Implementation steps of the Eight Queens Problem algorithm in PHP

Steps to implement the eight queens problem algorithm in PHP

Introduction:
The eight queens problem is a famous problem that plagues the field of computer science. It requires placing eight queens on an 8x8 chessboard. So that no two queens can attack each other. This article will give the algorithm steps to implement the Eight Queens Problem in PHP, and attach code examples.

1. Problem Analysis
The Eight Queens problem can be regarded as a typical backtracking problem. On an 8x8 chessboard, only one queen can be placed in each row, and the queen in each row cannot be in the same column, row, or diagonal as the queens in other rows.

2. Algorithm implementation steps

1. Initialize the chessboard: Create an 8x8 two-dimensional array as the chessboard, and initialize all its elements to 0, indicating that the queen has not been placed at the current position.
2. Backtracking algorithm: Starting from the first row, try to place the queen row by row. For each row, try to place a queen on each column and check if the condition of not being attacked is met. If the conditions are met, continue recursively to place the queen in the next row. If the conditions are not met, go back to the previous line and try again in another position.
3. End condition: When all queens are successfully placed on the chessboard, a solution is obtained. The backtracking ends when all rows have been tried without a solution.

3. PHP code example
The following is a code example that uses PHP to implement the Eight Queens Problem algorithm:

<?php

class EightQueens {
    private $board; // 棋盘
    private $solutions; // 存放所有解的数组

    public function __construct() {
        $this->board = array_fill(0, 8, array_fill(0, 8, 0));
        $this->solutions = array();
    }

    public function solve() {
        $this->placeQueen(0);
        return $this->solutions;
    }

    private function placeQueen($row) {
        if ($row == 8) {
            $this->solutions[] = $this->board;
            return;
        }

        for ($col = 0; $col < 8; $col++) {
            if ($this->isSafe($row, $col)) {
                $this->board[$row][$col] = 1; // 放置皇后

                // 递归放置下一行的皇后
                $this->placeQueen($row + 1);

                $this->board[$row][$col] = 0; // 回溯
            }
        }
    }

    private function isSafe($row, $col) {
        // 检查当前列是否已有皇后
        for ($i = 0; $i < $row; $i++) {
            if ($this->board[$i][$col] == 1) {
                return false;
            }
        }

        // 检查左上对角线是否有皇后
        $i = $row - 1;
        $j = $col - 1;
        while ($i >= 0 && $j >= 0) {
            if ($this->board[$i][$j] == 1) {
                return false;
            }
            $i--;
            $j--;
        }

        // 检查右上对角线是否有皇后
        $i = $row - 1;
        $j = $col + 1;
        while ($i >= 0 && $j < 8) {
            if ($this->board[$i][$j] == 1) {
                return false;
            }
            $i--;
            $j++;
        }

        return true;
    }
}

// 使用示例
$eightQueens = new EightQueens();
$solutions = $eightQueens->solve();

foreach ($solutions as $solution) {
    foreach ($solution as $row) {
        echo implode(" ", $row) . "
";
    }
    echo "
";
}

The above code implements the solution to the Eight Queens Problem through the backtracking algorithm. After running the program, all solutions that meet the conditions will be output. Each solution is represented by a two-dimensional array, where 1 represents the position of the queen.

Conclusion:
This article introduces the algorithm steps to implement the Eight Queens Problem in PHP, and attaches the corresponding code examples. Through this algorithm, we can find all solutions that meet the condition, that is, place eight queens on an 8x8 chessboard so that no two queens can attack each other. The backtracking algorithm is a common method for solving the Eight Queens problem and is also widely used in other similar problems.

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