add maximum product subarray

Author: x-zh

maximum_product_subarray.py

@@ -0,0 +1,52 @@
+import unittest
+
+
+class Solution:
+    # @param A, a list of integers
+    # @return an integer
+    def maxProduct(self, A):
+        # subproblem is maxProduct(A[n-1])
+        # looks like optimal substructrure, dp should be applicable
+        #
+        # let's use:
+        #   m: positive product for A[x:i], initial with 0
+        #   n: negative product for A[x:i], initial with 0
+        #
+        # for example [2,3,-2,4]
+        # i     2    3   -2   4
+        # m     2    6    0   4
+        # n     0    0   -12  -48
+        # best  2    6    6   6
+        if not A:
+            raise ValueError
+        if len(A) == 1:
+            return A[0]
+
+        m, n, best = 0, 0, float('-inf')
+        for i in A:
+            if i >= 0:
+                m, n = max(m * i, i), n * i
+            else:
+                m, n = n * i, min(m * i, i)
+            best = max(m, best)
+        return best
+
+
+
+class Test(unittest.TestCase):
+
+    def test(self):
+        s = Solution()
+        self.assertEqual(s.maxProduct([-2,0,-1]), 0)
+        self.assertEqual(s.maxProduct([-4,-3,-2]), 12)
+        self.assertEqual(s.maxProduct([2,3,-2,4]), 6)
+        self.assertEqual(s.maxProduct([-2]), -2)
+        self.assertEqual(s.maxProduct([0.1, 0.1, 2]), 2)
+        self.assertEqual(s.maxProduct([-2, 2, -2]), 8)
+        self.assertEqual(s.maxProduct([0, -2, 4]), 4)
+        self.assertEqual(s.maxProduct([0, -2, -2, 4]), 16)
+        self.assertEqual(s.maxProduct([1, -2, 2, 2, 4]), 16)
+
+
+if __name__ == '__main__':
+    unittest.main()