Minimum Number of Increments on Subarrays to Form a Target Array

Problem Description

You are given an integer array target. You have an integer array initial of the same size as target with all elements initially zeros. In one operation you can choose any subarray from initial and increment each value by one. Return the minimum number of operations to form a target array from initial.

Key Insights

• Each operation can increment any contiguous subarray, allowing for flexibility in how increments are applied.
• The difference between consecutive elements in target determines the number of operations needed; if the next element is larger, more increments are required.
• The total number of operations needed corresponds to the sum of positive differences between consecutive elements in target.

Space and Time Complexity

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

Solution

To solve the problem, we will iterate through the target array and calculate the difference between each element and its predecessor. We sum the positive differences, as these represent the increments needed to achieve the target values from the initial array. This approach uses a single pass through the array, making it efficient.

Code Solutions