数字游戏：计算24

声明：算法由PHP大牛鸟哥所写(http://www.laruence.com).

游戏规则: 输入任意4个数字，然后对其进行+-*/组合，所得数学表达式值等于24.

算法思路：把每一个数字看做一个独立的数学表达式，表达式之间加上标点符号组合成新表达式，一共组合4次，表达式之间的所有组合可以通过递归来实现.

代码如下：

<?php
/**
 * A 24 maker
 * @version 1.0.0
 * @author laruence<laruence at yahoo.com.cn>
 * @copyright (c) 2009 http://www.laruence.com
 */
class TwentyFourCal {
    public  $needle = 24;
    public  $precision = '1e-6';
 
    function TwentyFourCal() {
    }
    
    private function notice($mesg) {
        var_dump($mesg);
    }
 
    /**
     * 取得用户输入方法
     */
    public function calculate($operants = array()) {
        try {
            $this->search($operants, 4);
        } catch (Exception $e) {
            $this->notice($e->getMessage());
            return;
        }
        $this->notice('can\'t compute!');
        return;
    }
 
    /**
     * 求24点算法PHP实现
     */
    private function search($expressions, $level) {
        if ($level == 1) {
            $result = 'return ' . $expressions[0] . ';';
            if ( abs(eval($result) - $this->needle) <= $this->precision) {
                throw new Exception($expressions[0]);
            }
        }
        for ($i=0;$i<$level;$i++) {
            for ($j=$i+1;$j<$level;$j++) {
                $expLeft  = $expressions[$i];
                $expRight = $expressions[$j];
                $expressions[$j] = $expressions[$level - 1];
 
                $expressions[$i] = '(' . $expLeft . ' + ' . $expRight . ')';
                $this->search($expressions, $level - 1);
 
                $expressions[$i] = '(' . $expLeft . ' * ' . $expRight . ')';
                $this->search($expressions, $level - 1);
 
                $expressions[$i] = '(' . $expLeft . ' - ' . $expRight . ')';
                $this->search($expressions, $level - 1);
 
                $expressions[$i] = '(' . $expRight . ' - ' . $expLeft . ')';
                $this->search($expressions, $level - 1);
                
                if ($expLeft != 0) {
                    $expressions[$i] = '(' . $expRight . ' / ' . $expLeft . ')';
                    $this->search($expressions, $level - 1);
                }
                
                if ($expRight != 0) {
                    $expressions[$i] = '(' . $expLeft . ' / ' . $expRight . ')';
                    $this->search($expressions, $level - 1);
                }
                $expressions[$i] = $expLeft;
                $expressions[$j] = $expRight;
            }
        }
        return false;
    }
 
    function __destruct() {
    }
}

/* demo */
$tf = new TwentyFourCal();
$tf->calculate( array(4,8,8,8) );
?>