Factorial Zeros: Count Trailing Zeros in n! (CTCI 16.5)

TL;DR

• The Problem: CTCI problem 16.5 technical mechanics.
• The Approach: CTCI problem 16.5: count trailing zeros in n! by summing factors of 5 in O(log n) time.
• Complexity: Optimal Time and Memory bounds.

This article provides a clear breakdown of CTCI problem 16.5.

1. Context and Problem Statement

CTCI problem 16.5: count trailing zeros in n! by summing factors of 5 in O(log n) time.

2. Technical Code & Mechanics

public static int countFactZeros(int num) {
    int count = 0;
    if (num < 0) return -1;
    for (int i = 5; num / i > 0; i *= 5) {
        count += num / i;
    }
    return count;
}

3. Key Takeaways and Edge Cases

Always test boundary conditions and invalid input states.