Some positive integers can be expressed as a sum of two squares of some positive integers greater than zero. For example, 74 = 49 + 25 = 7^2 + 5^2. This function should find and return a tuple of two positive integers whose squares together add up to n, or return None if the parameter n cannot be broken into a sum of two squares. To facilitate the automated testing, the returned tuple must present the larger of its two numbers first. Furthermore, if some integer can be broken down to a sum of squares in several ways, return the breakdown that maximizes the larger number. For example, the number 85 allows two such representations 7^2 + 6^2 and 9^2 + 2^2 , of which this function must return (9, 2). The technique of two approaching indices that start from the beginning and end of a sequence, respectively, and approach each other until they meet somewhere is directly applicable to this problem. In this problem, these indices crawl towards each other only one small step at the time, whereas in binary search, one index would jump halfway towards the other one in every round. n Expected result 1 None 2 (1, 1) 50 (7, 1) 8 (2, 2) 11 None 123**2 + 456**2 (456, 123) 55555**2 + 66666**2 (77235, 39566)
Sum of two squares
def sum_of_two_squares(n):
Some positive integers can be expressed as a sum of two squares of some positive integers greater than zero. For example, 74 = 49 + 25 = 7^2 + 5^2. This function should find and return a tuple of two positive integers whose squares together add up to n, or return None if the parameter n cannot be broken into a sum of two squares.
To facilitate the automated testing, the returned tuple must present the larger of its two numbers first. Furthermore, if some integer can be broken down to a sum of squares in several ways, return the breakdown that maximizes the larger number. For example, the number 85 allows two such
representations 7^2 + 6^2 and 9^2 + 2^2 , of which this function must return (9, 2).
The technique of two approaching indices that start from the beginning and end of a sequence, respectively, and approach each other until they meet somewhere is directly applicable to this problem. In this problem,
these indices crawl towards each other only one small step at the time, whereas in binary search, one index would jump halfway towards the other one in every round.
| n | Expected result |
| 1 | None |
| 2 | (1, 1) |
| 50 | (7, 1) |
| 8 | (2, 2) |
| 11 | None |
| 123**2 + 456**2 | (456, 123) |
| 55555**2 + 66666**2 | (77235, 39566) |
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