Leetcode #1300: Sum of Mutated Array Closest to Target
In this guide, we solve Leetcode #1300 Sum of Mutated Array Closest to Target 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
Given an integer array arr and a target value target, return the integer value such that when we change all the integers larger than value in the given array to be equal to value, the sum of the array gets as close as possible (in absolute difference) to target. In case of a tie, return the minimum such integer.
Quick Facts
- Difficulty: Medium
- Premium: No
- Tags: Array, Binary Search, Sorting
Intuition
The problem structure suggests a monotonic decision, which makes binary search a natural fit.
By halving the search space each step, we reach the answer efficiently.
Approach
Search either directly on a sorted array or on the answer space using a check function.
Each check is fast, and the logarithmic search keeps the overall runtime low.
Steps:
- Define the search bounds.
- Check the mid point condition.
- Narrow the bounds until convergence.
Example
Input: arr = [4,9,3], target = 10
Output: 3
Explanation: When using 3 arr converts to [3, 3, 3] which sums 9 and that's the optimal answer.
Python Solution
class Solution:
def findBestValue(self, arr: List[int], target: int) -> int:
arr.sort()
s = list(accumulate(arr, initial=0))
ans, diff = 0, inf
for value in range(max(arr) + 1):
i = bisect_right(arr, value)
d = abs(s[i] + (len(arr) - i) * value - target)
if diff > d:
diff = d
ans = value
return ans
Complexity
The time complexity is O(log n) or O(n log n). The space complexity is O(1).
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.