Recursively find a collection of elements that conform to the rules:

part of the logic is based on the assumption that all elements in the collection are positive

<?php
/**
 * @title
 * @author start2004
 * @since 2018/5/10
 */

/**
 * [0,1,2,3,4,5,6,7,8,9],3
 * 330+0+3=30+1+231+1+1
 *  fun(,,3) ,.
 * 330+0+33
 * https://segmentfault.com/q/1010000014767442?utm_source=tag-newest
 */

ini_set('memory_limit', '8M');
$arr = [0,1,2,3,4,5,6,7,8,9];
$sum = 2;
$num = 3;
$resultArray = calc($arr, $sum, $num);
//var_dump($resultArray);


/**
 * @title 
 * @param array $arr
 * @param int $sum
 * @param int $num
 * @return array
 */
function calc($arr = [], $sum = 0, $num = 0){
    $resultArray = main($arr, $sum, $num);

    $listArray = [];
    if($resultArray){
        foreach ($resultArray as $rArray){
            /**
             * num>1
             * 
             * 1
             */
            if ($num=1 OR (array_unique($rArray)) > 1){

                /**
                 * 
                 */
                sort($rArray);
                if (in_array($rArray, $listArray) === false){
                    $listArray[] = $rArray;
                    echo implode(" + ", $rArray), " = {$sum}", PHP_EOL;
                }
            }
        }
    }

    /**
     * 
     */
    if (empty($listArray)){
        echo "sum = {$sum}, num = {$num}, no result.", PHP_EOL;
    }

    return $listArray;
}

/**
 * @title 
 * @param array $arr
 * @param int $sum
 * @param int $num
 * @param array $feed
 * @return array|bool
 */
function main($arr = [], $sum = 0, $num = 0, $feed = []){
    if($num < 1){
        return false;
    } elseif($num == 1){
        /**
         * num=1leftSumarr
         */
        if(in_array($sum, $arr) !== false){
            $feed[] = $sum;
            echoLine($sum, $sum, 0, $feed);
            return [$feed];
        } else {
            return false;
        }
    } else {
        $listArray = [];
        foreach ($arr as $val){
            /**
             * sum
             */
            if($val <= $sum){
                $leftSum = $sum-$val;
                $leftNum = $num-1;
                $leftFeed = array_merge($feed, [$val]);

                echoLine($val, $leftSum, $leftNum, $leftFeed);
                $resultArray = main($arr, $leftSum, $leftNum, $leftFeed);
                if($resultArray){
                    foreach ($resultArray as $rArray){
                        $listArray[] = $rArray;
                    }
                }
            }
        }
        return $listArray;
    }
}


/**
 * @title 
 * @param $key
 * @param $sum
 * @param $num
 * @param $feed
 */
function echoLine($key, $sum, $num, $feed){
    return ;
    $prefix = str_repeat("  ", count($feed)-1);
    echo $prefix;

    echo "key={$key}";
    if($num>0){
        echo ", sum={$sum}, num={$num}";
    }
    echo PHP_EOL;
}

/**
key=0, sum=2, num=2
  key=0, sum=2, num=1
    key=2
  key=1, sum=1, num=1
    key=1
  key=2, sum=0, num=1
    key=0
key=1, sum=1, num=2
  key=0, sum=1, num=1
    key=1
  key=1, sum=0, num=1
    key=0
key=2, sum=0, num=2
  key=0, sum=0, num=1
    key=0
*/