Leetcode #2457: Minimum Addition to Make Integer Beautiful
In this guide, we solve Leetcode #2457 Minimum Addition to Make Integer Beautiful in Python and focus on the core idea that makes the solution efficient.
You will see the intuition, the step-by-step method, and a clean Python implementation you can use in interviews.
Problem Statement
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.
Quick Facts
- Difficulty: Medium
- Premium: No
- Tags: Greedy, Math
Intuition
A locally optimal choice leads to a globally optimal result for this structure.
That means we can commit to decisions as we scan without backtracking.
Approach
Sort or preprocess if needed, then repeatedly take the best available local choice.
Maintain the minimal state necessary to validate the greedy decision.
Steps:
- Sort or preprocess as needed.
- Iterate and pick the best local option.
- Track the current solution.
Example
Input: n = 16, target = 6
Output: 4
Explanation: Initially n is 16 and its digit sum is 1 + 6 = 7. After adding 4, n becomes 20 and digit sum becomes 2 + 0 = 2. It can be shown that we can not make n beautiful with adding non-negative integer less than 4.
Python Solution
class Solution:
def makeIntegerBeautiful(self, n: int, target: int) -> int:
def f(x: int) -> int:
y = 0
while x:
y += x % 10
x //= 10
return y
x = 0
while f(n + x) > target:
y = n + x
p = 10
while y % 10 == 0:
y //= 10
p *= 10
x = (y // 10 + 1) * p - n
return x
Complexity
The time complexity is , where is the integer given in the problem. The space complexity is .
Edge Cases and Pitfalls
Watch for boundary values, empty inputs, and duplicate values where applicable. If the problem involves ordering or constraints, confirm the invariant is preserved at every step.
Summary
This Python solution focuses on the essential structure of the problem and keeps the implementation interview-friendly while meeting the constraints.