假的數學遊戲

題目如圖  看到階乘馬上想到斯大林公式       

防止溢出對兩邊取對數 

代碼如下

import math
def solve(x):
    l, r = 1, int(1e12)
    aim = x * math.log(x)
    mid = 0
    while (l < r):
        mid = (l + r) // 2
        value = const_ + mid * (math.log(mid) - 1) + 0.5 * math.log(mid)
        #print(l,r)
        #print(value,aim)
        if (value < aim):
            l = mid + 1
        else:
            r = mid

    return r

pi = 3.1415926
const_ = 0.5 * math.log(2 * pi)
x = int(input())
print(solve(x))