Create burst-balloons.py

Python/burst-balloons.py

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+# Time:  O(n^3)
+# Space: O(n^2)
+
+# Given n balloons, indexed from 0 to n-1. 
+# Each balloon is painted with a number on it 
+# represented by array nums. 
+# You are asked to burst all the balloons.
+# If the you burst balloon i you will get 
+# nums[left] * nums[i] * nums[right] coins. 
+# Here left and right are adjacent indices of i. 
+# After the burst, the left and right then
+# becomes adjacent.
+#
+# Find the maximum coins you can collect by 
+# bursting the balloons wisely.
+#
+# Note: 
+# (1) You may imagine nums[-1] = nums[n] = 1.
+#     They are not real therefore you can not burst them.
+# (2) 0 <= n <= 500, 0 <= nums[i] <= 100
+#
+# Example:
+#
+# Given [3, 1, 5, 8]
+#
+# Return 167
+#
+#     nums = [3,1,5,8] --> [3,5,8] -->   [3,8]   -->  [8]  --> []
+#   coins =  3*1*5      +  3*5*8    +  1*3*8      + 1*8*1   = 167
+#
+
+# TLE, although it could pass in C++.
+class Solution(object):
+    def maxCoins(self, nums):
+        """
+        :type nums: List[int]
+        :rtype: int
+        """
+        coins = [1] + [i for i in nums if i > 0] + [1]
+        n = len(coins)
+        max_coins = [[0 for _ in xrange(n)] for _ in xrange(n)]
+
+        for k in xrange(2, n):
+            for left in xrange(n - k):
+                right = left + k
+                for i in xrange(left + 1, right):
+                    max_coins[left][right] = max(max_coins[left][right], \
+                           coins[left] * coins[i] * coins[right] + \
+                           max_coins[left][i] + max_coins[i][right])
+
+        return max_coins[0][-1]
+