Sum Of Mutated Array Closest To Target - Leetcode Solution

The problem "Sum of Mutated Array Closest to Target" on LeetCode asks us to find the minimum possible value of the sum of a modified array that is closest to a given target value. The modified array is obtained by changing some elements of the original array to a new value based on a given condition. Let's go through the problem in detail and see how we can solve it.

Problem Statement:

Given an array nums of integers and an integer target, find the sum of the elements of nums after the modification of some of its elements. Each modification is defined as replacing one or more elements of nums by any positive integer value less than or equal to target.

The modification of each element is independent of each other, i.e., we can modify any element of the array regardless of the values of other elements. The task is to find the modified array whose sum of the values is closest to the target value. If there are multiple such arrays, return the minimum sum.

Approach:

The problem can be solved using binary search. Let's start with a minimum value for the modified array as 0 and a maximum value as the target value. We need to find the midpoint of these values and modify the array elements accordingly. If the sum of the modified array is less than the target value, we move the minimum pointer to the midpoint. Otherwise, we move the maximum pointer to the midpoint. We repeat this process until the minimum and maximum pointers converge, i.e., we have found the closest possible modified array sum to the target.

Algorithm:

1. Initialize the minimum value of the modified array as 0 and the maximum value as the target value.
2. Use binary search to find the midpoint of the minimum and maximum values.
3. Modify the array using the current midpoint value as the threshold.
4. If the sum of the modified array is less than the target value, move the minimum pointer to the midpoint + 1.
5. Otherwise, move the maximum pointer to the midpoint - 1.
6. Repeat steps 2-5 until the minimum and maximum pointers converge, i.e., we have found the closest possible modified array sum to the target.

Code:

Here is the Python code for the above algorithm.

class Solution:
    def findBestValue(self, nums: List[int], target: int) -> int:
        n = len(nums)
        left, right = 0, max(nums)
        while left <= right:
            mid = (left + right) // 2
            total = sum(min(num, mid) for num in nums)
            if total < target:
                left = mid + 1
            else:
                right = mid - 1
        ans1 = sum(min(num, left) for num in nums)
        ans2 = sum(min(num, left - 1) for num in nums)
        if abs(ans1 - target) >= abs(ans2 - target):
            return left - 1
        else:
            return left

Time Complexity: O(n log m), where n is the number of elements in the array and m is the maximum value of the array.

Space Complexity: O(1), constant extra space is used.

The above solution passed all the test cases and got accepted on LeetCode.

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