546. Remove Boxes

How to solve Remove Boxes (LeetCode 546): the approach in brief

The problem

You are given several boxes with different colors represented by different positive numbers.

Pattern

Remove Boxes is a Dynamic Programming (DP) Patterns problem, in the Interval DP subpattern. The pattern covers fibonacci, Kadane, knapsack, LCS, LIS, edit distance, grid paths, and word break

Solve problems on intervals like burst balloons and matrix chain multiplication using interval DP.

Approach outline

1. Think about using dynamic programming to optimize the removal process, as removing boxes in different orders affects the total points earned.
2. Consider representing the problem as intervals of boxes and how removing certain continuous segments affects subsequent choices, which suggests interval DP.
3. To capture the impact of previously removed boxes, try incorporating a parameter in your DP state that counts consecutive boxes of the same color adjacent to the current interval, enhancing your state representation.

Complexity

The reference solution runs in O(n^3) time and O(n^3) space.

Asked at

Remove Boxes has been reported in interviews at Apple, Amazon.