Create max-dot-product-of-two-subsequences.py

Author: kamyu104

Python/max-dot-product-of-two-subsequences.py

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+# Time:  O(m * n)
+# Space: O(min(m, n))
+
+class Solution(object):
+    def maxDotProduct(self, nums1, nums2):
+        """
+        :type nums1: List[int]
+        :type nums2: List[int]
+        :rtype: int
+        """
+        if len(nums1) < len(nums2):
+            return self.maxDotProduct(nums2, nums1)
+        dp = [[0]*len(nums2) for i in xrange(2)]
+        for i in xrange(len(nums1)):
+            for j in xrange(len(nums2)):
+                dp[i%2][j] = nums1[i]*nums2[j]
+                if i and j:
+                    dp[i%2][j] += max(dp[(i-1)%2][j-1], 0)
+                if i:
+                    dp[i%2][j] = max(dp[i%2][j], dp[(i-1)%2][j])
+                if j:
+                    dp[i%2][j] = max(dp[i%2][j], dp[i%2][j-1])
+        return dp[(len(nums1)-1)%2][-1]