python算法（枚举法）：如果a + b + c = 1000(a, b, c均为非负整数)，求满足a^2 + b^2 = c^2的所有可能的值。

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本文介绍了一种寻找满足勾股定理a^2+b^2=c^2且a+b+c=1000的所有非负整数解的方法。通过优化算法，减少不必要的计算，实现了快速查找。

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如果a + b + c = 1000(a, b, c均为非负整数)，求满足a^2 + b^2 = c^2的所有可能的值。

import time

def method():
    time_start = time.time()
    for a in range(1001):
        for b in range(1001):
            for c in range(1001):
                if a * a + b * b == c * c and a + b + c == 1000:
                    print('a = %d, b = %d, c = %d' % (a, b, c))
    time_end = time.time()
    print('总共耗时：%d' % (time_end - time_start))


def method_():
    time_start = time.time()
    for a in range(1001):
        for b in range(1001 - a):
            for c in range(1001):
                if a * a + b * b == c * c and a + b + c == 1000:
                    print('a = %d, b = %d, c = %d' % (a, b, c))
    time_end = time.time()
    print('总共耗时：%d' % (time_end - time_start))

def method_optimized():
    time_start = time.time()
    for a in range(1001):
        for b in range(1001):
            c = 1000 - a -b   # 减少时间复杂度
            if a * a + b * b == c * c:
                print('a = %d, b = %d, c = %d' % (a, b, c))
    time_end = time.time()
    print('总共耗时：%d' % (time_end - time_start))


if __name__ == '__main__':
    method()
    method_()
	method_optimized()