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K zeros after leetcode factorial function

2022-04-23 01:38:00 【Programmed ape no hair loss 2】

f(x) yes x! At the end is 0 The number of . Think about it x! = 1 * 2 * 3 * … * x, And 0! = 1 .

for example , f(3) = 0 , because 3! = 6 There is no 0 ; and f(11) = 2 , because 11!= 39916800 Terminal 2 individual 0 .
Given k, Find out if the return can meet f(x) = k Non-negative integer x The number of .

Example 1：

Input ：k = 0
Output ：5
explain ：0!, 1!, 2!, 3!, and 4! All conform to k = 0 Conditions .
Example 2：

Input ：k = 5
Output ：0
explain ： There is no such match x!, accord with k = 5 Conditions .
Example 3:

Input : k = 3
Output : 5

java Code ：

class Solution {
    public int preimageSizeFZF(long K) {
        long lo = K, hi = 10*K + 1;
        while (lo < hi) {
            long mi = lo + (hi - lo) / 2;
            long zmi = zeta(mi);
            if (zmi == K) return 5;
            else if (zmi < K) lo = mi + 1;
            else hi = mi;
        }
        return 0;
    }

    public long zeta(long x) {
        if (x == 0) return 0;
        return x/5 + zeta(x/5);
    }
}

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K zeros after leetcode factorial function

java Code ：

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