Add Trapping Rain Water solution in arrays

data_structures/arrays/trapping_rain_water.py

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+"""
+Trapping Rain Water
+
+Given an array of non-negative integers representing an elevation map where the width of each bar is 1,
+compute how much water it can trap after raining.
+
+Problem: LeetCode #42 (Hard)
+Link: https://leetcode.com/problems/trapping-rain-water
+
+Approach: Two Pointers
+Time Complexity: O(n)
+Space Complexity: O(1)
+
+Example:
+    Input: height = [0,1,0,2,1,0,1,3,2,1,2,1]
+    Output: 6
+"""
+
+
+def trap(height):
+    """
+    Calculate the amount of water trapped after raining.
+
+    Args:
+        height (List[int]): List of non-negative integers representing elevation map.
+
+    Returns:
+        int: Total units of trapped rainwater.
+
+    Raises:
+        TypeError: If input is not a list.
+        ValueError: If list contains negative values.
+    """
+    if not isinstance(height, list):
+        raise TypeError("Input must be a list of integers.")
+    if any(h < 0 for h in height):
+        raise ValueError("Elevation map cannot contain negative values.")
+
+    if len(height) < 3:
+        return 0  # At least 3 bars needed to trap water
+
+    left, right = 0, len(height) - 1
+    max_left, max_right = 0, 0
+    total_water = 0
+
+    while left < right:
+        if height[left] < height[right]:
+            if height[left] >= max_left:
+                max_left = height[left]
+            else:
+                total_water += max_left - height[left]
+            left += 1
+        else:
+            if height[right] >= max_right:
+                max_right = height[right]
+            else:
+                total_water += max_right - height[right]
+            right -= 1
+
+    return total_water
+
+
+# Example usage and test
+if __name__ == "__main__":
+    # Test case from LeetCode
+    elevation_map = [0, 1, 0, 2, 1, 0, 1, 3, 2, 1, 2, 1]
+    result = trap(elevation_map)
+    print(f"Trapped Rain Water: {result} units")  # Output: 6
+
+    # Additional edge cases
+    print(trap([]))           # 0
+    print(trap([1]))          # 0
+    print(trap([3, 0, 2, 0, 4]))  # 7