Minimum Addition to Make Integer Beautiful

Minimum Addition to Make Integer Beautiful

What is this problem about?

The Minimum Addition to Make Integer Beautiful problem gives you a large integer n and a target target. An integer is considered "beautiful" if the sum of its digits is less than or equal to target. You need to find the minimum non-negative integer x such that n + x is beautiful. Essentially, you are trying to round up n to a number where the digits "collapse" into zeros (via carries) to reduce the total digit sum.

Why is this asked in interviews?

This Minimum Addition to Make Integer Beautiful interview question is popular at companies like Infosys and Meta because it tests mathematical intuition and "carry" logic. It's not a standard data structure problem; instead, it requires you to think about how numbers change when you add to them. It reveals if a candidate can handle large numbers (beyond standard integer limits in some languages) and understands place value.

Algorithmic pattern used

The Greedy interview pattern is the most effective here. To reduce the sum of digits, you want to create "carries." For example, if n = 16 and the sum is too high, adding 4 makes it 20. The sum drops from 1+6=7 to 2+0=2. The strategy is to iteratively turn the last non-zero digit into a zero by rounding up to the next power of 10 (10, 100, 1000, etc.) until the digit sum satisfies the target.

Example explanation

Suppose n = 467 and target = 6.

1. Digit sum: 4+6+7 = 17 ( > 6).
2. Round to nearest 10: n = 470. Digit sum: 4+7+0 = 11 ( > 6).
3. Round to nearest 100: n = 500. Digit sum: 5+0+0 = 5 ( <= 6).
4. Beautiful number found: 500.
5. Minimum addition x = 500 - 467 = 33.

Common mistakes candidates make

• Incrementing by 1: Trying to add 1 repeatedly and checking the sum. This will be extremely slow for large differences.
• Not handling the carry correctly: Forgetting that rounding up 9 might change multiple digits (e.g., 99 becomes 100).
• Ignoring the "non-negative" constraint: Though rare, some might try to subtract to reach the target, but the problem asks for n + x.

Interview preparation tip

Brush up on your Math interview pattern skills, specifically how to isolate digits using the modulo operator (% 10) and how to truncate numbers using integer division (// 10). This problem is essentially a "rounding" exercise. Practice explaining how each rounding step is guaranteed to eventually reduce the digit sum (since you eventually reach a power of 10 like 1000..., which always has a digit sum of 1).