Split With Minimum Sum

Split With Minimum Sum

What is this problem about?

The Split With Minimum Sum coding problem gives you a positive integer $num$. You are asked to split the digits of $num$ into two new integers, $num1$ and $num2$, such that each digit of $num$ is used exactly once. The goal is to minimize the sum of $num1$ and $num2$.

Why is this asked in interviews?

This "Easy" problem is common at Amazon and Google. it tests your ability to apply a Greedy interview pattern and basic Math properties. The key insight is understanding how place value (units, tens, hundreds) affects the final sum and how to distribute digits to keep the most significant digits as small as possible.

Algorithmic pattern used

The pattern is Sorting and Greedy. To minimize the sum, you should use the smallest digits in the most significant positions (like the hundreds or tens place). You first extract all digits from $num$ and sort them in non-decreasing order. Then, you distribute the sorted digits one by one, alternating between $num1$ and $num2$. This ensures that both numbers have the smallest possible digits in their highest place values.

Example explanation (use your own example)

Suppose $num = 4325$.

1. Sort the digits: [2, 3, 4, 5].
2. Distribute them:
   • Digit 2 goes to $num1 = 2$.
   • Digit 3 goes to $num2 = 3$.
   • Digit 4 goes to $num1 = 24$.
   • Digit 5 goes to $num2 = 35$.
3. The sum is $24 + 35 = 59$. This is the minimum possible sum you can get from these digits.

Common mistakes candidates make

• Not sorting: Trying to pair digits without a clear strategy.
• Leading zeros: While the problem usually uses positive integers, some candidates worry about leading zeros unnecessarily (since $num1$ and $num2$ don't have to use all digits if they were zeros).
• Incorrect distribution: Using all the smallest digits for $num1$ and the largest for $num2$ (e.g., 23 and 45), which is usually less optimal than alternating.
• String conversion overhead: While common, converting to string and back to int repeatedly can be slower than using direct math (modulo and division).

Interview preparation tip

For Math and Greedy problems, always ask yourself: "What is the most 'expensive' part of the result, and how can I minimize it?" In this case, the most expensive part is the highest place value.