Hướng dẫn how to check pythagorean triples in python - cách kiểm tra bộ ba pythagore trong trăn

Tôi cần một chương trình cho phép ba số được nhập và đầu ra nếu chúng có thể tạo thành một bộ ba Pythagore (ví dụ: a^2 + b^2 = c^2 / hoặc / 3^2 + 4^2 = 5^).

Tôi có một giải pháp, nhưng tôi cảm thấy như nó thực sự không hiệu quả và tôi đã tự hỏi nếu có một giải pháp ngắn hơn, tốt hơn có sẵn?

Giải pháp của tôi cho đến nay:

nums = []

for num in range(0,3):
    nums.append(int(input("Enter a number")))

if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
       // Is a pythagorean triple

Vân vân..

Hướng dẫn how to check pythagorean triples in python - cách kiểm tra bộ ba pythagore trong trăn

Đã hỏi ngày 12 tháng 3 năm 2017 lúc 20:31Mar 12, 2017 at 20:31

Hướng dẫn how to check pythagorean triples in python - cách kiểm tra bộ ba pythagore trong trăn

3

Chỉ cần sắp xếp nums. Sau đó, bạn sẽ chỉ phải thực hiện một kiểm tra:

nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed

Đã trả lời ngày 12 tháng 3 năm 2017 lúc 20:41Mar 12, 2017 at 20:41

MaratmaratMarat

14.2k2 Huy hiệu vàng37 Huy hiệu bạc45 Huy hiệu đồng2 gold badges37 silver badges45 bronze badges

Một bộ ba Pythagore là một tập hợp ba số nguyên dương A, B và C sao cho A2 + B2 = C2. Đưa ra một giới hạn, tạo ra tất cả các bộ ba Pythagore với các giá trị nhỏ hơn giới hạn đã cho.

Input : limit = 20
Output : 3 4 5
         8 6 10
         5 12 13
         15 8 17
         12 16 20

Một giải pháp đơn giản là tạo ra các bộ ba này nhỏ hơn giới hạn được cho bằng cách sử dụng ba vòng lồng nhau. Đối với mỗi bộ ba, hãy kiểm tra xem điều kiện Pythagore có đúng không, nếu đúng, sau đó in bộ ba. Độ phức tạp thời gian của giải pháp này là O (giới hạn3) trong đó ‘giới hạn được đưa ra giới hạn.Simple Solution is to generate these triplets smaller than given limit using three nested loop. For every triplet, check if Pythagorean condition is true, if true, then print the triplet. Time complexity of this solution is O(limit3) where ‘limit’ is given limit.

Một giải pháp hiệu quả có thể in tất cả các bộ ba trong thời gian O (k) trong đó k là số lượng ba bản in. Ý tưởng là sử dụng mối quan hệ tổng vuông của bộ ba Pythagore, tức là, việc bổ sung các hình vuông của A và B bằng với bình phương C, chúng ta có thể viết số này theo m và n sao cho, & nbsp; & nbsp;Efficient Solution can print all triplets in O(k) time where k is number of triplets printed. The idea is to use square sum relation of Pythagorean triplet, i.e., addition of squares of a and b is equal to square of c, we can write these number in terms of m and n such that,  

       a = m2 - n2
       b = 2 * m * n
       c  = m2 + n2
because,
       a2 = m4 + n4 – 2 * m2 * n2
       b2 = 4 * m2 * n2
       c2 = m4 + n4 + 2* m2 * n2

Chúng ta có thể thấy rằng A2 + B2 = C2, vì vậy thay vì lặp lại cho A, B và C, chúng ta có thể lặp lại cho M và N và có thể tạo các bộ ba này. & NBSP;

Dưới đây là việc thực hiện ý tưởng trên: & nbsp; & nbsp;

C++

#include

void pythagoreanTriplets(int

nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
0

nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
1

nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
2int
nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
4

nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
2int
nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
7

nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
2
nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
9
Input : limit = 20
Output : 3 4 5
         8 6 10
         5 12 13
         15 8 17
         12 16 20
0

Input : limit = 20
Output : 3 4 5
         8 6 10
         5 12 13
         15 8 17
         12 16 20
1
Input : limit = 20
Output : 3 4 5
         8 6 10
         5 12 13
         15 8 17
         12 16 20
2
Input : limit = 20
Output : 3 4 5
         8 6 10
         5 12 13
         15 8 17
         12 16 20
3int
Input : limit = 20
Output : 3 4 5
         8 6 10
         5 12 13
         15 8 17
         12 16 20
5

Input : limit = 20
Output : 3 4 5
         8 6 10
         5 12 13
         15 8 17
         12 16 20
6
Input : limit = 20
Output : 3 4 5
         8 6 10
         5 12 13
         15 8 17
         12 16 20
7

Input : limit = 20
Output : 3 4 5
         8 6 10
         5 12 13
         15 8 17
         12 16 20
6
Input : limit = 20
Output : 3 4 5
         8 6 10
         5 12 13
         15 8 17
         12 16 20
9

Input : limit = 20
Output : 3 4 5
         8 6 10
         5 12 13
         15 8 17
         12 16 20
6
       a = m2 - n2
       b = 2 * m * n
       c  = m2 + n2
because,
       a2 = m4 + n4 – 2 * m2 * n2
       b2 = 4 * m2 * n2
       c2 = m4 + n4 + 2* m2 * n2
1

Input : limit = 20
Output : 3 4 5
         8 6 10
         5 12 13
         15 8 17
         12 16 20
6
       a = m2 - n2
       b = 2 * m * n
       c  = m2 + n2
because,
       a2 = m4 + n4 – 2 * m2 * n2
       b2 = 4 * m2 * n2
       c2 = m4 + n4 + 2* m2 * n2
3
       a = m2 - n2
       b = 2 * m * n
       c  = m2 + n2
because,
       a2 = m4 + n4 – 2 * m2 * n2
       b2 = 4 * m2 * n2
       c2 = m4 + n4 + 2* m2 * n2
4

       a = m2 - n2
       b = 2 * m * n
       c  = m2 + n2
because,
       a2 = m4 + n4 – 2 * m2 * n2
       b2 = 4 * m2 * n2
       c2 = m4 + n4 + 2* m2 * n2
5
       a = m2 - n2
       b = 2 * m * n
       c  = m2 + n2
because,
       a2 = m4 + n4 – 2 * m2 * n2
       b2 = 4 * m2 * n2
       c2 = m4 + n4 + 2* m2 * n2
6
       a = m2 - n2
       b = 2 * m * n
       c  = m2 + n2
because,
       a2 = m4 + n4 – 2 * m2 * n2
       b2 = 4 * m2 * n2
       c2 = m4 + n4 + 2* m2 * n2
7

Input : limit = 20
Output : 3 4 5
         8 6 10
         5 12 13
         15 8 17
         12 16 20
6
       a = m2 - n2
       b = 2 * m * n
       c  = m2 + n2
because,
       a2 = m4 + n4 – 2 * m2 * n2
       b2 = 4 * m2 * n2
       c2 = m4 + n4 + 2* m2 * n2
9
Input : limit = 20
Output : 3 4 5
         8 6 10
         5 12 13
         15 8 17
         12 16 20
3
3 4 5
8 6 10
5 12 13
15 8 17
12 16 20
1
3 4 5
8 6 10
5 12 13
15 8 17
12 16 20
2

Input : limit = 20
Output : 3 4 5
         8 6 10
         5 12 13
         15 8 17
         12 16 20
1
3 4 5
8 6 10
5 12 13
15 8 17
12 16 20
4

Input : limit = 20
Output : 3 4 5
         8 6 10
         5 12 13
         15 8 17
         12 16 20
1
3 4 5
8 6 10
5 12 13
15 8 17
12 16 20
6

nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
2
3 4 5
8 6 10
5 12 13
15 8 17
12 16 20
4

3 4 5
8 6 10
5 12 13
15 8 17
12 16 20
4

int nums1

nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
1

nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
2int nums5

nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
2nums7

nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
2nums9 #include 0

3 4 5
8 6 10
5 12 13
15 8 17
12 16 20
4

Java

#include 2 #include 3

#include 2 #include 5

#include 6 #include 7

nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
2#include 9 void pythagoreanTriplets(int
nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
0

nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
2
nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
1

Input : limit = 20
Output : 3 4 5
         8 6 10
         5 12 13
         15 8 17
         12 16 20
1int void8void9
       a = m2 - n2
       b = 2 * m * n
       c  = m2 + n2
because,
       a2 = m4 + n4 – 2 * m2 * n2
       b2 = 4 * m2 * n2
       c2 = m4 + n4 + 2* m2 * n2
7

Input : limit = 20
Output : 3 4 5
         8 6 10
         5 12 13
         15 8 17
         12 16 20
1int pythagoreanTriplets(3pythagoreanTriplets(4
       a = m2 - n2
       b = 2 * m * n
       c  = m2 + n2
because,
       a2 = m4 + n4 – 2 * m2 * n2
       b2 = 4 * m2 * n2
       c2 = m4 + n4 + 2* m2 * n2
7

Input : limit = 20
Output : 3 4 5
         8 6 10
         5 12 13
         15 8 17
         12 16 20
1
nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
9
Input : limit = 20
Output : 3 4 5
         8 6 10
         5 12 13
         15 8 17
         12 16 20
0

Input : limit = 20
Output : 3 4 5
         8 6 10
         5 12 13
         15 8 17
         12 16 20
6
Input : limit = 20
Output : 3 4 5
         8 6 10
         5 12 13
         15 8 17
         12 16 20
2
Input : limit = 20
Output : 3 4 5
         8 6 10
         5 12 13
         15 8 17
         12 16 20
3int int3int4int5

       a = m2 - n2
       b = 2 * m * n
       c  = m2 + n2
because,
       a2 = m4 + n4 – 2 * m2 * n2
       b2 = 4 * m2 * n2
       c2 = m4 + n4 + 2* m2 * n2
5
Input : limit = 20
Output : 3 4 5
         8 6 10
         5 12 13
         15 8 17
         12 16 20
7

       a = m2 - n2
       b = 2 * m * n
       c  = m2 + n2
because,
       a2 = m4 + n4 – 2 * m2 * n2
       b2 = 4 * m2 * n2
       c2 = m4 + n4 + 2* m2 * n2
5int9pythagoreanTriplets(4
nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
01

       a = m2 - n2
       b = 2 * m * n
       c  = m2 + n2
because,
       a2 = m4 + n4 – 2 * m2 * n2
       b2 = 4 * m2 * n2
       c2 = m4 + n4 + 2* m2 * n2
5
       a = m2 - n2
       b = 2 * m * n
       c  = m2 + n2
because,
       a2 = m4 + n4 – 2 * m2 * n2
       b2 = 4 * m2 * n2
       c2 = m4 + n4 + 2* m2 * n2
1

       a = m2 - n2
       b = 2 * m * n
       c  = m2 + n2
because,
       a2 = m4 + n4 – 2 * m2 * n2
       b2 = 4 * m2 * n2
       c2 = m4 + n4 + 2* m2 * n2
5
       a = m2 - n2
       b = 2 * m * n
       c  = m2 + n2
because,
       a2 = m4 + n4 – 2 * m2 * n2
       b2 = 4 * m2 * n2
       c2 = m4 + n4 + 2* m2 * n2
3
       a = m2 - n2
       b = 2 * m * n
       c  = m2 + n2
because,
       a2 = m4 + n4 – 2 * m2 * n2
       b2 = 4 * m2 * n2
       c2 = m4 + n4 + 2* m2 * n2
4

nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
07
       a = m2 - n2
       b = 2 * m * n
       c  = m2 + n2
because,
       a2 = m4 + n4 – 2 * m2 * n2
       b2 = 4 * m2 * n2
       c2 = m4 + n4 + 2* m2 * n2
6
       a = m2 - n2
       b = 2 * m * n
       c  = m2 + n2
because,
       a2 = m4 + n4 – 2 * m2 * n2
       b2 = 4 * m2 * n2
       c2 = m4 + n4 + 2* m2 * n2
7

       a = m2 - n2
       b = 2 * m * n
       c  = m2 + n2
because,
       a2 = m4 + n4 – 2 * m2 * n2
       b2 = 4 * m2 * n2
       c2 = m4 + n4 + 2* m2 * n2
5
nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
11
nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
12
nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
13
nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
12
nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
15

Input : limit = 20
Output : 3 4 5
         8 6 10
         5 12 13
         15 8 17
         12 16 20
6
3 4 5
8 6 10
5 12 13
15 8 17
12 16 20
4

Input : limit = 20
Output : 3 4 5
         8 6 10
         5 12 13
         15 8 17
         12 16 20
6
3 4 5
8 6 10
5 12 13
15 8 17
12 16 20
6

Input : limit = 20
Output : 3 4 5
         8 6 10
         5 12 13
         15 8 17
         12 16 20
1
3 4 5
8 6 10
5 12 13
15 8 17
12 16 20
4

nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
2
3 4 5
8 6 10
5 12 13
15 8 17
12 16 20
4

nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
2
nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
25 #include 9 void
nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
28

nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
2
nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
1

Input : limit = 20
Output : 3 4 5
         8 6 10
         5 12 13
         15 8 17
         12 16 20
1int
nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
33
nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
34
       a = m2 - n2
       b = 2 * m * n
       c  = m2 + n2
because,
       a2 = m4 + n4 – 2 * m2 * n2
       b2 = 4 * m2 * n2
       c2 = m4 + n4 + 2* m2 * n2
7

Input : limit = 20
Output : 3 4 5
         8 6 10
         5 12 13
         15 8 17
         12 16 20
1nums7

nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
2
3 4 5
8 6 10
5 12 13
15 8 17
12 16 20
4

3 4 5
8 6 10
5 12 13
15 8 17
12 16 20
4

Python3

nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
41
nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
42

nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
2
nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
44
nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
45 void9
nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
47pythagoreanTriplets(4

nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
2
nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
9
nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
51

Input : limit = 20
Output : 3 4 5
         8 6 10
         5 12 13
         15 8 17
         12 16 20
1
Input : limit = 20
Output : 3 4 5
         8 6 10
         5 12 13
         15 8 17
         12 16 20
2
nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
54
nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
55
nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
56
Input : limit = 20
Output : 3 4 5
         8 6 10
         5 12 13
         15 8 17
         12 16 20
3int4
nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
59

Input : limit = 20
Output : 3 4 5
         8 6 10
         5 12 13
         15 8 17
         12 16 20
6
nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
61
nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
45
nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
63
nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
64
nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
63
nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
66
nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
54__

Input : limit = 20
Output : 3 4 5
         8 6 10
         5 12 13
         15 8 17
         12 16 20
6
nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
71
nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
45 pythagoreanTriplets(4
nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
64
nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
63
nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
64
nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
69

Input : limit = 20
Output : 3 4 5
         8 6 10
         5 12 13
         15 8 17
         12 16 20
6
nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
79
nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
45
nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
63
nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
64
nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
63
nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
84
nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
54__

Input : limit = 20
Output : 3 4 5
         8 6 10
         5 12 13
         15 8 17
         12 16 20
6
       a = m2 - n2
       b = 2 * m * n
       c  = m2 + n2
because,
       a2 = m4 + n4 – 2 * m2 * n2
       b2 = 4 * m2 * n2
       c2 = m4 + n4 + 2* m2 * n2
3
nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
90

       a = m2 - n2
       b = 2 * m * n
       c  = m2 + n2
because,
       a2 = m4 + n4 – 2 * m2 * n2
       b2 = 4 * m2 * n2
       c2 = m4 + n4 + 2* m2 * n2
5
       a = m2 - n2
       b = 2 * m * n
       c  = m2 + n2
because,
       a2 = m4 + n4 – 2 * m2 * n2
       b2 = 4 * m2 * n2
       c2 = m4 + n4 + 2* m2 * n2
6

Input : limit = 20
Output : 3 4 5
         8 6 10
         5 12 13
         15 8 17
         12 16 20
6
nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
94
nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
95

Input : limit = 20
Output : 3 4 5
         8 6 10
         5 12 13
         15 8 17
         12 16 20
1
nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
63
nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
45
nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
63
nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
84 int4

       a = m2 - n2
       b = 2 * m * n
       c  = m2 + n2
because,
       a2 = m4 + n4 – 2 * m2 * n2
       b2 = 4 * m2 * n2
       c2 = m4 + n4 + 2* m2 * n2
3
Input : limit = 20
Output : 3 4 5
         8 6 10
         5 12 13
         15 8 17
         12 16 20
03
nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
45
nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
45
Input : limit = 20
Output : 3 4 5
         8 6 10
         5 12 13
         15 8 17
         12 16 20
06
Input : limit = 20
Output : 3 4 5
         8 6 10
         5 12 13
         15 8 17
         12 16 20
07

nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
2
Input : limit = 20
Output : 3 4 5
         8 6 10
         5 12 13
         15 8 17
         12 16 20
09
nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
45
nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
34

nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
2
Input : limit = 20
Output : 3 4 5
         8 6 10
         5 12 13
         15 8 17
         12 16 20
13

C#

Input : limit = 20
Output : 3 4 5
         8 6 10
         5 12 13
         15 8 17
         12 16 20
14
Input : limit = 20
Output : 3 4 5
         8 6 10
         5 12 13
         15 8 17
         12 16 20
15

#include 6 #include 7

nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
2#include 9 void pythagoreanTriplets(int
nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
0

nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
2
nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
1

Input : limit = 20
Output : 3 4 5
         8 6 10
         5 12 13
         15 8 17
         12 16 20
1int void8void9
       a = m2 - n2
       b = 2 * m * n
       c  = m2 + n2
because,
       a2 = m4 + n4 – 2 * m2 * n2
       b2 = 4 * m2 * n2
       c2 = m4 + n4 + 2* m2 * n2
7

Input : limit = 20
Output : 3 4 5
         8 6 10
         5 12 13
         15 8 17
         12 16 20
1int pythagoreanTriplets(3pythagoreanTriplets(4
       a = m2 - n2
       b = 2 * m * n
       c  = m2 + n2
because,
       a2 = m4 + n4 – 2 * m2 * n2
       b2 = 4 * m2 * n2
       c2 = m4 + n4 + 2* m2 * n2
7

Input : limit = 20
Output : 3 4 5
         8 6 10
         5 12 13
         15 8 17
         12 16 20
1
nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
9
Input : limit = 20
Output : 3 4 5
         8 6 10
         5 12 13
         15 8 17
         12 16 20
0

Input : limit = 20
Output : 3 4 5
         8 6 10
         5 12 13
         15 8 17
         12 16 20
6
Input : limit = 20
Output : 3 4 5
         8 6 10
         5 12 13
         15 8 17
         12 16 20
2
Input : limit = 20
Output : 3 4 5
         8 6 10
         5 12 13
         15 8 17
         12 16 20
3int int3int4int5

Input : limit = 20
Output : 3 4 5
         8 6 10
         5 12 13
         15 8 17
         12 16 20
6
nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
1

       a = m2 - n2
       b = 2 * m * n
       c  = m2 + n2
because,
       a2 = m4 + n4 – 2 * m2 * n2
       b2 = 4 * m2 * n2
       c2 = m4 + n4 + 2* m2 * n2
5
Input : limit = 20
Output : 3 4 5
         8 6 10
         5 12 13
         15 8 17
         12 16 20
7

       a = m2 - n2
       b = 2 * m * n
       c  = m2 + n2
because,
       a2 = m4 + n4 – 2 * m2 * n2
       b2 = 4 * m2 * n2
       c2 = m4 + n4 + 2* m2 * n2
5
Input : limit = 20
Output : 3 4 5
         8 6 10
         5 12 13
         15 8 17
         12 16 20
9

       a = m2 - n2
       b = 2 * m * n
       c  = m2 + n2
because,
       a2 = m4 + n4 – 2 * m2 * n2
       b2 = 4 * m2 * n2
       c2 = m4 + n4 + 2* m2 * n2
5
       a = m2 - n2
       b = 2 * m * n
       c  = m2 + n2
because,
       a2 = m4 + n4 – 2 * m2 * n2
       b2 = 4 * m2 * n2
       c2 = m4 + n4 + 2* m2 * n2
1

       a = m2 - n2
       b = 2 * m * n
       c  = m2 + n2
because,
       a2 = m4 + n4 – 2 * m2 * n2
       b2 = 4 * m2 * n2
       c2 = m4 + n4 + 2* m2 * n2
5
       a = m2 - n2
       b = 2 * m * n
       c  = m2 + n2
because,
       a2 = m4 + n4 – 2 * m2 * n2
       b2 = 4 * m2 * n2
       c2 = m4 + n4 + 2* m2 * n2
3
       a = m2 - n2
       b = 2 * m * n
       c  = m2 + n2
because,
       a2 = m4 + n4 – 2 * m2 * n2
       b2 = 4 * m2 * n2
       c2 = m4 + n4 + 2* m2 * n2
4

nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
07
       a = m2 - n2
       b = 2 * m * n
       c  = m2 + n2
because,
       a2 = m4 + n4 – 2 * m2 * n2
       b2 = 4 * m2 * n2
       c2 = m4 + n4 + 2* m2 * n2
6
       a = m2 - n2
       b = 2 * m * n
       c  = m2 + n2
because,
       a2 = m4 + n4 – 2 * m2 * n2
       b2 = 4 * m2 * n2
       c2 = m4 + n4 + 2* m2 * n2
7

       a = m2 - n2
       b = 2 * m * n
       c  = m2 + n2
because,
       a2 = m4 + n4 – 2 * m2 * n2
       b2 = 4 * m2 * n2
       c2 = m4 + n4 + 2* m2 * n2
5
Input : limit = 20
Output : 3 4 5
         8 6 10
         5 12 13
         15 8 17
         12 16 20
55
nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
12

       a = m2 - n2
       b = 2 * m * n
       c  = m2 + n2
because,
       a2 = m4 + n4 – 2 * m2 * n2
       b2 = 4 * m2 * n2
       c2 = m4 + n4 + 2* m2 * n2
5
nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
11
nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
12
nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
13
nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
12
nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
15

Input : limit = 20
Output : 3 4 5
         8 6 10
         5 12 13
         15 8 17
         12 16 20
6
3 4 5
8 6 10
5 12 13
15 8 17
12 16 20
4

Input : limit = 20
Output : 3 4 5
         8 6 10
         5 12 13
         15 8 17
         12 16 20
6
3 4 5
8 6 10
5 12 13
15 8 17
12 16 20
6

nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
2
nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
25 #include 9 void
nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
28

nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
2
3 4 5
8 6 10
5 12 13
15 8 17
12 16 20
4

nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
2
nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
1

nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
2
nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
1

Input : limit = 20
Output : 3 4 5
         8 6 10
         5 12 13
         15 8 17
         12 16 20
1int
nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
33
nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
34
       a = m2 - n2
       b = 2 * m * n
       c  = m2 + n2
because,
       a2 = m4 + n4 – 2 * m2 * n2
       b2 = 4 * m2 * n2
       c2 = m4 + n4 + 2* m2 * n2
7

Input : limit = 20
Output : 3 4 5
         8 6 10
         5 12 13
         15 8 17
         12 16 20
1nums7

nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
2
3 4 5
8 6 10
5 12 13
15 8 17
12 16 20
4

3 4 5
8 6 10
5 12 13
15 8 17
12 16 20
4

nums.sort() # now nums[2] is the largest element if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)): print "It is" # or whatever # no more checks needed 41 nums.sort() # now nums[2] is the largest element if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)): print "It is" # or whatever # no more checks needed 42

Input : limit = 20
Output : 3 4 5
         8 6 10
         5 12 13
         15 8 17
         12 16 20
84

nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
2
nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
44
nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
45 void9
nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
47pythagoreanTriplets(4

nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
1

nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
2
Input : limit = 20
Output : 3 4 5
         8 6 10
         5 12 13
         15 8 17
         12 16 20
91
       a = m2 - n2
       b = 2 * m * n
       c  = m2 + n2
because,
       a2 = m4 + n4 – 2 * m2 * n2
       b2 = 4 * m2 * n2
       c2 = m4 + n4 + 2* m2 * n2
7

nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
2
Input : limit = 20
Output : 3 4 5
         8 6 10
         5 12 13
         15 8 17
         12 16 20
94
       a = m2 - n2
       b = 2 * m * n
       c  = m2 + n2
because,
       a2 = m4 + n4 – 2 * m2 * n2
       b2 = 4 * m2 * n2
       c2 = m4 + n4 + 2* m2 * n2
7

nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
2
Input : limit = 20
Output : 3 4 5
         8 6 10
         5 12 13
         15 8 17
         12 16 20
97
Input : limit = 20
Output : 3 4 5
         8 6 10
         5 12 13
         15 8 17
         12 16 20
98

nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
2
nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
9
nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
51

Input : limit = 20
Output : 3 4 5
         8 6 10
         5 12 13
         15 8 17
         12 16 20
1
Input : limit = 20
Output : 3 4 5
         8 6 10
         5 12 13
         15 8 17
         12 16 20
2
nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
54
nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
55
nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
56
Input : limit = 20
Output : 3 4 5
         8 6 10
         5 12 13
         15 8 17
         12 16 20
3int4
nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
59

nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
2
nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
1

Input : limit = 20
Output : 3 4 5
         8 6 10
         5 12 13
         15 8 17
         12 16 20
6
nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
61
nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
45
nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
63
nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
64
nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
63
nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
66
nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
54__

Input : limit = 20
Output : 3 4 5
         8 6 10
         5 12 13
         15 8 17
         12 16 20
1
nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
1

Input : limit = 20
Output : 3 4 5
         8 6 10
         5 12 13
         15 8 17
         12 16 20
6
nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
71
nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
45 pythagoreanTriplets(4
nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
64
nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
63
nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
64
nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
69

Input : limit = 20
Output : 3 4 5
         8 6 10
         5 12 13
         15 8 17
         12 16 20
6
nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
79
nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
45
nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
63
nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
64
nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
63
nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
84
nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
54__

Input : limit = 20
Output : 3 4 5
         8 6 10
         5 12 13
         15 8 17
         12 16 20
6
       a = m2 - n2
       b = 2 * m * n
       c  = m2 + n2
because,
       a2 = m4 + n4 – 2 * m2 * n2
       b2 = 4 * m2 * n2
       c2 = m4 + n4 + 2* m2 * n2
3
nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
90

Input : limit = 20
Output : 3 4 5
         8 6 10
         5 12 13
         15 8 17
         12 16 20
1
nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
63
nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
45
nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
63
nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
84 int4

       a = m2 - n2
       b = 2 * m * n
       c  = m2 + n2
because,
       a2 = m4 + n4 – 2 * m2 * n2
       b2 = 4 * m2 * n2
       c2 = m4 + n4 + 2* m2 * n2
3
Input : limit = 20
Output : 3 4 5
         8 6 10
         5 12 13
         15 8 17
         12 16 20
03
nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
45
nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
45
Input : limit = 20
Output : 3 4 5
         8 6 10
         5 12 13
         15 8 17
         12 16 20
06
Input : limit = 20
Output : 3 4 5
         8 6 10
         5 12 13
         15 8 17
         12 16 20
07

nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
2
Input : limit = 20
Output : 3 4 5
         8 6 10
         5 12 13
         15 8 17
         12 16 20
09
nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
45
nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
34

Input : limit = 20
Output : 3 4 5
         8 6 10
         5 12 13
         15 8 17
         12 16 20
1
3 4 5
8 6 10
5 12 13
15 8 17
12 16 20
4

Input : limit = 20
Output : 3 4 5
         8 6 10
         5 12 13
         15 8 17
         12 16 20
1
       a = m2 - n2
       b = 2 * m * n
       c  = m2 + n2
because,
       a2 = m4 + n4 – 2 * m2 * n2
       b2 = 4 * m2 * n2
       c2 = m4 + n4 + 2* m2 * n2
00
       a = m2 - n2
       b = 2 * m * n
       c  = m2 + n2
because,
       a2 = m4 + n4 – 2 * m2 * n2
       b2 = 4 * m2 * n2
       c2 = m4 + n4 + 2* m2 * n2
81

nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
2
3 4 5
8 6 10
5 12 13
15 8 17
12 16 20
4

3 4 5
8 6 10
5 12 13
15 8 17
12 16 20
4

Input : limit = 20
Output : 3 4 5
         8 6 10
         5 12 13
         15 8 17
         12 16 20
14
Input : limit = 20
Output : 3 4 5
         8 6 10
         5 12 13
         15 8 17
         12 16 20
15

nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
2pythagoreanTriplets(
Input : limit = 20
Output : 3 4 5
         8 6 10
         5 12 13
         15 8 17
         12 16 20
87
       a = m2 - n2
       b = 2 * m * n
       c  = m2 + n2
because,
       a2 = m4 + n4 – 2 * m2 * n2
       b2 = 4 * m2 * n2
       c2 = m4 + n4 + 2* m2 * n2
91

       a = m2 - n2
       b = 2 * m * n
       c  = m2 + n2
because,
       a2 = m4 + n4 – 2 * m2 * n2
       b2 = 4 * m2 * n2
       c2 = m4 + n4 + 2* m2 * n2
92

Input : limit = 20 Output : 3 4 5 8 6 10 5 12 13 15 8 17 12 16 201int nums.sort() # now nums[2] is the largest element if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)): print "It is" # or whatever # no more checks needed 4

       a = m2 - n2
       b = 2 * m * n
       c  = m2 + n2
because,
       a2 = m4 + n4 – 2 * m2 * n2
       b2 = 4 * m2 * n2
       c2 = m4 + n4 + 2* m2 * n2
93

Input : limit = 20
Output : 3 4 5
         8 6 10
         5 12 13
         15 8 17
         12 16 20
1int
nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
7

nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
1

nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
2
       a = m2 - n2
       b = 2 * m * n
       c  = m2 + n2
because,
       a2 = m4 + n4 – 2 * m2 * n2
       b2 = 4 * m2 * n2
       c2 = m4 + n4 + 2* m2 * n2
98

nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
2
3 4 5
8 6 10
5 12 13
15 8 17
12 16 20
00

Input : limit = 20
Output : 3 4 5
         8 6 10
         5 12 13
         15 8 17
         12 16 20
6
Input : limit = 20
Output : 3 4 5
         8 6 10
         5 12 13
         15 8 17
         12 16 20
2
Input : limit = 20
Output : 3 4 5
         8 6 10
         5 12 13
         15 8 17
         12 16 20
3int
Input : limit = 20
Output : 3 4 5
         8 6 10
         5 12 13
         15 8 17
         12 16 20
39

nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
2
nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
1

Input : limit = 20
Output : 3 4 5
         8 6 10
         5 12 13
         15 8 17
         12 16 20
1
Input : limit = 20
Output : 3 4 5
         8 6 10
         5 12 13
         15 8 17
         12 16 20
2
3 4 5
8 6 10
5 12 13
15 8 17
12 16 20
08

Input : limit = 20
Output : 3 4 5
         8 6 10
         5 12 13
         15 8 17
         12 16 20
1
nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
1

Input : limit = 20
Output : 3 4 5
         8 6 10
         5 12 13
         15 8 17
         12 16 20
6
Input : limit = 20
Output : 3 4 5
         8 6 10
         5 12 13
         15 8 17
         12 16 20
7

Input : limit = 20
Output : 3 4 5
         8 6 10
         5 12 13
         15 8 17
         12 16 20
6
Input : limit = 20
Output : 3 4 5
         8 6 10
         5 12 13
         15 8 17
         12 16 20
9

Input : limit = 20
Output : 3 4 5
         8 6 10
         5 12 13
         15 8 17
         12 16 20
6
       a = m2 - n2
       b = 2 * m * n
       c  = m2 + n2
because,
       a2 = m4 + n4 – 2 * m2 * n2
       b2 = 4 * m2 * n2
       c2 = m4 + n4 + 2* m2 * n2
1

Input : limit = 20
Output : 3 4 5
         8 6 10
         5 12 13
         15 8 17
         12 16 20
6
       a = m2 - n2
       b = 2 * m * n
       c  = m2 + n2
because,
       a2 = m4 + n4 – 2 * m2 * n2
       b2 = 4 * m2 * n2
       c2 = m4 + n4 + 2* m2 * n2
3
       a = m2 - n2
       b = 2 * m * n
       c  = m2 + n2
because,
       a2 = m4 + n4 – 2 * m2 * n2
       b2 = 4 * m2 * n2
       c2 = m4 + n4 + 2* m2 * n2
4

       a = m2 - n2
       b = 2 * m * n
       c  = m2 + n2
because,
       a2 = m4 + n4 – 2 * m2 * n2
       b2 = 4 * m2 * n2
       c2 = m4 + n4 + 2* m2 * n2
5
       a = m2 - n2
       b = 2 * m * n
       c  = m2 + n2
because,
       a2 = m4 + n4 – 2 * m2 * n2
       b2 = 4 * m2 * n2
       c2 = m4 + n4 + 2* m2 * n2
6
       a = m2 - n2
       b = 2 * m * n
       c  = m2 + n2
because,
       a2 = m4 + n4 – 2 * m2 * n2
       b2 = 4 * m2 * n2
       c2 = m4 + n4 + 2* m2 * n2
7

Input : limit = 20
Output : 3 4 5
         8 6 10
         5 12 13
         15 8 17
         12 16 20
1int
nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
33
nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
34
       a = m2 - n2
       b = 2 * m * n
       c  = m2 + n2
because,
       a2 = m4 + n4 – 2 * m2 * n2
       b2 = 4 * m2 * n2
       c2 = m4 + n4 + 2* m2 * n2
7

nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
41
nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
42

Input : limit = 20
Output : 3 4 5
         8 6 10
         5 12 13
         15 8 17
         12 16 20
1
3 4 5
8 6 10
5 12 13
15 8 17
12 16 20
4

Input : limit = 20
Output : 3 4 5
         8 6 10
         5 12 13
         15 8 17
         12 16 20
1
3 4 5
8 6 10
5 12 13
15 8 17
12 16 20
6

nums.sort()  # now nums[2] is the largest element
if ((nums[0] ** 2) + (nums[1] ** 2) == (nums[2] ** 2)):
    print "It is"  # or whatever
# no more checks needed
2
3 4 5
8 6 10
5 12 13
15 8 17
12 16 20
4

3 4 5
8 6 10
5 12 13
15 8 17
12 16 20
4

3 4 5
8 6 10
5 12 13
15 8 17
12 16 20
39

nums7

3 4 5
8 6 10
5 12 13
15 8 17
12 16 20
41

Đầu ra

3 4 5
8 6 10
5 12 13
15 8 17
12 16 20

Độ phức tạp về thời gian của phương pháp này là O (k) trong đó k là số lượng ba lần được in cho một giới hạn nhất định (chúng tôi chỉ lặp cho M và N và mọi lần lặp lại đều in một bộ ba) biến of this approach is O(k) where k is number of triplets printed for a given limit (We iterate for m and n only and every iteration prints a triplet)
Auxiliary space: O(1) as it is using constant space for variables

Lưu ý: Phương pháp trên không tạo ra tất cả các bộ ba nhỏ hơn một giới hạn nhất định. Ví dụ: 9 12 12 15, đó là bộ ba hợp lệ không được in bằng phương pháp trên. Cảm ơn Sid Agrawal đã chỉ ra điều này. The above method doesn’t generate all triplets smaller than a given limit. For example “9 12 15” which is a valid triplet is not printed by above method. Thanks to Sid Agrawal for pointing this out. 
References: 
https://en.wikipedia.org/wiki/Formulas_for_generating_Pythagorean_triples

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Làm thế nào để bạn kiểm tra xem đó có phải là bộ ba Pythagore không?

Đưa ra một mảng các số nguyên, hãy viết một hàm trả về đúng nếu có một bộ ba (A, B, C) thỏa mãn A2 + B2 = C2.Có một bộ ba Pythagore (3, 4, 5).Không có bộ ba Pythagore.write a function that returns true if there is a triplet (a, b, c) that satisfies a2 + b2 = c2. There is a Pythagorean triplet (3, 4, 5). There is no Pythagorean triplet.

Triplet Python Pythagore là gì?

Một bộ ba Pythagore là một tập hợp ba số tự nhiên, {a, b, c}, trong đó, a² + b² = c² và như vậy, a a set of three natural numbers, {a, b, c}, for which, a² + b² = c² and such that, a < b < c. For example, 3² + 4² = 9 + 16 = 25 = 5².

Làm thế nào để bạn tìm thấy bộ ba Pythagore của một số?

Làm thế nào để tạo thành một bộ ba Pythagore..
Nếu số là lẻ: vuông số n và sau đó chia cho nó 2. lấy số nguyên ngay trước và sau số đó, tức là (n2/2 -0.5) và (n2/2 +0.5).....
Nếu số chẵn: lấy một nửa số N đó và sau đó vuông nó.Triplet Pythagore = N, (n/2) 2-1, (n/2) 2+1 ..