Golden interview programmers - 16.05 factorial face questions mantissa (factor 5)

1. Topic

Design an algorithm to calculate n factorial of the number of trailing zeros.

示例 1:
输入: 3
输出: 0
解释: 3! = 6, 尾数中没有零。

示例 2:
输入: 5
输出: 1
解释: 5! = 120, 尾数中有 1 个零.
说明: 你算法的时间复杂度应为 O(log n) 。

Source: stay button (LeetCode)
link: https: //leetcode-cn.com/problems/factorial-zeros-lcci
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2. Problem Solving

• N see how many there are factors of 5
• Source tail 0 is 10, that is 5x an even number, the even better than over five, so you can find the number of 5
• Note also that 25 = 5x5, there are two 5,125 = 5x5x5, there are three 5 .. . .

class Solution {
public:
    int trailingZeroes(int n) {
    	int count = 0;
    	while(n)
    	{
    		count += n/5;
    		n /= 5;
    	}
    	return count;
    }
};