背包问题 PHP通过回溯法解决0-1背包问题代码

<?php

    $v_arr = array(11,21,31,33,43,53,55,65);
    $w_arr = array(1,11,21,23,33,43,45,55);
    $n = count($w_arr );

    //测试输出
    var_dump(bknap1(110));

//var_dump(bound(139,89,7,110));

    function bound($v,$w,$k,$W_total){
        global $v_arr,$w_arr,$n;
        $b = $v;
        $c = $w;
        //var_dump($W_total);var_dump($n);var_dump($k);var_dump($v);var_dump($w);//die;
        for($i=$k+1;$i<$n;$i++){
            $c = $c + $w_arr[$i];
            //var_dump($W_total);var_dump($c);
            if($c<$W_total)
                $b += $v_arr[$i];
            else{
            //var_dump((1-($c-$W_total)/$w_arr[$i])*$v_arr[$i]);
                $b = $b+(1-($c-$W_total)/$w_arr[$i])*$v_arr[$i];
                return $b;  
            }

        }
        /*var_dump('------bound head');
        var_dump($k);
        var_dump($b);
        var_dump('------bound end');*/
        return $b;  
    }

    function bknap1($W_total){
        global $v_arr,$w_arr,$n;
        $cw = $cp = 0;
        $k = 0;
        $fp = -1;
        while(true){
            while($k<$n && $cw+$w_arr[$k]<=$W_total){
                $cw += $w_arr[$k];
                $cp += $v_arr[$k];
                $Y_arr[$k] = 1;
                $k +=1;
            }
            //var_dump($cw);var_dump($cp);var_dump($Y_arr);var_dump($k);var_dump($n);die;
            if($k==$n){
                $fp = $cp;
                $fw = $cw;
                $k = $n-1;
                $X_arr = $Y_arr;
                //bound($cp,$cw,$k,$W_total);
                //var_dump(bound($cp,$cw,$k,$W_total),$fp,$k);die;
                //var_dump($fp);var_dump($fw);var_dump($Y_arr);var_dump($k);var_dump($n);die;
            }else{
                $Y_arr[$k] = 0;
            }
            //var_dump($Y_arr);var_dump($k);var_dump($n);//die;
            //var_dump(bound($cp,$cw,$k,$W_total),$fp);die;
            while(bound($cp,$cw,$k,$W_total)<=$fp)
            {
                while($k>=0 && $Y_arr[$k]!=1){
                    $k -= 1;
                }
                if($k<0)
                {
                    return $X_arr;
                }
                var_dump($k);
                $Y_arr[$k] = 0;
                $cw -= $w_arr[$k];
                $cp -= $v_arr[$k];
            }
            $k += 1;
        }
    }

?>