Maximum Segment Sum After Removals

Maximum Segment Sum After Removals

1. What is this problem about?

The Maximum Segment Sum After Removals coding problem involves an array of integers and a sequence of removal queries. In each step, an element at a specified index is removed, breaking the array into smaller contiguous segments. After each removal, you need to find the maximum sum among all remaining segments.

2. Why is this asked in interviews?

This "Hard" problem is asked by Infosys and Medianet because it tests a candidate's ability to think in reverse. While calculating segments after removals is difficult (as segments break apart), calculating segments as elements are added is much easier using a Disjoint Set Union (DSU) data structure. It evaluates your proficiency with complex data structures and prefix sums.

3. Algorithmic pattern used

This problem follows the Union Find (DSU) and Prefix Sum interview pattern. The trick is to process the removal queries in reverse order. Start with an empty array and add elements back one by one. As you add an element, check if its neighbors are already present. If they are, "union" them into a single segment and update the segment sum. The answer is the maximum segment sum found during this reverse process.

4. Example explanation

Array: [1, 2, 5, 2], Removals: [1, 2, 0, 3]. Reverse: Add index 3 (val 2), then 0 (val 1), then 2 (val 5), then 1 (val 2).

1. Add index 3: Segment {3}, Sum = 2. Max = 2.
2. Add index 0: Segments {0}, {3}. Max = 2.
3. Add index 2: Segment {2, 3}, Sum = 5+2=7. Max = 7.
4. Add index 1: Segment {0, 1, 2, 3}, Sum = 10. Max = 10. The results (in original order) would be the maxes before each addition in the reverse sequence.

5. Common mistakes candidates make

The most common mistake is trying to solve the problem in the forward direction. Re-calculating all segment sums after every removal leads to O(N²) complexity. Another error is failing to correctly implement the Union Find logic, specifically the part that tracks the sum of each connected component.

6. Interview preparation tip

When you see a problem involving "removals" and "segment properties," always ask: "Would this be easier if I added elements instead?" The "Reverse Processing, Union Find interview pattern" is a powerful technique for these types of dynamic connectivity problems.