Create nqueens.cpp

cpp/nqueens.cpp

@@ -0,0 +1,76 @@
+#include <iostream>
+#include <vector>
+
+using namespace std;
+
+bool isSafe(vector<vector<int>>& board, int row, int col, int N) {
+    // Check if there is a queen in the same column
+    for (int i = 0; i < row; ++i) {
+        if (board[i][col] == 1) {
+            return false;
+        }
+    }
+
+    // Check upper-left diagonal
+    for (int i = row, j = col; i >= 0 && j >= 0; --i, --j) {
+        if (board[i][j] == 1) {
+            return false;
+        }
+    }
+
+    // Check upper-right diagonal
+    for (int i = row, j = col; i >= 0 && j < N; --i, ++j) {
+        if (board[i][j] == 1) {
+            return false;
+        }
+    }
+
+    return true;
+}
+
+bool solveNQueens(vector<vector<int>>& board, int row, int N) {
+    if (row == N) {
+        // All queens are placed successfully
+        return true;
+    }
+
+    for (int col = 0; col < N; ++col) {
+        if (isSafe(board, row, col, N)) {
+            board[row][col] = 1;  // Place the queen
+
+            // Recur to place the rest of the queens
+            if (solveNQueens(board, row + 1, N)) {
+                return true;
+            }
+
+            // If placing the queen in board[row][col] doesn't lead to a solution,
+            // then backtrack and try the next column
+            board[row][col] = 0;  // Backtrack
+        }
+    }
+
+    // If no queen can be placed in this row, return false
+    return false;
+}
+
+int main() {
+    int N;
+    cout << "Enter the value of N: ";
+    cin >> N;
+
+    vector<vector<int>> board(N, vector<int>(N, 0));
+
+    if (solveNQueens(board, 0, N)) {
+        // Print the solution
+        for (int i = 0; i < N; ++i) {
+            for (int j = 0; j < N; ++j) {
+                cout << board[i][j] << " ";
+            }
+            cout << endl;
+        }
+    } else {
+        cout << "No solution found." << endl;
+    }
+
+    return 0;
+}