PHP는 동적 프로그래밍 배낭 문제를 구현합니다.

f(n,m)=max{f(n-1,m),f(n-1,m-w[n])+P(n,m)}

people:5
carDetail[0][technician]:2
carDetail[0][amount]:49
carDetail[0][type]:全车安检
carDetail[1][technician]:2
carDetail[1][amount]:499
carDetail[1][type]:深度诊断
carDetail[2][technician]:3
carDetail[2][amount]:1300
carDetail[2][type]:二手车检测
carDetail[3][technician]:1
carDetail[3][amount]:10
carDetail[3][type]:空调专项检测

<?php
// 动态规划
error_reporting(E_ALL ^ E_NOTICE);
$t1 = microtime(true);
class bestMatch
{
    public function getMethod($postData)
    {
        $peopleArr = $gainArr = $nameArr = [0];
        foreach ($postData[&#39;carDetail&#39;] as $val) {
            // 初始化各个套餐：所需人数、利润和套餐名称数组
            $peopleArr[] = $val[&#39;technician&#39;];
            $gainArr[] = $val[&#39;amount&#39;];
            $nameArr[] = $val[&#39;type&#39;];
        }
        // 获取人数总数（背包）
        $totalPeople = $postData[&#39;people&#39;];
        // 做检测单数
        $items = count($peopleArr);
        // 利润列表 - 初始状态
        $cacheMap[] = array_fill(1, $items, 0);
        // 套餐列表 - 初始状态
        $cacheMapName[] = array_fill(1, $items, &#39;&#39;);
        //中间的各种决策(依次放入物品a,b,c,d,e)
        // 第一个循环是总人数
        for($i = 1; $i <= $totalPeople; $i++)
        {
            // 第二个循环是套餐
            for($j = 1; $j < $items; $j++)
            {
                $requiredPeople = $peopleArr[$j];
                $gain = $gainArr[$j];
                $name = $nameArr[$j];
                // 上一行坐标数
                $preLine = $j-1;
                $prevGain = $cacheMap[$preLine][$i];
                $prevName = $cacheMapName[$preLine][$i];
                if($requiredPeople > $i)
                {
                    $cacheMap[$j][$i] = $prevGain;
                    $cacheMapName[$j][$i] = $prevName;
                }
                else
                {
                    // 剩余价值
                    if ($i-$requiredPeople >= 0) {
                        $surplusPeople = $i-$requiredPeople;
                        $surplusGain = $cacheMap[$preLine][$surplusPeople];
                        $surplusName = $cacheMapName[$preLine][$surplusPeople];
                    }else {
                        $surplusGain = 0;
                        $surplusName = &#39;&#39;;
                    }
                    $nowTotalGain = $gain + $surplusGain;
                    $cacheMap[$j][$i] = max($prevGain, $nowTotalGain);
                    if ($prevGain > $nowTotalGain) {
                        $cacheMapName[$j][$i] = $prevName;
                    }else{
                        $cacheMapName[$j][$i] = $name.&#39;+&#39;.$surplusName;
                    }
                }
            }
        }
        $actual = count($postData[&#39;carDetail&#39;]);
        return [
            &#39;maxMatch&#39; => $cacheMap[$actual][$totalPeople],
            &#39;maxMatchName&#39; => trim($cacheMapName[$actual][$totalPeople],&#39;+&#39;)
        ];
    }
}
$bestMatch = new bestMatch;
if (empty($_POST) || isset($_POST[&#39;people&#39;]) && $_POST[&#39;people&#39;] > 0) {
    die(&#39;提交参数有误&#39;);
}
$res = $bestMatch->getMethod($_POST);
$t2 = microtime(true);
echo &#39;动态规划: &#39;.&#39;<br/>&#39;;
echo &#39;最佳金额: &#39;.$res[&#39;maxMatch&#39;].&#39;<br/>&#39;;
echo &#39;最佳套餐搭配: &#39;.$res[&#39;maxMatchName&#39;].&#39;<br/>&#39;;
echo &#39;耗时&#39;.round($t2-$t1,7).&#39;秒&#39;.&#39;<br/>&#39; ;
echo &#39;消耗内存: &#39; . memory_get_usage().&#39;字节&#39;.&#39;<br/>&#39; ;

<?php
// 递归查询
error_reporting(E_ALL ^ E_NOTICE);
$t1 = microtime(true);
class optimal
{
    public function getSortList($array,$index = 0,$up =0,&$result =[])
    {
        for ($i=$index; $i < count($array); $i++) {
            if($index > 0 ){
                $value[&#39;name&#39;] = $up[&#39;name&#39;].&#39;+&#39;.$array[$i][&#39;type&#39;];
                $value[&#39;amount&#39;] = bcadd($up[&#39;amount&#39;],$array[$i][&#39;amount&#39;]);
                $value[&#39;technician&#39;] = bcadd($up[&#39;technician&#39;],$array[$i][&#39;technician&#39;]);
            }else{
                $value[&#39;name&#39;] = $array[$i][&#39;type&#39;];
                $value[&#39;amount&#39;] = bcadd($array[$i][&#39;amount&#39;],0);
                $value[&#39;technician&#39;] = bcadd($array[$i][&#39;technician&#39;],0);
            }
            $result[]  = $value;
            $this->getSortList($array,$i+1,$value,$result);
        }
        return $result ;
    }
    public function getMethod($postData)
    {
        $people = $postData[&#39;people&#39;];
        $carDetail = $postData[&#39;carDetail&#39;];
        $allResult = $this->getSortList($carDetail);
        $bestMatch = [];
        foreach ($allResult as $val) {
            if ($val[&#39;technician&#39;] <= $people) {
                if ($bestMatch) {
                    if ($val[&#39;amount&#39;] > $bestMatch[&#39;amount&#39;]) {
                        $bestMatch = $val;
                    }
                }else{
                    $bestMatch = $val;
                }
            }
        }
        return $bestMatch;
    }
}
$optimal = new optimal();
if (empty($_POST) || isset($_POST[&#39;people&#39;]) && $_POST[&#39;people&#39;] > 0) {
    die(&#39;提交参数有误&#39;);
}
$bestMatch = $optimal->getMethod($_POST);
$t2 = microtime(true);
echo &#39;递归查询: &#39;.&#39;<br/>&#39;;
echo &#39;最佳金额: &#39;.$bestMatch[&#39;amount&#39;].&#39;<br/>&#39;;
echo &#39;最佳套餐搭配: &#39;.$bestMatch[&#39;name&#39;].&#39;<br/>&#39;;
echo &#39;耗时&#39;.round($t2-$t1,7).&#39;秒&#39;.&#39;<br/>&#39; ;
echo &#39;消耗内存: &#39; . memory_get_usage().&#39;字节&#39;.&#39;<br/>&#39; ;