Create Maze Problem in C++.md

Maze Problem in C++.md

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+# Maze Problem with Rates in C++
+
+This C++ program demonstrates how to add rates to a maze problem and find the shortest path using the A* algorithm.
+
+## Important Points
+
+- Define the maze size and cell rates:
+  - `const int ROWS = 5;` and `const int COLS = 5;` represent the size of the maze.
+  - `const int cellRates[ROWS][COLS]` defines rates for each cell in the maze.
+
+- Possible movements:
+  - `const int dx[]` and `const int dy[]` represent possible movements (up, down, left, right).
+
+- `Node` structure:
+  - `Node` struct represents a cell in the maze and contains `x`, `y`, `cost`, and `heuristic` values.
+  - Custom comparison operator (`operator>`) for the priority queue.
+
+- `isValid` function:
+  - Checks if a given cell is within the maze boundaries.
+
+- `calculateHeuristic` function:
+  - Calculates the heuristic (Manhattan distance) for A* algorithm.
+
+- `findShortestPath` function:
+  - Implements A* algorithm with rates considered in the cost calculation.
+
+- Main function:
+  - Takes user input for start and destination coordinates.
+  - Calls `findShortestPath` and displays the shortest path cost.
+
+## Usage
+
+1. Enter start coordinates (x y).
+2. Enter destination coordinates (x y).
+3. The program calculates and displays the shortest path cost.
+
+Make sure to adjust the maze size and cell rates according to your specific problem.
+
+# Code
+```C++
+#include <iostream>
+#include <vector>
+#include <queue>
+#include <cmath>
+
+using namespace std;
+
+// Define the maze size (you can adjust this as needed)
+const int ROWS = 5;
+const int COLS = 5;
+
+// Define cell rates in the maze (adjust as needed)
+const int cellRates[ROWS][COLS] = {
+    {1, 1, 1, 1, 1},
+    {1, 2, 1, 1, 1},
+    {1, 1, 3, 1, 1},
+    {1, 1, 1, 2, 1},
+    {1, 1, 1, 1, 1}
+};
+
+// Define possible movements (up, down, left, right)
+const int dx[] = {-1, 1, 0, 0};
+const int dy[] = {0, 0, -1, 1};
+
+struct Node {
+    int x, y, cost, heuristic;
+
+    Node(int _x, int _y, int _cost, int _heuristic)
+        : x(_x), y(_y), cost(_cost), heuristic(_heuristic) {}
+
+    // Define comparison operator for priority queue
+    bool operator>(const Node& other) const {
+        return cost + heuristic > other.cost + other.heuristic;
+    }
+};
+
+bool isValid(int x, int y) {
+    return x >= 0 && x < ROWS && y >= 0 && y < COLS;
+}
+
+int calculateHeuristic(int x, int y, int destX, int destY) {
+    // Calculate Manhattan distance as heuristic
+    return abs(x - destX) + abs(y - destY);
+}
+
+int findShortestPath(int startX, int startY, int destX, int destY) {
+    vector<vector<int>> cost(ROWS, vector<int>(COLS, INT_MAX));
+    priority_queue<Node, vector<Node>, greater<Node>> pq;
+
+    cost[startX][startY] = 0;
+    pq.emplace(startX, startY, 0, calculateHeuristic(startX, startY, destX, destY));
+
+    while (!pq.empty()) {
+        Node curr = pq.top();
+        pq.pop();
+
+        int x = curr.x;
+        int y = curr.y;
+        int currCost = curr.cost;
+
+        if (x == destX && y == destY) {
+            return currCost;
+        }
+
+        for (int i = 0; i < 4; ++i) {
+            int newX = x + dx[i];
+            int newY = y + dy[i];
+
+            if (isValid(newX, newY)) {
+                int newCost = currCost + cellRates[newX][newY]; // Include the rate in the cost
+
+                if (newCost < cost[newX][newY]) {
+                    cost[newX][newY] = newCost;
+                    pq.emplace(newX, newY, newCost, calculateHeuristic(newX, newY, destX, destY));
+                }
+            }
+        }
+    }
+
+    return -1; // No path found
+}
+
+int main() {
+    int startX, startY, destX, destY;
+
+    cout << "Enter start coordinates (x y): ";
+    cin >> startX >> startY;
+
+    cout << "Enter destination coordinates (x y): ";
+    cin >> destX >> destY;
+
+    if (isValid(startX, startY) && isValid(destX, destY)) {
+        int shortestPathCost = findShortestPath(startX, startY, destX, destY);
+
+        if (shortestPathCost != -1) {
+            cout << "Shortest path cost: " << shortestPathCost << endl;
+        } else {
+            cout << "No path found." << endl;
+        }
+    } else {
+        cout << "Invalid coordinates entered." << endl;
+    }
+
+    return 0;
+}
+```