Merge pull request #138 from sujanrupu/main

Added N-Queens Problem Solution

Author: admirerr

CPP/Backtracking/N_queens.cpp

@@ -0,0 +1,84 @@
+/*
+Problem statement : 
+
+The n-queens puzzle is the problem of placing n queens on an n x n chessboard such that no two queens attack each other.
+
+Given an integer n, return all distinct solutions to the n-queens puzzle. You may return the answer in any order.
+
+Each solution contains a distinct board configuration of the n-queens' placement, where 'Q' and '.' both indicate a queen and an empty space, respectively.
+  Input: n = 4
+Output: [[".Q..","...Q","Q...","..Q."],["..Q.","Q...","...Q",".Q.."]]
+Explanation: There exist two distinct solutions to the 4-queens puzzle as shown above
+Example 2:
+
+Input: n = 1
+Output: [["Q"]]
+ 
+
+Constraints:
+
+1 <= n <= 9
+*/
+
+#include <bits/stdc++.h>
+using namespace std;
+
+class Solution {
+public:
+    // check if placing queen at (row,col) is safe
+    bool isSafe(vector<vector<int>>& board, int row, int col) {
+        int x = row, y = col;
+        while (y >= 0) if (board[x][y--] == 1) return false;
+        x = row; y = col;
+        while (x < board.size() && y >= 0) if (board[x++][y--] == 1) return false;
+        x = row; y = col;
+        while (x >= 0 && y >= 0) if (board[x--][y--] == 1) return false;
+        return true;
+    }
+
+    // convert board to string format
+    void addSol(vector<vector<int>>& board, int n, vector<vector<string>>& ans) {
+        vector<string> arr;
+        for (int i = 0; i < n; i++) {
+            string str = "";
+            for (int j = 0; j < n; j++)
+                str.push_back(board[i][j] ? 'Q' : '.');
+            arr.push_back(str);
+        }
+        ans.push_back(arr);
+    }
+
+    // backtrack to find all solutions
+    void solve(vector<vector<int>>& board, int n, int col, vector<vector<string>>& ans) {
+        if (col == n) { addSol(board, n, ans); return; }
+        for (int row = 0; row < n; row++) {
+            if (isSafe(board, row, col)) {
+                board[row][col] = 1;
+                solve(board, n, col + 1, ans);
+                board[row][col] = 0;
+            }
+        }
+    }
+
+    vector<vector<string>> solveNQueens(int n) {
+        vector<vector<int>> board(n, vector<int>(n, 0));
+        vector<vector<string>> ans;
+        solve(board, n, 0, ans);
+        return ans;
+    }
+};
+
+int main() {
+    int n;
+    cout << "Enter number of queens: ";
+    cin >> n;
+    Solution s;
+    auto res = s.solveNQueens(n);
+    cout << "Total Solutions: " << res.size() << "\n\n";
+    for (auto& sol : res) {
+        for (auto& row : sol)
+            cout << row << "\n";
+        cout << "\n";
+    }
+    return 0;
+}