Convert Integer to the Sum of Two No-Zero Integers

Convert Integer to the Sum of Two No-Zero Integers

What is this problem about?

The Convert Integer to the Sum of Two No-Zero Integers interview question asks you to take a positive integer n and find any two positive integers a and b such that a + b = n and neither a nor b contains the digit '0' in its decimal representation.

Why is this asked in interviews?

This Convert Integer to the Sum of Two No-Zero Integers coding problem is a simple simulation and verification task common at Microsoft and Hudson River Trading. It tests basic arithmetic and the ability to write a "check" helper function to validate specific properties of a number.

Algorithmic pattern used

This follows the Math interview pattern, specifically a Linear Search.

1. Start a loop with a = 1.
2. Calculate b = n - a.
3. Check if a contains any '0' digit.
4. Check if b contains any '0' digit.
5. If both are "No-Zero" integers, return [a, b].
6. Otherwise, increment a and repeat.

Example explanation

Input: n = 11

1. a=1, b=10. 10 contains a 0.
2. a=2, b=9. Both 2 and 9 are "No-Zero." Result: [2, 9].

Input: n = 101

1. a=1, b=100. (Invalid)
2. a=2, b=99. Both 2 and 99 are "No-Zero." Result: [2, 99].

Common mistakes candidates make

• Inefficient Check: Converting the number to a string in every iteration just to check for the character '0'. Using mathematical digit extraction (% 10 and / 10) is generally more idiomatic for math problems.
• Infinite loop: Not starting a at 1 or failing to realize that a solution is guaranteed to exist.
• Boundary conditions: Not checking both a and b for the zero digit.

Interview preparation tip

Always write clean helper functions. A function like isNoZero(num) makes your main loop much more readable and easier to debug during a live coding session.