Merge pull request #1844 from khurshed07/main

Create Trapping Rain Water Problem.md

docs/Stack/Trapping Rain Water Problem.md

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+---
+id: trapping-rain-water
+title: Trapping Rain Water
+sidebar_label: Trapping Rain Water
+sidebar_position: 1
+description: Documentation for the Trapping Rain Water algorithm to calculate water trapped between bars of varying heights.
+tags: [algorithm, water-trapping, stack]
+---
+
+# Trapping Rain Water
+
+The **Trapping Rain Water** algorithm calculates the amount of water that can be trapped between bars of varying heights.
+
+## Problem Statement
+Given an array of non-negative integers representing the heights of bars, calculate how much water can be trapped after raining.
+
+## Approach
+1. Use a stack to keep track of the indices of the bars.
+2. Iterate through each bar in the array.
+3. For each bar, if it's taller than the one on the stack's top, calculate the trapped water.
+4. Repeat until all bars are processed.
+
+### Code Implementation
+Below is a C++ implementation of the Trapping Rain Water algorithm.
+
+```cpp
+#include <iostream>
+#include <vector>
+#include <stack>
+using namespace std;
+
+int maxWater(vector<int>& arr) {
+    stack<int> st;
+    int res = 0;
+    for (int i = 0; i < arr.size(); i++) {
+        while (!st.empty() && arr[st.top()] < arr[i]) {
+            int pop_height = arr[st.top()];
+            st.pop();
+            if (st.empty()) break;
+            int distance = i - st.top() - 1;
+            int water = min(arr[st.top()], arr[i]) - pop_height;
+            res += distance * water;
+        }
+        st.push(i);
+    }
+    return res;
+}
+```
+
+### Math Formulas
+The formula for trapped water between two bars can be expressed as:
+
+$$ \text{Water} = \text{distance} \times (\min(\text{height}_{left}, \text{height}_{right}) - \text{height}_{current}) $$
+
+### Diagrams
+The following Mermaid diagram represents the steps for processing bars to trap water:
+
+```mermaid
+graph TD;
+    A[Start] --> B[Initialize Stack];
+    B --> C[Loop through each bar];
+    C --> D{Is current bar taller than stack top?};
+    D -->|Yes| E[Pop stack and calculate trapped water];
+    D -->|No| F[Push index to stack];
+    E --> C;
+    F --> C;
+    C --> G[End];
+```
+
+