讲两道常考的阶乘算法题

172. 阶乘后的零 https://leetcode.cn/problems/factorial-trailing-zeroes

172. Factorial Trailing Zeroes https://leetcode.com/problems/factorial-trailing-zeroes

793. 阶乘函数后 K 个零 https://leetcode.cn/problems/preimage-size-of-factorial-zeroes-function

793. Preimage Size of Factorial Zeroes Function https://leetcode.com/problems/preimage-size-of-factorial-zeroes-function

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读完本文，你不仅学会了算法套路，还可以顺便解决如下题目：

LeetCode	Difficulty
172. Factorial Trailing Zeroes	🟠
793. Preimage Size of Factorial Zeroes Function	🔴

Prerequisites

Before reading this article, you need to learn:

• Binary Search Framework Explained

You often encounter factorial-related questions in written exams. Today, we'll discuss two common questions:

1. Given a non-negative integer n, calculate how many trailing zeros are in the factorial result n!.

This is also LeetCode problem #172 "Factorial Trailing Zeroes." For example, if the input is n = 5, the algorithm returns 1 because 5! = 120, which has one trailing zero.

The function signature is:

int trailingZeroes(int n);

2. Given a non-negative integer K, calculate how many integers n exist such that the factorial result n! has exactly K trailing zeros.

This is also LeetCode problem #793 "Preimage Size of Factorial Zeroes Function." For example, if the input is K = 1, the algorithm returns 5 because the factorials 5!, 6!, 7!, 8!, 9! each have exactly one trailing zero, meaning there are 5 values of n that satisfy the condition.

The function signature is:

int preimageSizeFZF(int K);

I've grouped these two problems together because they share common characteristics. Let's analyze them one by one.

172. Factorial Trailing Zeroes

793. Kth Number with K Trailing Zeros

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