Trap Rain Water

Traping_rain_water.cpp

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+#include <vector>
+#include <algorithm>
+#include <iostream>
+
+class Solution {
+public:
+    /**
+     * Computes the amount of water trapped after raining using the Two-Pointer technique.
+     * Time Complexity: O(n)
+     * Space Complexity: O(1)
+     *
+     * @param height A vector of non-negative integers representing the elevation map.
+     * @return The total units of water trapped.
+     */
+    int trap(std::vector<int>& height) {
+        if (height.empty() || height.size() < 3) {
+            return 0; // Need at least 3 bars to trap water
+        }
+
+        int left = 0;
+        int right = height.size() - 1;
+        int leftMax = 0;
+        int rightMax = 0;
+        int trappedWater = 0;
+
+        // The water trapped at any position 'i' is determined by the minimum of 
+        // the tallest bar to the left and the tallest bar to the right, minus the current height.
+        // We move the pointer pointing to the lower max height, as that side is the current limiting factor.
+        while (left < right) {
+            if (height[left] < height[right]) {
+                // The water at 'left' is limited by leftMax, because we know rightMax >= height[right] > height[left].
+                // Therefore, rightMax is guaranteed to be high enough to contain the water.
+                if (height[left] >= leftMax) {
+                    leftMax = height[left];
+                } else {
+                    trappedWater += leftMax - height[left];
+                }
+                left++;
+            } else {
+                // The water at 'right' is limited by rightMax, because we know leftMax >= height[left] >= height[right].
+                // Therefore, leftMax is guaranteed to be high enough to contain the water.
+                if (height[right] >= rightMax) {
+                    rightMax = height[right];
+                } else {
+                    trappedWater += rightMax - height[right];
+                }
+                right--;
+            }
+        }
+
+        return trappedWater;
+    }
+};
+
+/*
+// Example Usage (for testing locally):
+int main() {
+    Solution s;
+    std::vector<int> height1 = {0, 1, 0, 2, 1, 0, 1, 3, 2, 1, 2, 1};
+    std::cout << "Trapped Water (Example 1): " << s.trap(height1) << std::endl; // Output: 6
+
+    std::vector<int> height2 = {4, 2, 0, 3, 2, 5};
+    std::cout << "Trapped Water (Example 2): " << s.trap(height2) << std::endl; // Output: 9
+
+    return 0;
+}
+*/