Add: NQueen

NQueen problem solved using backtracking

Author: arvin2000dev

src/Other/NQueen.php

@@ -0,0 +1,89 @@
+<?php
+
+/**
+ * NQueen Algorithm
+ *
+ * @author   Arvin Atri  <[email protected]>
+ * @date     2023/12/06
+ * @license  MIT
+ */
+/*
+|--------------------------------------------------------------------------
+| NQueen Algorithm
+|--------------------------------------------------------------------------
+|
+| Arrange N queens on an NxN chessboard without attacking each other diagonally,
+| horizontally, or vertically—a classic problem in combinatorial optimization and
+| recursion.
+|
+*/
+
+class NQueen
+{
+
+    //Variable to store the dimensions of the chessboard
+    protected int $n;
+
+    //Chessboard represented as an array
+    protected array $board;
+
+    //Constructor to initialize the chessboard dimensions and fill it with zeros
+    public function __construct(int $n)
+    {
+        $this->n = $n;
+        $this->board = array_fill(0, $this->n, array_fill(0, $this->n, 0));
+    }
+
+    public function solve_n_queen($col = 0): void
+    {
+        if ($col >= $this->n) {
+            $this->print_result();
+        }
+
+        //Iterating through each row in the current column
+        for ($row = 0; $row < $this->n; $row++) {
+            if ($this->move_is_promising($row, $col)) {
+                //Placing the queen at the current position
+                $this->board[$row][$col] = 1;
+                //Recursively solving for the next column
+                $this->solve_n_queen($col + 1);
+                //Backtracking by removing the queen from the current position
+                $this->board[$row][$col] = 0;
+            }
+        }
+    }
+
+    public function move_is_promising($row, $col): bool
+    {
+        //Checking if there is no queen in the same row
+        for ($index = 0; $index < $col; $index++)
+            if ($this->board[$row][$index])
+                return false;
+
+        //Checking if there is no queen on the upper-left diagonal
+        for ($i = $row, $j = $col; $i >= 0 && $j >= 0; $i--, $j--)
+            if ($this->board[$i][$j])
+                return false;
+
+        //Checking if there is no queen on the lower-left diagonal
+        for ($i = $row, $j = $col; $i < $this->n && $j >= 0; $i++, $j--)
+            if ($this->board[$i][$j])
+                return false;
+
+        //If no conflicts are found, the move is promising
+        return true;
+    }
+
+    public function print_result(): void
+    {
+        for ($i = 0; $i < $this->n; $i++) {
+            for ($j = 0; $j < $this->n; $j++)
+                echo $this->board[$i][$j];
+            echo "\n";
+        }
+        echo "\n";
+    }
+}
+
+$dimensions = 4;
+(new NQueen($dimensions))->solve_n_queen();