546. Remove Boxes

Problem Link

Description

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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

Solution

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Python3

import functools
class Solution:
    def removeBoxes(self, boxes: List[int]) -> int:
        @functools.lru_cache(None)
        def dfs(i,j,k):
            if i>j: return 0
            cnt=0
            while (i+cnt)<=j and boxes[i]==boxes[i+cnt]:
                cnt+=1
            i2=i+cnt
            res=dfs(i2,j,0)+(k+cnt)**2
            for m in range(i2,j+1):
                if boxes[m]==boxes[i]:
                    res=max(res, dfs(i2,m-1,0)+dfs(m,j,k+cnt))
            return res
        return dfs(0,len(boxes)-1,0)