# Time:  O(n^3) ~ O(n^4)
# Space: O(n^3)

# 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 (composed of k boxes, k >= 1),
# remove them and get k*k points.
# Find the maximum points you can get.
#
# Example 1:
# Input:
#
# [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)
# Note: The number of boxes n would not exceed 100.

class Solution(object):
    def removeBoxes(self, boxes):
        """
        :type boxes: List[int]
        :rtype: int
        """
        def dfs(boxes, l, r, k, lookup):
            if l > r: return 0
            if lookup[l][r][k]: return lookup[l][r][k]

            ll, kk = l, k
            while l < r and boxes[l+1] == boxes[l]:
                l += 1
                k += 1
            result = dfs(boxes, l+1, r, 0, lookup) + (k+1) ** 2
            for i in xrange(l+1, r+1):
                if boxes[i] == boxes[l]:
                    result = max(result, dfs(boxes, l+1, i-1, 0, lookup) + dfs(boxes, i, r, k+1, lookup))
            lookup[ll][r][kk] = result
            return result

        lookup = [[[0]*len(boxes) for _ in xrange(len(boxes)) ] for _ in xrange(len(boxes)) ]
        return dfs(boxes, 0, len(boxes)-1, 0, lookup)

Create remove-boxes.py