Question

I have a solution to the below problem in PHP.
But it is taking too much time to execute for 10 digit numbers. I want to know where am I going wrong ?
I am new to dynamic programming .Can someone have a look at this ?

Problem

In Byteland they have a very strange monetary system.

Each Bytelandian gold coin has an integer number written on it. A coin n
can be exchanged in a bank into three coins: n/2, n/3 and n/4.
But these numbers are all rounded down (the banks have to make a profit).

You can also sell Bytelandian coins for American dollars. The exchange
rate is 1:1. But you can not buy Bytelandian coins.

You have one gold coin. What is the maximum amount of American dollars
you can get for it?

========================================================

<?php 
$maxA=array();

function exchange($money)
{
        if($money == 0)
        {
               return $money;
        }
        if(isset($maxA[$money]))
        {
                $temp = $maxA[$money]; // gets the maximum dollars for N
        }
        else
        {
           $temp = 0;
        }
        if($temp == 0)
        {
            $m = $money/2;
            $m = floor($m);
            $o = $money/3;
            $o = floor($o);
            $n = $money/4;
            $n = floor($n);
            $total = $m+$n+$o;

       if(isset($maxA[$m]))
        {
             $m = $maxA[$m];

        }
        else
        {
           $m = exchange($m);
        }
        if(isset($maxA[$n]))
        {
         $n = $maxA[$n];
        }
        else
        {
           $n = exchange($n);
        }
        if(isset($maxA[$o]))
        {
           $o = $maxA[$o];
        }
        else
        {
           $o = exchange($o);
        }

       $temp = max($total,$m+$n+$o,$money);
       $maxA[$money]=$temp;  //store the value
        }

return $temp; 
}

$A=array();
while(1)
{
      $handle = fopen ("php://stdin","r");
      $line = fgets($handle);
      if(feof($handle))
      {
          break;
      }
      array_push($A,trim($line));
}

$count =count($A);
for($i=0;$i<$count;$i++)
{
      $val = exchange($A[$i]);
      print "$val \n";
 }
?>

Answer 1

Here a reformatted version of the code for the ones (like I) who could understand the above. It doesn’t improve anything.

function exchange($money) {
    static $maxA = array(0 => 0);

    if (isset($maxA[$money])) {
        return $money;
    }

    $m = floor($money/2);
    $o = floor($money/3);
    $n = floor($money/4);
    $total = $m+$n+$o;

    if (isset($maxA[$m])) {
        $m = $maxA[$m];
    } else {
        $m = exchange($m);
    }

    if (isset($maxA[$n])) {
        $n = $maxA[$n];
    } else {
        $n = exchange($n);
    }
    if (isset($maxA[$o])) {
        $o = $maxA[$o];
    } else {
        $o = exchange($o);
    }

    return $maxA[$money] = max($total, $m + $n + $o, $money);
}