giá trị khóa tại Index I I được coi là cha mẹ của cặp giá trị khóa tại các chỉ số 2K+1 và 2K+2.i‘ is considered to be the parent of key-value pair at the indices 2k+1 and 2k+2.
  • Đối với một min-heap, khóa/giá trị cha mẹ phải nhỏ hơn con cái.
  • Đối với tối đa, khóa/giá trị cha mẹ phải lớn hơn con cái.

Examples:

Từ điển bình thường: {11: 2, 0: 4, 5: 9, 22: 7}

HEAP Dựa trên các khóa của từ điển: {0: 4, 1: 1, 5: 9, 22: 7, 11: 2}{0: 4, 1: 1, 5: 9, 22: 7, 11: 2}

HEAP Dựa trên các giá trị của từ điển: {11: 2, 0: 4, 5: 9, 22: 7}{11: 2, 0: 4, 5: 9, 22: 7}

Bài viết này cho thấy cách duy trì một từ điển trong một min-heap bằng mô-đun FEAPQ.

Từ điển bình thường như một đống

Từ điển bình thường với số nguyên/chuỗi là khóa có thể được duy trì trong cấu trúc heap với sự trợ giúp của mô -đun FEAPQ. Nhưng mô -đun này hy vọng một danh sách sẽ được thông qua. Vì vậy, cách tiếp cận được sử dụng ở đây là:

  1. Chuyển đổi các cặp giá trị khóa thành một danh sách các bộ dữ liệu.
  2. Chuyển danh sách các bộ dữ liệu cho hàm heapify ().heapify() function.
  3. Chuyển đổi danh sách kết quả thành một từ điển một lần nữa.

LƯU Ý: Các heapify () trên các bộ dữ liệu xem xét phần tử đầu tiên trong tuple cho quy trình. Do đó, theo mặc định, các từ điển được duy trì trong đống, chỉ dựa trên khóa.The heapify() on tuples considers the first element in the tuple for the process. Thus, by default, the dictionaries are maintained in heap, based on the key only.

Ví dụ 1: Dựa trên khóa cho số nguyên

Hãy xem xét một từ điển trong đó các khóa là số nguyên dương và các giá trị là hình vuông của chúng. Bây giờ, điều này nên được duy trì trong một đống.

Python3

import heapq as hq

dict_1 =

After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
5=
After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
7
After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
8

After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
9
Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
0
Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
1
Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
2

Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
3

After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
9
Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
0
Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
6
Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
2

After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
5= import0import1

After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
9
Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
0import4
Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
2

Đầu ra

dictionary into list : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified list of tuples : [(2, 4), (3, 9), (5, 25), (11, 121)]
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}

Ví dụ 2: Dựa trên khóa cho chuỗi & nbsp;

Hãy xem xét một từ điển có sự kết hợp của bảng chữ cái là khóa và đánh số của chúng là giá trị. Ví dụ: ABC ABC: 123. Điều này phải được duy trì trong Heap. & NBSP;abc” : 123. This has to be maintained in heap. 

Python3

import heapq as hq

dict_1 =

After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
5=
After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
7
After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
8

After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
9
Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
0
Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
1
Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
2

Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
3

After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
9
Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
0
Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
6
Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
2

After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
5= import0import1

After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
9
Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
0import4
Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
2

Output:

Đầu ra
Heapified list of tuples : [(‘ab’, 12), (‘fg’, 67), (‘cd’, 34), (‘ij’, 910), (‘yz’, 2526)] 
Dictionary as heap : {‘ab’: 12, ‘fg’: 67, ‘cd’: 34, ‘ij’: 910, ‘yz’: 2526}

Ví dụ 2: Dựa trên khóa cho chuỗi & nbsp; value

Hãy xem xét một từ điển có sự kết hợp của bảng chữ cái là khóa và đánh số của chúng là giá trị. Ví dụ: ABC ABC: 123. Điều này phải được duy trì trong Heap. & NBSP;

  1. dict_1 =
  2. Từ điển vào danh sách: [('yz', 2526), ​​('ab', 12), ('cd', 34), ('ij', 910), ('fg', 67)] & nbsp; Tuples: [('ab', 12), ('fg', 67), ('cd', 34), ('ij', 910), ('yz', 2526)] & nbsp; từ điển như đống: {{ 'AB': 12, 'fg': 67, 'cd': 34, 'ij': 910, 'yz': 2526}heapify().
  3. Ví dụ 3: Dựa trên giá trị

Cách tiếp cận hơi khác nhau ở đây. Các bước được thực hiện là:

Example:

Python3

import heapq as hq

dict_1 =

Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
13=
Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
15

After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
5=
After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
7
After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
8

Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
20
Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
21

Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
22

After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
9
Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
0
Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
25
Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
26

Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
27=
Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
15

After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
5= import0import1

Đầu ra

Ví dụ 2: Dựa trên khóa cho chuỗi & nbsp;

Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
55
Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
56

Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
27=import0
Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
60

Hãy xem xét một từ điển có sự kết hợp của bảng chữ cái là khóa và đánh số của chúng là giá trị. Ví dụ: ABC ABC: 123. Điều này phải được duy trì trong Heap. & NBSP;

Đầu ra

Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}

Ví dụ 2: Dựa trên khóa cho chuỗi & nbsp;

Hãy xem xét một từ điển có sự kết hợp của bảng chữ cái là khóa và đánh số của chúng là giá trị. Ví dụ: ABC ABC: 123. Điều này phải được duy trì trong Heap. & NBSP;

  • dict_1 =
  • Từ điển vào danh sách: [('yz', 2526), ​​('ab', 12), ('cd', 34), ('ij', 910), ('fg', 67)] & nbsp; Tuples: [('ab', 12), ('fg', 67), ('cd', 34), ('ij', 910), ('yz', 2526)] & nbsp; từ điển như đống: {{ 'AB': 12, 'fg': 67, 'cd': 34, 'ij': 910, 'yz': 2526}heapify().
  • Ví dụ 3: Dựa trên giá trị

LƯU Ý: Các heapify () trên các bộ dữ liệu xem xét phần tử đầu tiên trong tuple cho quy trình. Do đó, theo mặc định, các từ điển được duy trì trong đống, chỉ dựa trên khóa.The heapify() on tuples considers the first element in the tuple for the process. Thus, by default, the dictionaries are maintained in heap, based on the key only.

Ví dụ: & nbsp; 

Python3

import heapq as hq

114=

Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
6911118
Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
1
Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
73
Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
3118
Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
5
Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
73
Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
7118
Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
9
Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
73
After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
1118
After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
3
Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
85

Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
13=
Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
15

Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
13=
Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
91
Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
16
Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
17
Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
18

After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
9
Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
0
After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
02
Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
26

Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
22

After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
9
Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
0
After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
07
Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
26

After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
09=import0
After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
12

After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
9
Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
0
After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
15
After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
16

Đầu ra

After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}

Từ điển lồng nhau

Trong trường hợp từ điển lồng nhau, nhiệm vụ thực hiện nhiều bước hơn để duy trì từ điển trong đống. Nếu từ điển phải được duy trì dựa trên khóa trong từ điển bên trong, thì phương pháp sau đây có thể được sử dụng.

  • Chuyển đổi từ điển thành danh sách các bộ dữ liệu trong đó khóa của từ điển bên ngoài là tuple [0] và từ điển bên trong là tuple [1].
  • Trích xuất các giá trị của khóa trong từ điển bên trong vào một danh sách.
  • Áp dụng Heapify () trong danh sách đó.heapify() on that list.
  • Xây dựng lại một từ điển mới bằng cách đặt hàng chúng dựa trên các kết quả được đặt.

Ví dụ, hãy xem xét một hồ sơ của nhân viên là một từ điển lồng nhau. Hồ sơ xuất hiện như được đưa ra dưới đây: & nbsp;

{

& nbsp; & nbsp;

& nbsp; & nbsp; & nbsp; & nbsp; tên tên "

& nbsp; & nbsp; & nbsp; & nbsp; "tuổi": 22,

& nbsp; & nbsp; & nbsp; & NBSP; Chỉ định trực tuyến

& nbsp; & nbsp; & nbsp; & NBSP;

& nbsp; & nbsp;},

& nbsp; & nbsp;

& nbsp; & nbsp; & nbsp; & nbsp; tên của tên

& nbsp; & nbsp; & nbsp; & nbsp; "tuổi": 20,

& nbsp; & nbsp; & nbsp; & NBSP; Chỉ định của người Viking

& nbsp; & nbsp; & nbsp; & NBSP;

& nbsp; & nbsp;},

& nbsp; & nbsp;

& nbsp; & nbsp; & nbsp; & nbsp; tên của tên

& nbsp; & nbsp; & nbsp; & nbsp; "tuổi": 20,

& nbsp; & nbsp; & nbsp; & NBSP; Chỉ định của người Viking

& nbsp; & nbsp; & nbsp; & NBSP;

& nbsp; & nbsp;},

& nbsp; & nbsp;

& nbsp; & nbsp; & nbsp; & nbsp; tên của tên

& nbsp; & nbsp; & nbsp; & nbsp; "tuổi": 20,

& nbsp; & nbsp; & nbsp; & NBSP; Chỉ định của người Viking

& nbsp; & nbsp; & nbsp; & NBSP;

& nbsp; & nbsp;

& nbsp; & nbsp; & nbsp; & nbsp; tên của tên

& nbsp; & nbsp; & nbsp; & nbsp; "tuổi": 42,

& nbsp; & nbsp; & nbsp; & NBSP; Chỉ định của người Viking: Người quản lý trực tuyến, 

Python3

& nbsp; & nbsp; & nbsp; & NBSP;

& nbsp; & nbsp;

Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
20
After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
9
Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
0
After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
27
After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
28
After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
29
After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
30

Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
20
After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
32
After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
33

& nbsp; & nbsp; & nbsp; & nbsp; tên tên "
Step 2: Define the function that performs heapification. Takes the list of tuples as parameter. 

Python3

& nbsp; & nbsp; & nbsp; & NBSP;

Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
20
After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
37=
Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
15

& nbsp; & nbsp;}

}

Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
20
After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
9
Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
0
After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
59
After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
60
After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
29
After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
30

Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
20
After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
64

Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
20
After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
9
Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
0
After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
68
After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
60
After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
29
After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
30

Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
20
After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
09=
Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
15

Bây giờ chúng ta hãy duy trì điều này trong một min-heap dựa trên các giá trị lương. Do đó, nhân viên có mức lương tối thiểu xuất hiện dưới dạng kỷ lục đầu tiên. Để dễ đọc và hiểu rõ hơn, chúng ta có thể chia mã thành các chức năng.

Bước 1: & nbsp; Xác định chức năng để chuyển đổi từ điển thành danh sách & nbsp;

After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
17
After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
18

Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
06
Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
07

Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
20
After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
20=
After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
7____
After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
23

& nbsp; Bước 2: Xác định chức năng thực hiện quá trình hấp thụ. Lấy danh sách các bộ dữ liệu làm tham số. & Nbsp;

After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
17
After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
35

Python3

Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
16={

Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
20
Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
20
Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
21

Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
44
Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
23118
Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
25
Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
00

Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
44
Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
28118
Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
30
Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
00

Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
44
Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
33
Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
0
Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
35
Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
00

Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
44
Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
38118
Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
40

Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
20
Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
42

Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
20
Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
44
Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
21

Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
20
Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
16
Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
17
Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
18
Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
33
Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
0
Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
35
Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
00
Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
37
After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
49

Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
44
Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
28118
Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
54
Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
00

Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
44
Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
33118
Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
59
Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
00

Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
44
Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
38118
Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
64

Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
20
Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
42

Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
20
Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
68
Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
21

Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
44
Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
23118
Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
73
Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
00

Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
44
Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
28118
Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
78
Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
00

Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
44
Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
33118
Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
83
Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
00

Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
44
Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
38118
Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
88

Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
20
Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
42

Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
20
Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
92
Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
21

Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
44
Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
23118
Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
97
Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
00

Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
44
Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
28118
Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
78
Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
00

Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
44
Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
33118
Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
83
Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
00

Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
44
Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
38118import12

Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
20
After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
4

After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
4

After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
20=import18

After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
09=import21

After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
9
Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
0import4
After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
16

Bây giờ đặt tất cả các mã với nhau, chúng tôi nhận được một từ điển lồng nhau được duy trì trong đống, dựa trên các giá trị của mức lương.

Python3

import heapq as hq

After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
17
After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
18

Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
20
After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
20=
After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
7____
After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
23

Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
20
After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
9
Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
0
After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
27
After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
28
After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
29
After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
30

Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
20
After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
32
After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
33

After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
17
After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
35

Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
20
After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
37=
Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
15

Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
20
Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
16
Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
17
Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
18
Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
33
Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
0
Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
35
Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
00
Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
37
After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
49

Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
44
After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
51
After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
52
After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
53
After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
54
After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
55

Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
20
After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
9
Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
0
After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
59
After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
60
After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
29
After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
30

Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
20
After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
64

Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
20
After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
9
Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
0import79
After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
60
After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
29
After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
30

Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
20
After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
09=
Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
15

Is

Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
44___

Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
55
Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
45
After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
98
After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
525
After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
53
After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
54
Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
022

Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
06
Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
07

Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
20
After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
09=import0
Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
12

Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
20
After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
32
After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
09

Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
16={

Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
20
Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
20
Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
21

Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
44
Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
23118
Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
25
Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
00

Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
44
Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
28118
Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
30
Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
00

Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
44
Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
33
Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
0
Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
35
Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
00

Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
44
Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
38118
Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
40

Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
20
Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
42

Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
20
Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
44
Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
21

Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
44
Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
23118
Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
49
Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
00

Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
44
Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
28118
Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
54
Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
00

Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
44
Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
33118
Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
59
Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
00

Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
44
Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
38118
Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
64

Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
20
Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
42

Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
20
Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
68
Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
21

Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
44
Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
23118
Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
73
Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
00

Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
44
Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
28118
Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
78
Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
00

Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
44___

Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
44
Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
38118
Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
88

Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
20
Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
42

Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
20
Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
92
Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
21

Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
44
Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
23118
Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
97
Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
00

Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
44
Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
28118
Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
78
Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
00

Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
44
Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
33118
Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
83
Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
00

Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
44
Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
38118import12

Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
20
After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
4

After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
4

After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
20=import18

After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
09=import21

After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
9
Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
0import4
After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
16

Đầu ra

Từ điển như danh sách [('Emp01, {' tên ':' Kate ',' Age ': 22,' Chỉ định ':' Nhà phân tích ',' Mức lương ': 30000}), (' Emp02 ′, {'Tên': 'Rina', 'tuổi': 20, 'chỉ định': 'lập trình viên', 'tiền lương': 25000}), ('emp03 ′, {' name ':' vikas ',' tuổi ': 42,' chỉ định ': 'Người quản lý', 'Mức lương': 35000}), ('Emp04 ′, {' Tên ':' Manish ',' Age ': 42,' Chỉ định ':' Người quản lý ',' Mức lương ': 15000})]]

& nbsp; trước khi Heapify: [30000, 25000, 35000, 15000] & nbsp;

& nbsp; sau khi Heapify: [15000, 25000, 35000, 30000] & nbsp;

Từ điển như Heap: {'emp04 ′: {' name ':' manish ',' tuổi ': 42,' chỉ định ':' người quản lý ',' tiền lương ': 15000},' emp02 ′: {'name': 'rina ',' Tuổi ': 20,' Chỉ định ':' Lập trình viên ',' Mức lương ': 25000},' Emp03: {'Tên': 'Vikas', 'Tuổi': 42, 'Chỉ định': 'Người quản lý', 'Mức lương': 35000}, 'Emp01 ′: {' name ':' Kate ',' Age ': 22,' Chỉ định ':' Nhà phân tích ',' Mức lương ': 30000}}

Chèn vào từ điển được duy trì dưới dạng một đống

Việc chèn các giá trị mới có thể được thực hiện trực tiếp bằng phương thức Heppush () trong mô -đun Heapq. Cú pháp của nó như sau.heappush() method in the heapq module. Its syntax is as follows.

HEAPQ. Heppush (Danh sách, New_Value)

Bây giờ, danh sách các bộ dữ liệu cùng với một tuple mới có thể được chuyển đến hàm này để thêm cặp giá trị khóa mới.

Thí dụ :

Python3

import heapq as hq

Các

Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
13=
Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
15

Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
13=
Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
91
Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
16
Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
17
Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
18

After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
9
Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
0dict_1 74
Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
26

Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
22

After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
9
Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
0dict_1 79
Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
26

After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
09=import0
After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
12

After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
9
Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
0import4
After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
16

dict_1 89

After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
52
Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
00
After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
52dict_1 93

After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
9
Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
0dict_1 96
Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
26

After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
09=import0
After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
12

After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
9
Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
0=04
After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
16

Output:

Danh sách các bộ dữ liệu: [(11, 121), (2, 4), (5, 25), (3, 9)] & nbsp; sau khi tăng cường: [(2, 4), (3, 9), (5, 5,25), (11, 121)] & nbsp; từ điển dưới dạng heap: {2: 4, 3: 9, 5: 25, 11: 121} & nbsp; sau khi chèn & heapify, (5, 25), (11, 121), (3, 9)] & nbsp; từ điển mới: {1: 1, 2: 4, 5: 25, 11: 121, 3: 9}
After heapification : [(2, 4), (3, 9), (5, 25), (11, 121)] 
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121} 
After insertion & heapification [(1, 1), (2, 4), (5, 25), (11, 121), (3, 9)] 
New dictionary : {1: 1, 2: 4, 5: 25, 11: 121, 3: 9}

Một phương pháp khác có thể được thực hiện là có một chức năng tăng cường từ điển và gọi nó sau khi cập nhật từ điển. & NBSP;

Thí dụ :

Python3

import heapq as hq

After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
17 =09

Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
20=11=
After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
7=14

Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
20=16

Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
20=11=import0=21

Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
20
After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
9
Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
0import4=26

=27={11118

Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
1
Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
00
Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
3118
Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
5
Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
00
Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
7118
Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
9
Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
00
After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
1118
After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
3
After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
4

After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
9
Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
030748
After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
30

=50

=51

Values of the dict after heapification : [4, 9, 25, 121]
Final dictionary : {2: 4, 3: 9, 5: 25, 11: 121}
5
Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
02==55

=51

After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
52
Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
02=
After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
52

After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
9
Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
0=63=64

After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
9
Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}
0=67
After extraction : [(11, 121), (2, 4), (5, 25), (3, 9)]
Heapified key-value pairs : [(2, 4), (3, 9), (5, 25), (11, 121)]
Heapified dictionaries : {2: 4, 3: 9, 5: 25, 11: 121}
30

=50

Đầu ra

Before adding new values
Dictionary as heap : {2: 4, 3: 9, 5: 25, 11: 121}
Updated dictionary : {11: 121, 2: 4, 5: 25, 3: 9, 4: 16, 1: 1}
After adding new values
Dictionary as heap : {1: 1, 2: 4, 5: 25, 3: 9, 4: 16, 11: 121}