041 Trapping Rain Water

Author: idf

041 Trapping Rain Water py3.py

@@ -0,0 +1,37 @@
+#!/usr/bin/python3
+"""
+Given n non-negative integers representing an elevation map where the width of
+each bar is 1, compute how much water it is able to trap after raining.
+
+
+The above elevation map is represented by array [0,1,0,2,1,0,1,3,2,1,2,1]. In
+this case, 6 units of rain water (blue section) are being trapped.
+
+Example:
+Input: [0,1,0,2,1,0,1,3,2,1,2,1]
+Output: 6
+"""
+
+class Solution:
+    def trap(self, height: List[int]) -> int:
+        """
+        At each position, the water is determined by the left and right max
+
+        Let lefts[i] be the max(height[:i])
+        Let rights[i] be the max(height[i:])
+        """
+        n = len(height)
+        lefts = [0 for _ in range(n+1)]
+        rights = [0 for _ in range(n+1)]
+        for i in range(1, n+1):  # i, index of lefts
+            lefts[i] = max(lefts[i-1], height[i-1])
+        for i in range(n-1, -1, -1):
+            rights[i] = max(rights[i+1], height[i])
+
+        ret = 0
+        for i in range(n):
+            ret += max(
+                0,
+                min(lefts[i], rights[i+1]) - height[i]
+            )
+        return ret