<?php
$total = 3.60; // valor total a ser testado
echo "Para um total de $total:\n\n";
$dados = array('0.10','0.20','0.30','0.50',
               '3.00','3.30','4.00','5.00',
               '1.00','1.10','2.00','2.20');
foreach ($dados as $d) 
	$dadosf[] = floatval($d); // cria array paralelo em float para facilitar
 
for ($i = 0; $i < sizeof($dados) - 1; $i++) 
	$base[]=array($i); // cria os primeiros valores de base
 
for ($n = 2;$n < sizeof($dados); $n++) {
	foreach ($base as $i => $b1) { // soma os números de base
		$soma_base[$i]=0;
		foreach ($b1 as $b2) {
			$soma_base[$i] += $dadosf[$b2];
		}
	}
	$base2 = [];
	for ($b = 0; $b < sizeof($base); $b++) {
		$u = sizeof($base[$b])-1; // último elemento da base
		for ($p = $base[$b][$u] + 1; $p < sizeof($dados); $p++) {
			if (number_format($soma_base[$b] + $dadosf[$p], 3) == number_format($total, 3)) { // *** encontrou combinação da soma ***
				echo 'Combinação ' . ++$c . ': ';
				for ($d = 0; $d <= $u; $d++) { 
					echo $dados[$base[$b][$d]] . ' + ';
				}
				echo $dados[$p] . ' = ' . $total . "\n";
			}
			$base2[] = $base[$b];
			$base2[sizeof($base2)-1][] = $p;
 
		}
	}
	$base = $base2;
}
 

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