Merge pull request #286 from RohitVishwakarma8840/patch-1

N*N Queen Bactracking

C++/Backtracking/N*N Queen Bactracking

@@ -0,0 +1,57 @@
+#include <bits/stdc++.h>
+using namespace std;
+
+void printSolution(vector<vector<int>>& board, int N) {
+    for (int i = 0; i < N; ++i) {
+        for (int j = 0; j < N; ++j) {
+            cout << (board[i][j] ? "Q " : ". ");
+        }
+        cout << endl;
+    }
+    cout << endl;
+}
+
+bool isSafe(vector<vector<int>>& board, int row, int col, int N) {
+    for (int i = 0; i < col; ++i)
+        if (board[row][i]) return false;
+
+    for (int i = row, j = col; i >= 0 && j >= 0; --i, --j)
+        if (board[i][j]) return false;
+
+    for (int i = row, j = col; i < N && j >= 0; ++i, --j)
+        if (board[i][j]) return false;
+
+    return true;
+}
+
+bool solveNQueensUtil(vector<vector<int>>& board, int col, int N) {
+    if (col >= N) {
+        printSolution(board, N);
+        return true;
+    }
+
+    bool res = false;
+    for (int i = 0; i < N; ++i) {
+        if (isSafe(board, i, col, N)) {
+            board[i][col] = 1;
+            res = solveNQueensUtil(board, col + 1, N) || res;
+            board[i][col] = 0;
+        }
+    }
+    return res;
+}
+
+void solveNQueens(int N) {
+    vector<vector<int>> board(N, vector<int>(N, 0));
+    if (!solveNQueensUtil(board, 0, N)) {
+        cout << "No solution exists\n";
+    }
+}
+
+int main() {
+    int N;
+    cout << "Enter the number of queens: ";
+    cin >> N;
+    solveNQueens(N);
+    return 0;
+}