Is Remove Boxes easy or hard?

Remove Boxes is classified as a Hard problem on LeetCode. The difficulty comes from recognizing the need for a third DP dimension to track carried boxes and from handling interval merging logic efficiently.

Remove Boxes Python/Java solution

Python and Java implementations usually use recursive dynamic programming with memoization. A function dp(l, r, k) computes the best score for a subarray while caching results in a dictionary or 3D array. C++ implementations often use a bottom-up 3D DP table for the same state transition.

How to solve Remove Boxes in O(n)?

Remove Boxes cannot be solved in O(n) time with known approaches. The structure of the problem requires considering merges between non‑adjacent boxes of the same color, which creates many overlapping states. The best known solution uses 3D dynamic programming with O(n^4) time complexity.

What is the best approach for Remove Boxes?

The standard solution uses 3D dynamic programming with memoization. The state dp(l, r, k) represents the maximum score for boxes between indices l and r with k extra boxes equal to boxes[r] attached to the right. This allows merging separated boxes of the same color later to gain larger k^2 scores. The optimized solution runs in O(n^4) time and O(n^3) space.

Is Remove Boxes asked at Google/Amazon/Meta?

Remove Boxes is a classic hard dynamic programming problem that appears in advanced interview preparation sets. Variations of interval DP and memoized recursion used in this problem are common in interviews at companies like Google, Amazon, and Meta. Interviewers often focus on the reasoning behind the dp(l, r, k) state.

What data structure is used in Remove Boxes?

The core data structure is a 3D dynamic programming table or memoization cache. It stores results for states defined by the left index, right index, and the number of same-colored boxes carried forward. Arrays or hash maps are commonly used to store these DP states.

What is the time complexity of Remove Boxes?

The optimized dynamic programming solution runs in O(n^4) time and O(n^3) space. The DP state has three dimensions (l, r, k), producing about O(n^3) states, and each state may iterate through possible merge positions inside the interval. The naive recursive solution without memoization has exponential time complexity.

546. Remove Boxes - Practice Online

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

You may experience several rounds to remove boxes until there is no box left. Each time you can choose some continuous boxes with the same color (i.e., composed of k boxes, k >= 1), remove them and get k * k points.

Return the maximum points you can get.

Example 1:

Input: boxes = [1,3,2,2,2,3,4,3,1]
Output: 23
Explanation:
[1, 3, 2, 2, 2, 3, 4, 3, 1] 
----> [1, 3, 3, 4, 3, 1] (3*3=9 points) 
----> [1, 3, 3, 3, 1] (1*1=1 points) 
----> [1, 1] (3*3=9 points) 
----> [] (2*2=4 points)

Example 2:

Input: boxes = [1,1,1]
Output: 9

Example 3:

Input: boxes = [1]
Output: 1

Constraints:

1 <= boxes.length <= 100
1 <= boxes[i] <= 100