Two Classic Factorial Problems on LeetCode
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| LeetCode | Difficulty |
|---|---|
| 172. Factorial Trailing Zeroes | 🟠 |
| 793. Preimage Size of Factorial Zeroes Function | 🔴 |
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.