Compute Decimal Representation - Solution & Explanation

Problem Overview: Given an integer, compute its decimal representation as a sequence of digits. Instead of relying on built-in string conversion, you explicitly derive each digit using basic arithmetic operations.

Approach 1: Simulation with Division and Modulo (O(d) time, O(d) space)

The straightforward method simulates how humans extract digits from a number. Repeatedly apply num % 10 to get the least significant digit, append it to a result container, then update the number using num // 10. Continue until the value becomes zero. Because digits are collected from least significant to most significant, reverse the result at the end to restore the correct order.

This method directly models decimal decomposition. Each iteration isolates one digit, so the loop runs once per digit in the number. The number of iterations is proportional to the digit count d, giving O(d) time complexity. The output array stores all digits, so space complexity is also O(d). The approach relies only on arithmetic operations and a dynamic array, which makes it predictable and language‑agnostic.

This technique appears frequently in problems involving manual number processing, base conversions, and digit manipulation. Understanding it helps with tasks like reversing numbers, checking palindromes, or implementing custom numeric formats using math operations and array storage.

Recommended for interviews: The simulation approach is exactly what interviewers expect. It demonstrates that you understand how decimal numbers are constructed from digits using division and modulo. Even though many languages provide built‑in conversions, implementing the digit extraction manually shows control over fundamental math operations and array manipulation.