题解 | #将真分数分解为埃及分数#

import itertools

while True:
    try: 
        a, b = map(int, input().split('/'))
        v = 0
        nums = []

        for n in itertools.count(start=2):
            if a/b > v+1/n:
                v += 1/n
                nums.append(f'1/{n}')
            elif a/b == v+1/n:
                nums.append(f'1/{n}')
                break

        print('+'.join(nums))

    except: 
        break


# 1. if a/b == v + 1/n, break and output result
# 2. if a/b > v + 1/n, append k to num
# 3. if a/b < v+1/n, keep looping but skip n, i.e. dont append current n to num.

一种贪心算法的思路，每次都加入求和后不超过真分数的最大埃及分数，然而超时了