LeetCode-in-Java

793. Preimage Size of Factorial Zeroes Function

Hard

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 two zeroes at the end.

Given an integer k, return the number of 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.

Example 3:

Input: k = 3

Output: 5

Constraints:

• 0 <= k <= 109

Solution

public class Solution {
    public int preimageSizeFZF(int k) {
        long left = 0;
        long right = 5L * (k + 1);
        while (left < right - 1) {
            long mid = left + (right - left) / 2;
            int cnt = countZeros(mid);
            if (cnt == k) {
                return 5;
            } else if (cnt < k) {
                left = mid;
            } else {
                right = mid;
            }
        }
        return countZeros(left) == k || countZeros(right) == k ? 5 : 0;
    }

    private int countZeros(long n) {
        long rst = 0;
        while (n > 0) {
            rst += n / 5;
            n /= 5;
        }
        return (int) rst;
    }
}

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