From 3660ce667a7702ad447e2d7ccef756912f487e11 Mon Sep 17 00:00:00 2001
From: Pradnya Gaitonde <116059908+PradnyaGaitonde@users.noreply.github.com>
Date: Thu, 13 Jun 2024 14:54:57 +0530
Subject: [PATCH] Create 0042-trapping-rain-water.md

Added solution for Leetcode problem 42.
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+---
+id: trapping-rain-water
+title: Trapping Rain Water(LeetCode)
+sidebar_label: 0042-Trapping Rain Water
+tags:
+  - Array
+  - Two Pointers
+  - Dynamic Programming
+  - Stack
+  - Monotonic Stack
+description: Given n non-negative integers representing an elevation map where the width of each bar is 1, compute how much water it can trap after raining.
+sidebar_position: 42
+---
+
+## Problem Statement
+
+Given `n` non-negative integers representing an elevation map where the width of each bar is `1`, compute how much water it can trap after raining.
+
+### Examples
+
+**Example 1:**
+
+![image](https://github.com/PradnyaGaitonde/codeharborhub.github.io/assets/116059908/bbfea3b4-4ed2-4d9c-ab6f-551d3a935a49)
+```plaintext
+Input: height = [0,1,0,2,1,0,1,3,2,1,2,1]
+Output: 6
+Explanation: The above elevation map (black section) 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 2:**
+
+```plaintext
+Input: height = [4,2,0,3,2,5]
+Output: 9
+```
+
+### Constraints
+
+- `n == height.length`
+- `1 <= n <= 2 * 104`
+- `0 <= height[i] <= 105`
+
+## Solution
+
+The Trapping Rain Water problem involves calculating how much water can be trapped between bars after raining, 
+given an array representing the elevation map.
+
+### Approach : Two-Pointer Technique
+
+This approach uses two pointers to traverse the height array from both ends, maintaining the maximum height encountered from the left and the right. 
+The trapped water is calculated based on the minimum of these maximum heights.
+
+#### Explanation:
+
+1. Initialize two pointers: `left` at the start of the array and `right` at the end.
+2. Maintain two variables: `leftMax` for the maximum height encountered from the left and `rightMax` for the maximum height from the right.
+3. Iterate through the array using the two pointers:
+4. If the height at the left pointer is less than the height at the right pointer:
+* Move the left pointer to the right.
+* Update `leftMax` if the new height is greater than `leftMax`.
+* Calculate trapped water at the left pointer if the new height is less than `leftMax`.
+5. If the height at the right pointer is less than or equal to the height at the left pointer:
+* Move the right pointer to the left.
+* Update `rightMax` if the new height is greater than `rightMax`.
+* Calculate trapped water at the right pointer if the new height is less than `rightMax`.
+6. Continue this process until the left and right pointers meet.
+7. The total trapped water is the sum of water calculated at each step.
+
+#### Algorithm
+
+1. Initialize `left` at 0, `right` at the end of the array.
+2. Set `leftMax` to the first element, `rightMax` to the last element.
+3. While `left` is less than `right`:
+4. If `leftMax` is less than `rightMax`:
+* Increment `left`.
+* Update `leftMax` if the new height is greater.
+* Add the difference between `leftMax` and the current height to the water.
+4. Else:
+* Decrement `right`.
+* Update `rightMax` if the new height is greater.
+* Add the difference between `rightMax` and the current height to the water.
+5. Return the total trapped water.
+  
+#### Implementation
+
+C++ Solution:
+
+```C++
+class Solution {
+public:
+    int trap(vector<int>& height) {
+        int n = height.size();
+        int lmax = height[0];
+        int rmax = height[n-1];
+        int lpos = 1;
+        int rpos = n-2;
+        int water = 0;
+        while (lpos <= rpos) {
+            if (height[lpos] >= lmax) {
+                lmax = height[lpos];
+                lpos++;
+            } else if (height[rpos] >= rmax) {
+                rmax = height[rpos];
+                rpos--;
+            } else if (lmax <= rmax && height[lpos] < lmax) {
+                water += lmax - height[lpos];
+                lpos++;
+            } else {
+                water += rmax - height[rpos];
+                rpos--;
+            }
+        }
+        return water;
+    }
+};
+```
+
+Java Solution:
+
+```Java
+class Solution {
+    public int trap(int[] height) {
+        int left = 0, right = height.length - 1;
+        int leftMax = height[0], rightMax = height[height.length - 1];
+        int water = 0;
+        while (left < right) {
+            if (leftMax < rightMax) {
+                left++;
+                if (leftMax < height[left]) {
+                    leftMax = height[left];
+                } else {
+                    water += leftMax - height[left];
+                }
+            } else {
+                right--;
+                if (rightMax < height[right]) {
+                    rightMax = height[right];
+                } else {
+                    water += rightMax - height[right];
+                }
+            }
+        }
+        return water;
+    }
+}
+```
+
+Python Solution:
+
+```Python
+class Solution:
+    def sumBackets(self, height: list[int], left, right):
+        minHeightLeft = height[left]
+        total = 0
+        leftBacket = 0
+        locationMinLeft = left
+
+        while left < right:
+            if height[left] < minHeightLeft:
+                leftBacket += minHeightLeft - height[left]                
+            else:
+                minHeightLeft = height[left]
+                total += leftBacket
+                leftBacket = 0
+                locationMinLeft = left            
+            left += 1
+            
+        if minHeightLeft <= height[right]:
+            return total + leftBacket, right
+        else:      
+            return total, locationMinLeft
+
+    def sumBacketsReverce(self, height: list[int], left, right):
+        minHeightRight = height[right]
+        total = 0
+        rightBacket = 0
+        locationMinRight = right
+
+        while left < right:
+            if height[right] < minHeightRight:
+                rightBacket += minHeightRight - height[right]                
+            else:
+                minHeightRight = height[right]
+                total += rightBacket
+                rightBacket = 0
+                locationMinRight = right            
+            right -= 1
+
+        if minHeightRight <= height[left]:
+            return total + rightBacket, left
+        else:
+            return total, locationMinRight
+    
+    def trap(self, height: List[int]) -> int:                      
+        right = len(height) - 1
+        left = 0
+        totalSum = 0
+
+        while left < right - 1:            
+            if height[left] < height[right]:
+                total, left = self.sumBackets(height, left, right)    
+            else:
+                total, right = self.sumBacketsReverce(height, left, right)        
+            totalSum += total       
+             
+        return totalSum
+```
+### Complexity Analysis
+
+- **Time complexity**: O(n), where n is the number of elements in the height array. The array is traversed once.
+- **Space complexity**: O(1), as no extra space is used except for variables.