From 3980f8703c6b06efb07aab56a9c9ed2aefc27878 Mon Sep 17 00:00:00 2001
From: Mayank <mrunknown3212@gmail.com>
Date: Thu, 30 Oct 2025 22:03:42 +0530
Subject: [PATCH] Added N-Queens Problem (Backtracking) in JavaScript with
 clear comments

---
 Algorithms/N-QueensProblem.js | 57 +++++++++++++++++++++++++++++++++++
 1 file changed, 57 insertions(+)
 create mode 100644 Algorithms/N-QueensProblem.js

diff --git a/Algorithms/N-QueensProblem.js b/Algorithms/N-QueensProblem.js
new file mode 100644
index 0000000..0654648
--- /dev/null
+++ b/Algorithms/N-QueensProblem.js
@@ -0,0 +1,57 @@
+// N-Queens problem using backtracking
+function solveNQueens(n) {
+  const board = Array.from({ length: n }, () => Array(n).fill(".")); // Create n×n board
+  const result = [];
+
+  // Helper function to check if placing a queen is safe
+  function isSafe(row, col) {
+    // Check the same column above
+    for (let i = 0; i < row; i++) {
+      if (board[i][col] === "Q") return false;
+    }
+
+    // Check upper left diagonal
+    for (let i = row - 1, j = col - 1; i >= 0 && j >= 0; i--, j--) {
+      if (board[i][j] === "Q") return false;
+    }
+
+    // Check upper right diagonal
+    for (let i = row - 1, j = col + 1; i >= 0 && j < n; i--, j++) {
+      if (board[i][j] === "Q") return false;
+    }
+
+    return true; // Safe position
+  }
+
+  // Backtracking function
+  function solve(row) {
+    // Base case: all queens are placed
+    if (row === n) {
+      // Push a copy of current board to result
+      result.push(board.map(r => r.join("")));
+      return;
+    }
+
+    // Try placing queen in each column of current row
+    for (let col = 0; col < n; col++) {
+      if (isSafe(row, col)) {
+        board[row][col] = "Q";   // Place queen
+        solve(row + 1);          // Move to next row
+        board[row][col] = ".";   // Backtrack (remove queen)
+      }
+    }
+  }
+
+  solve(0); // Start from row 0
+  return result;
+}
+
+// Example usage
+const n = 4;
+const solutions = solveNQueens(n);
+
+console.log(`Total solutions for ${n}-Queens: ${solutions.length}`);
+solutions.forEach((sol, i) => {
+  console.log(`\nSolution ${i + 1}:`);
+  sol.forEach(row => console.log(row));
+});