dp maxsubarray

Maximum Subarray II.py

@@ -0,0 +1,60 @@
+"""
+Given an array of integers, find two non-overlapping subarrays which have the largest sum.
+
+The number in each subarray should be contiguous.
+
+Return the largest sum.
+
+Note
+The subarray should contain at least one number
+
+Example
+For given [1, 3, -1, 2, -1, 2], the two subarrays are [1, 3] and [2, -1, 2] or [1, 3, -1, 2] and [2], they both have
+the largest sum 7.
+
+Challenge
+Can you do it in time complexity O(n) ?
+"""
+__author__ = 'Danyang'
+class Solution:
+    def maxTwoSubArrays(self, nums):
+        """
+        dp max subarray
+
+        fi for subarry that ends WITH OR BEFORE i
+         
+        f1 for forward sweeping
+        f2 for backward sweeping
+        :param nums: A list of integers
+        :return: An integer denotes the sum of max two non-overlapping subarrays
+        """
+        n = len(nums)
+
+        f = [[-1<<31 for _ in xrange(n+1)] for _ in xrange(2)]
+
+        cur = 0
+        for i in xrange(1, n+1):
+            cur += nums[i-1]
+            f[0][i] = max(nums[i-1], f[0][i-1], cur)
+            if cur<0:
+                cur = 0
+
+        cur = 0
+        for i in xrange(n-1, -1, -1):
+            cur += nums[i]
+            f[1][i] = max(nums[i], f[1][i+1], cur)
+            if cur<0:
+                cur = 0
+
+        maxa = -1<<31
+        for i in xrange(1, n):
+            maxa = max(maxa, f[0][i]+f[1][i])
+        return maxa
+
+if __name__=="__main__":
+    print Solution().maxTwoSubArrays([1, 3, -1, 2, -1, 2])
+
+
+
+
+