LeetCode Weekly Contest 74 793. Preimage Size of Factorial Zeroes Function【二分】

793. Preimage Size of Factorial Zeroes Function

Let f(x) be the number of zeroes at the end of x!. (Recall that x! = 1 * 2 * 3 * … * x, and by convention, 0! = 1.)

For example, f(3) = 0 because 3! = 6 has no zeroes at the end, while f(11) = 2 because 11! = 39916800 has 2 zeroes at the end. Given K, find how many non-negative integers x have the property that f(x) = K.

Example 1:

Input: K = 0

Output: 5

Explanation: 0!, 1!, 2!, 3!, and 4! end with K = 0 zeroes.

Example 2:

Input: K = 5

Output: 0

Explanation: There is no x such that x! ends in K = 5 zeroes.

Note:

K will be an integer in the range [0, 10^9].

题意： 问你有多少个数的阶乘后面有k个零

分析： 首先我们先反过来求，当知道一个数，求有多少零，我们只需不断除5即可，因为每个我们都可以分解一个2和5，从而得到一个零，然后我们二分这个答案，我们找下界，然后我们再查找k+1的下届，中间的就是答案

参考代码

class Solution {
public:

bool check(long long m, int K) {
long long res = 0;
while (m) {
res += m / 5;
m /= 5;
}
if(res >= K) {
return true;
} return false;
}

int f(int K) {
long long l = 0;
long long r = 1000000000000000000LL;
long long res;
while (l <= r) {
long long mid = l + r >> 1;
if(check(mid,K)) {
res = mid;
r = mid - 1;
} else l = mid + 1;
}
return res;
}

int preimageSizeFZF(int K) {
long long l = f(K);
long long r = f(K + 1);
return r - l;
}
};