Minimum Number of Increments on Subarrays to Form a Target Array - Video Solutions

Problem Overview: You start with an array of zeros and can increment any subarray by 1 in a single operation. The goal is to construct the given target array using the minimum number of such operations.

Approach 1: Difference Array Method (O(n) time, O(1) space)

The key observation is that increments only matter when the array value increases compared to the previous index. If target[i] is greater than target[i-1], you must start additional increment operations equal to the difference. When the value decreases or stays the same, previously started operations already cover that segment. Iterate through the array once, compute max(0, target[i] - target[i-1]), and accumulate the result. Conceptually, this acts like a difference array where positive increases represent new subarray increments that must start at that position. The approach is extremely efficient and only tracks the previous value, making the space complexity constant.

This technique frequently appears in array transformation problems where operations propagate across ranges. Instead of simulating each increment operation, you compute how many operations must start at each index.

Approach 2: Greedy Incrementation (O(n) time, O(1) space)

The greedy interpretation views the target array as layers of increments stacked vertically. Every time the height increases compared to the previous position, a new layer must start. If the height drops, some layers simply end earlier. The minimum operations equal the sum of all positive height increases while scanning from left to right. Initialize the answer with target[0] since you must perform that many operations starting at index 0, then iterate and add target[i] - target[i-1] whenever the difference is positive.

This greedy insight avoids complex simulation or dynamic programming. It also connects to patterns seen in greedy and monotonic stack problems where only upward transitions create new work. Even though the problem is labeled Hard, the optimal solution is a simple linear pass once the correct observation is made.

Recommended for interviews: The greedy/difference-array reasoning is what interviewers expect. Explaining why only positive increases matter demonstrates strong problem decomposition. Showing a naive simulation first can help communicate understanding, but the optimal O(n) scan proves you can identify the structural pattern behind range increment operations.