Python世界：力扣题633，平方数之和，中等

news2024/11/14 0:32:58

Python世界：力扣题633，平方数之和，中等

- 任务背景
- 思路分析
- 代码实现
- 测试套件
- 本文小结

任务背景

问题来自力扣题目633. Sum of Square Numbers，大意如下：

Given a non-negative integer c, decide whether there’re two integers a and b such that a^2 + b^2 = c.

翻译下，需求是：对给定数字c，确定是否有两个整数满足a^2+b^2=c

思路分析

二分法思路

默认a,b均为非负，且b不小于a
在0-sqrt©之间遍历a，直到a=b相遇或a>b跳出循环
cs = sqrt©
此移动方式不通
- 若b=sqrt(c-a^2) 圆整后，重加回满足目标，且b不小于a中断
- 若b<a，a收缩为下界
- 若b>a，a收缩为上界
换为low/high双指针左右移动
- 将0-cs之间的数平方和组合罗列为一种有序组合
- 初始位：t = low^2+high2，是在有序组合的中间
- 若t > c，则缩小high
- 若t < c，则增大low
- 与纯二分区别在于，不仅单一mid在移动

代码实现

import math

class Solution(object):
    def judgeSquareSum(self, c):
        """
        :type c: int
        :rtype: bool
        """
        res = False
        cs = int(math.sqrt(c)) + 1
        low = 0
        high = cs
        while (low <= high): # two pointer
            t = low**2 + high**2
            if (t < c):
                low += 1
            elif (t > c):
                high -= 1
            else:
                return True
        return res

测试套件

单例测试demo：

# one case test
c = 5 # 1+4
c = 4 # 0+4
c = 3 # false
c = 13 # 4+9
c = 12 # false
c = 169 # 12^2+5^2

sol = Solution()
res = sol.judgeSquareSum(c)
print(res)

测试套demo：

# 导入单元测试
import unittest


def test_base(self, c, ret):
    sol = Solution()
    res = sol.judgeSquareSum(c)
    self.assertEqual(res, ret)    


# 编写测试套
class TestSol(unittest.TestCase):
    # 不在
    def test_special1(self):
        c = 3
        ret = False
        test_base(self, c, ret)

    # 下边界
    def test_special2(self):
        c = 0
        ret = True
        test_base(self, c, ret)

    # 上边界
    def test_special3(self):
        c = 2**31 - 1
        ret = False
        test_base(self, c, ret)

    def test_common1(self):
        c = 5
        ret = True
        test_base(self, c, ret)

    def test_common2(self):
        c = 13
        ret = True
        test_base(self, c, ret)

    def test_common3(self):
        c = 169
        ret = True
        test_base(self, c, ret)


# 含测试套版本主调
if __name__ == '__main__':
    print('start!')
    unittest.main() # 启动单元测试
    print('done!')