Get lowest price on sum of combinations in given array - php

Question

This code is working fine when the array length is 8 or 10 only. When we are checking this same code for more than 10 array length.it get loading not showing the results.
How do reduce my code. If you have algorithm please share. Please help me.
This program working flow:
$allowed_per_room_accommodation =[2,3,6,5,3,5,2,5,4];
$allowed_per_room_price =[10,30,60,40,30,50,20,60,80];
$search_accommodation = 10;
i am get subsets = [5,5],[5,3,2],[6,4],[6,2,2],[5,2,3],[3,2,5]
Show lowest price room and then equal of 10 accommodation; output like as [5,3,2];
<?php
$dp=array(array());
$GLOBALS['final']=[];
$GLOBALS['room_key']=[];
function display($v,$room_key)
{
$GLOBALS['final'][] = $v;
$GLOBALS['room_key'][] = $room_key;
}
function printSubsetsRec($arr, $i, $sum, $p,$dp,$room_key='')
{
// If we reached end and sum is non-zero. We print
// p[] only if arr[0] is equal to sun OR dp[0][sum]
// is true.
if ($i == 0 && $sum != 0 && $dp[0][$sum]) {
array_push($p,$arr[$i]);
array_push($room_key,$i);
display($p,$room_key);
return $p;
}
// If $sum becomes 0
if ($i == 0 && $sum == 0) {
display($p,$room_key);
return $p;
}
// If given sum can be achieved after ignoring
// current element.
if (isset($dp[$i-1][$sum])) {
// Create a new vector to store path
// if(!is_array(#$b))
// $b = array();
$b = $p;
printSubsetsRec($arr, $i-1, $sum, $b,$dp,$room_key);
}
// If given $sum can be achieved after considering
// current element.
if ($sum >= $arr[$i] && isset($dp[$i-1][$sum-$arr[$i]]))
{
if(!is_array($p))
$p = array();
if(!is_array($room_key))
$room_key = array();
array_push($p,$arr[$i]);
array_push($room_key,$i);
printSubsetsRec($arr, $i-1, $sum-$arr[$i], $p,$dp,$room_key);
}
}
// Prints all subsets of arr[0..n-1] with sum 0.
function printAllSubsets($arr, $n, $sum,$get=[])
{
if ($n == 0 || $sum < 0)
return;
// Sum 0 can always be achieved with 0 elements
// $dp = new bool*[$n];
$dp = array();
for ($i=0; $i<$n; ++$i)
{
// $dp[$i][$sum + 1]=true;
$dp[$i][0] = true;
}
// Sum arr[0] can be achieved with single element
if ($arr[0] <= $sum)
$dp[0][$arr[0]] = true;
// Fill rest of the entries in dp[][]
for ($i = 1; $i < $n; ++$i) {
for ($j = 0; $j < $sum + 1; ++$j) {
// echo $i.'d'.$j.'.ds';
$dp[$i][$j] = ($arr[$i] <= $j) ? (isset($dp[$i-1][$j])?$dp[$i-1][$j]:false) | (isset($dp[$i-1][$j-$arr[$i]])?($dp[$i-1][$j-$arr[$i]]):false) : (isset($dp[$i - 1][$j])?($dp[$i - 1][$j]):false);
}
}
if (isset($dp[$n-1][$sum]) == false) {
return "There are no subsets with";
}
$p;
printSubsetsRec($arr, $n-1, $sum, $p='',$dp);
}
$blockSize = array('2','3','6','5','3','5','2','5','4');
$blockvalue = array('10','30','60','40','30','50','20','60','80');
$blockname = array("map","compass","water","sandwich","glucose","tin","banana","apple","cheese");
$processSize = 10;
$m = count($blockSize);
$n = count($processSize);
// sum of sets in array
printAllSubsets($blockSize, $m, $processSize);
$final_subset_room = '';
$final_set_room_keys = '';
$final_set_room =[];
if($GLOBALS['room_key']){
foreach ($GLOBALS['room_key'] as $set_rooms_key => $set_rooms) {
$tot = 0;
foreach ($set_rooms as $set_rooms) {
$tot += $blockvalue[$set_rooms];
}
$final_set_room[$set_rooms_key] = $tot;
}
asort($final_set_room);
$final_set_room_first_key = key($final_set_room);
$final_all_room['set_room_keys'] = $GLOBALS['room_key'][$final_set_room_first_key];
$final_all_room_price['set_room_price'] = $final_set_room[$final_set_room_first_key];
}
if(isset($final_all_room_price)){
asort($final_all_room_price);
$final_all_room_first_key = key($final_all_room_price);
foreach ($final_all_room['set_room_keys'] as $key_room) {
echo $blockname[$key_room].'---'. $blockvalue[$key_room];
echo '<br>';
}
}
else
echo 'No Results';
?>

Answer 1

I'm assuming your task is, given a list rooms, each with the amount of people it can accommodate and the price, to accommodate 10 people (or any other quantity).
This problem is similar to 0-1 knapsack problem which is solvable in polynomial time. In knapsack problem one aims to maximize the price, here we aim to minimize it. Another thing that is different from classic knapsack problem is that full room cost is charged even if the room is not completely occupied. It may reduce the effectiveness of the algorithm proposed at Wikipedia. Anyway, the implementation isn't going to be straightforward if you have never worked with dynamic programming before.
If you want to know more, CLRS book on algorithms discusses dynamic programming in Chapter 15, and knapsack problem in Chapter 16. In the latter chapter they also prove that 0-1 knapsack problem doesn't have trivial greedy solution.