Minimum Addition to Make Integer Beautiful

Problem Description

You are given two positive integers n and target. An integer is considered beautiful if the sum of its digits is less than or equal to target. Return the minimum non-negative integer x such that n + x is beautiful. The input will be generated such that it is always possible to make n beautiful.

Key Insights

• The problem requires checking the digit sum of a number and adjusting it to meet a target value.
• To make n beautiful, we can increment n by a non-negative integer x until the digit sum is less than or equal to target.
• The digit sum can be easily calculated by converting the number to a string and summing the integer values of its characters.
• The approach involves incrementally finding the next number after n that has a digit sum ≤ target.

Space and Time Complexity

Time Complexity: O(d), where d is the number of digits in n (up to 12). Space Complexity: O(1), as we are using a constant amount of space.

Solution

To solve the problem, we will use a greedy approach. We will repeatedly check the digit sum of n + x for increasing values of x until the sum is less than or equal to target. The algorithm can be summarized as follows:

1. Initialize x to 0.
2. While the digit sum of n + x is greater than target, increment x and check again.
3. Return the value of x when the condition is met.

We will utilize an iterative approach to compute the digit sum each time we increment x.

Code Solutions