793. Preimage Size of Factorial Zeroes Function

LWC 74: 793. Preimage Size of Factorial Zeroes Function

Problem:

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].

思路： 考虑125!有多少个0？实际上是求1 * 2 * 3 * … * 125 有多少个5。

Java版本：