This Hard-level problem requires transforming a source array into a target array using the minimum number of operations. In one operation, you can choose a contiguous subarray and either increment or decrement all its elements by 1. This is a significant step up in difficulty because the operations are range-based, and overlapping ranges can be used to optimize the total count.
Top-tier companies like Microsoft, Amazon, and Google ask this to see if a candidate can handle complex array manipulation and range-based optimization. It tests the ability to convert a problem about "range updates" into a simpler one about "point updates" using the concept of differences. It also probes your understanding of Monotonic Stacks or Greedy strategies for managing overlapping intervals.
The most effective pattern involves looking at the "difference array" or the "increments needed" at each step. If you need to change nums to target, define diff[i] = target[i] - nums[i]. The problem then becomes: "What is the minimum number of range operations to make an array of zeros into diff?" This is equivalent to finding the sum of "new" increments required as you traverse the array. If the current difference is greater than the previous one (and both have the same sign), you only need current_diff - previous_diff additional operations.
nums = [0, 0, 0], target = [1, 3, 2].
diff array: [1, 3, 2].diff = 1. Operations = 1.diff = 3. Since 3 > 1, we need 3 - 1 = 2 more operations. Total = 3.diff = 2. Since 2 < 3, no "new" operations started here; the range operation from index 1 can "cover" this index. Total remains 3.
Final answer: 3 operations.A major pitfall is trying to use standard range-update data structures like Segment Trees, which are too heavy and don't directly give the "minimum operations" count. Candidates also struggle with handling transitions between positive and negative differences; a range operation cannot simultaneously increment and decrement. Failing to reset the "previous difference" when the sign changes is a frequent logic error.
Study the "Difference Array" technique. It's a powerful trick that turns range updates into two point updates. Also, practice problems related to "Minimum number of increments to make array equal," as this problem is a generalization of that concept. Understanding how "greedy" works in the context of contiguous ranges will help you solve many hard-level array problems.
| Title | Difficulty | Topics | LeetCode |
|---|---|---|---|
| Minimum Number of Increments on Subarrays to Form a Target Array | Hard | Solve | |
| Minimum Cost Tree From Leaf Values | Medium | Solve | |
| Maximum Balanced Shipments | Medium | Solve | |
| Maximum Array Hopping Score I | Medium | Solve | |
| Maximum Number of Books You Can Take | Hard | Solve |