Count the Digits That Divide a Number - Video Solutions

Problem Overview: Given an integer num, count how many of its digits evenly divide the number. For each digit d in the number, check if num % d == 0. Ignore digits that are zero since division by zero is undefined.

Approach 1: Iterative Check Using Modulus (O(d) time, O(1) space)

This approach works directly with the number using basic math operations. Repeatedly extract the last digit using digit = temp % 10, then remove it with integer division temp /= 10. For each extracted digit, check if it is non-zero and whether num % digit == 0. If the condition holds, increment the count.

The key insight is that you only need to examine each digit once. Modulus operations provide both digit extraction and divisibility checks efficiently. Since the number of digits is d = log10(num), the loop runs d times. This keeps the time complexity O(d) and space complexity O(1). This method is preferred when you want minimal memory usage and direct arithmetic operations.

Approach 2: Leveraging String Conversion (O(d) time, O(d) space)

Instead of repeatedly extracting digits mathematically, convert the integer into a string. Iterate over each character, convert it back to an integer digit, and check whether it divides the original number. Skip characters representing 0 to avoid division errors.

This approach trades arithmetic digit extraction for easier iteration using string traversal. The divisibility check still uses the modulo operation from math. Time complexity remains O(d) because each digit is processed once. Space complexity becomes O(d) due to the temporary string representation.

Recommended for interviews: The iterative modulus approach is the expected solution. It demonstrates understanding of digit extraction, modulo arithmetic, and constant-space iteration. The string approach is perfectly valid but slightly less optimal in space. Showing the arithmetic solution first signals strong fundamentals with number manipulation.