From 7ae6409ecaac46aeabf29d79a2b49fb424cc612f Mon Sep 17 00:00:00 2001
From: Sayak Rana <72291718+Sayak-Rana@users.noreply.github.com>
Date: Tue, 10 Oct 2023 23:31:15 +0530
Subject: [PATCH] Create n_queen_prob.cpp

N Queen Problem
---
 n_queen_prob.cpp | 80 ++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 80 insertions(+)
 create mode 100644 n_queen_prob.cpp

diff --git a/n_queen_prob.cpp b/n_queen_prob.cpp
new file mode 100644
index 00000000..1d3828a5
--- /dev/null
+++ b/n_queen_prob.cpp
@@ -0,0 +1,80 @@
+#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 have been placed successfully
+        return true;
+    }
+
+    for (int col = 0; col < n; ++col) {
+        if (isSafe(board, row, col, n)) {
+            board[row][col] = 1;  // Place the queen
+
+            if (solveNQueens(board, row + 1, n)) {
+                return true;
+            }
+
+            board[row][col] = 0;  // Backtrack if no solution found
+        }
+    }
+
+    return false;  // No safe placement in this row
+}
+
+void printBoard(vector<vector<int>>& board, int n) {
+    for (int i = 0; i < n; ++i) {
+        for (int j = 0; j < n; ++j) {
+            if (board[i][j] == 1) {
+                cout << "Q ";
+            } else {
+                cout << ". ";
+            }
+        }
+        cout << endl;
+    }
+}
+
+int main() {
+    int n;
+    cout << "Enter the value of N for N-Queens: ";
+    cin >> n;
+
+    vector<vector<int>> board(n, vector<int>(n, 0));
+
+    if (solveNQueens(board, 0, n)) {
+        cout << "Solution exists. Here is the board:\n";
+        printBoard(board, n);
+    } else {
+        cout << "No solution exists for N = " << n << endl;
+    }
+
+    return 0;
+}