Algorithmic Challenge: Writing a Code to Increment an Array of Digits

Incrementing an Array of Digits: Acing Your FAANG PM Interview

Product management interviews at top tech companies like FAANG often include technical questions that test a candidate’s analytical and problem-solving abilities. For PM candidates who may come across coding questions, this blog post delves into the practical question: “Write a code to increment an array of digits (0 to 9).” Here we will break down how to approach such a coding challenge strategically, even if you are not a seasoned coder, but aim to impress your interviewers with a logical and effective solution.

Detailed Guide on Framework Application

To address this coding problem, let’s rely on a systematic approach to break down the steps needed to construct an algorithmic solution. We’ll be using a simple, yet robust, problem-solving framework that includes understanding the problem, outlining a step-by-step algorithm, and then coding it in a popular programming language like Python.

1. Understand the Problem: Clarify the problem statement and define the expected behavior of the code. You’re supposed to add one to a number represented by an array of single-digit integers.
2. Outline the Algorithm:
   • Start from the last digit of the array.
   • Add one to the last digit and handle the carry over if it exceeds 9.
   • Propagate the carry over towards the more significant digits if necessary.
   • If you have carry over at the most significant digit, add a new digit at the beginning of the array.
3. Code the Solution: Commit your algorithm to code using a programming language. Below is a Python example based on the outlined algorithm.

Here’s a simple Python code snippet:

  def increment_array(digits):
    n = len(digits)
    # Start with the least significant digit
    for i in range(n-1, -1, -1):
      if digits[i] < 9:
        digits[i] += 1
        return digits
      digits[i] = 0 # If all digits were 9, we got here since we didn't hit the return statement in the loop
      # We need to add an additional digit
      return [1] + digits
  

This code assumes that the input is a valid list of digits, and it handles the increment operation as outlined.

During the interview, when communicating your thought process and solution, comment on each step you take when crafting your algorithm and explain why that step is necessary. Also, discuss test cases you would consider, from the simplest (e.g., [1, 2, 3] which becomes [1, 2, 4]) to the most complex (e.g., [9, 9, 9] which becomes [1, 0, 0, 0]), to verify that your code handles all potential scenarios.

Conclusion

Writing a code to increment an array of digits is a common technical interview question that tests your ability to think algorithmically and solve problems in a clear, concise manner. Breaking down the challenge into understandable parts and coding a solution is central to demonstrating these critical PM skills. Practice coding and articulating your approach regularly so that you can confidently tackle similar technical questions in your FAANG interviews. Good luck on your journey!