Minimum Operations to Make All Array Elements Equal

Problem Description

You are given an array nums consisting of positive integers. You are also given an integer array queries of size m. For the ith query, you want to make all of the elements of nums equal to queries[i]. You can perform the following operation on the array any number of times: Increase or decrease an element of the array by 1. Return an array answer of size m where answer[i] is the minimum number of operations to make all elements of nums equal to queries[i]. Note that after each query the array is reset to its original state.

Key Insights

• Each query requires calculating the total operations needed to change all elements of nums to a specific target.
• The operation count for each element is the absolute difference between the element and the target.
• Efficiently handling multiple queries can be achieved using sorting and prefix sums to avoid recalculating for each query.

Space and Time Complexity

Time Complexity: O(n log n + m) where n is the size of nums (for sorting) and m is the number of queries (for processing). Space Complexity: O(n) for the prefix sum array.

Solution

To solve the problem, we will take the following steps:

1. Sort the nums array to facilitate efficient calculation of operations.
2. Precompute a prefix sum array that holds the cumulative sums of nums.
3. For each query, use binary search to find the appropriate index in the sorted array and calculate the total operations using the prefix sums.
4. Return the results for all queries in an array.

Code Solutions