how to optimise this code? - php

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);
}

Answer 2

I still have my code from this problem. But it's in c++. It's by no means the most efficient, but it passed. It might not be too hard to port to php.
#include <cstdio>
#include <queue>
using namespace std;
unsigned long results;
queue to_test;
int main()
{
char tmp_val[30];
unsigned long coin_value = 1;
while (coin_value)
{
scanf("%s", tmp_val);
coin_value = 0;
results = 0;
for (int w = 0; tmp_val[w] != '\0'; w++)
{
coin_value *= 10;
coin_value += tmp_val[w] - 0x30;
}
if (coin_value != 0)
{
to_test.push(coin_value);
while(!to_test.empty())
{
unsigned long tester = to_test.front();
to_test.pop();
unsigned long over2 = tester/2;
unsigned long over3 = tester/3;
unsigned long over4 = tester/4;
if (tester < over2 + over3 + over4)
{
to_test.push(over2);
to_test.push(over3);
to_test.push(over4);
}
else
{
results += tester;
}
}
printf("%lu\n", results);
}
}
}