Create check-if-there-is-a-valid-parentheses-string-path.py

Author: kamyu104

Python/check-if-there-is-a-valid-parentheses-string-path.py

@@ -0,0 +1,45 @@
+# Time:  O(m * n)
+# Space: O(n)
+
+import collections
+
+
+# dp, optimized from solution2
+class Solution(object):
+    def hasValidPath(self, grid):
+        """
+        :type grid: List[List[str]]
+        :rtype: bool
+        """
+        if (len(grid)+len(grid[0])-1)%2:
+            return False
+        dp = [[float("inf"), float("-inf")] for _ in xrange(len(grid[0])+1)]
+        for i in xrange(len(grid)):
+            dp[0] = [0, 0] if not i else [float("inf"), float("-inf")]
+            for j in xrange(len(grid[0])):
+                d = 1 if grid[i][j] == '(' else -1
+                dp[j+1] = [min(dp[j+1][0], dp[j][0])+d, max(dp[j+1][1], dp[j][1])+d]
+                if dp[j+1][1] < 0:
+                    dp[j+1] = [float("inf"), float("-inf")]
+                else:
+                    dp[j+1][0] = max(dp[j+1][0], dp[j+1][1]%2)
+        return dp[len(grid[0])][0] == 0
+
+
+# Time:  O((m * n) * (m + n) / 32)
+# Space: O(n * (m + n) / 32)
+# dp
+class Solution2(object):
+    def hasValidPath(self, grid):
+        """
+        :type grid: List[List[str]]
+        :rtype: bool
+        """
+        if (len(grid)+len(grid[0])-1)%2:
+            return False
+        dp = [0]*(len(grid[0])+1)
+        for i in xrange(len(grid)):
+            dp[0] = int(not i)
+            for j in xrange(len(grid[0])):
+                dp[j+1] = (dp[j]|dp[j+1])<<1 if grid[i][j] == '(' else (dp[j]|dp[j+1])>>1
+        return dp[-1]&1