Create trapping rain water.py

trapping rain water.py

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+class Solution(object):
+    def trap(self, height):
+        """
+        :type height: List[int]
+        :rtype: int
+        """
+        result, left, right, level = 0, 0, len(height)-1, 0
+        while left < right:
+            if height[left] < height[right]:
+                lower = height[left]
+                left += 1
+            else:
+                lower = height[right]
+                right -= 1
+            level = max(level, lower)
+            result += level-lower
+        return result
+
+
+# Time:  O(n)
+# Space: O(1)
+class Solution2(object):
+    # @param A, a list of integers
+    # @return an integer
+    def trap(self, A):
+        result = 0
+        top = 0
+        for i in xrange(len(A)):
+            if A[top] < A[i]:
+                top = i
+
+        second_top = 0
+        for i in xrange(top):
+            if A[second_top] < A[i]:
+                second_top = i
+            result += A[second_top] - A[i]
+
+        second_top = len(A) - 1
+        for i in reversed(xrange(top, len(A))):
+            if A[second_top] < A[i]:
+                second_top = i
+            result += A[second_top] - A[i]
+
+        return result
+
+# Time:  O(n)
+# Space: O(n)
+class Solution3(object):
+    # @param A, a list of integers
+    # @return an integer
+    def trap(self, A):
+        result = 0
+        stack = []
+
+        for i in xrange(len(A)):
+            mid_height = 0
+            while stack:
+                [pos, height] = stack.pop()
+                result += (min(height, A[i]) - mid_height) * (i - pos - 1)
+                mid_height = height
+
+                if A[i] < height:
+                    stack.append([pos, height])
+                    break
+            stack.append([i, A[i]])
+
+        return result