Minimum Operations to Make Array Equal to Target

Problem Description

You are given two positive integer arrays nums and target, of the same length. In a single operation, you can select any subarray of nums and increment each element within that subarray by 1 or decrement each element within that subarray by 1. Return the minimum number of operations required to make nums equal to the array target.

Key Insights

• The problem can be reduced to calculating the difference between corresponding elements of the nums and target arrays.
• The absolute difference between each element in nums and target can be managed in a single operation if the differences are contiguous.
• The minimum operations can be calculated by counting the number of contiguous segments where the difference changes.

Space and Time Complexity

Time Complexity: O(n)
Space Complexity: O(1)

Solution

To solve the problem, we can use a greedy approach. We will compute the differences between nums and target, and then iterate through these differences to count the number of contiguous segments that require operations. Each segment can be adjusted in a single operation.

1. Calculate the difference array where each element is target[i] - nums[i].
2. Count the number of contiguous segments where the difference is non-zero.
3. Each segment represents a required operation.

Code Solutions