此答案基于 גלעד-ברקן 的答案。我按照他的要求把它贴在这里。虽然没有一个答案是我正在寻找的答案，但我发现这是发布的最佳选择。这是我目前使用的修改后的算法：
<?php
function leastChange($inventory, $price){
//NOTE: Hard coded these in the function for my purposes, but $coin value can be passed as a parameter for a more general-purpose algorithm
$num_coin_types = 4;
$coin_value = [10,5,3,1];
$have = 0;
for ($i=0; $i < $num_coin_types; $i++){
$have += $inventory[$i] * $coin_value[$i];
}
//NOTE: Check to see if you have enough money to make this purchase
if ($price > $have){
$error = ["error", "Insufficient Funds"];
return $error;
}
$stack = [[0,$price,$have,[]]];
$best = [-max($coin_value),[]];
while (!empty($stack)){
// each stack call traverses a different set of parameters
$parameters = array_pop($stack);
$i = $parameters[0];
$owed = $parameters[1];
$have = $parameters[2];
$result = $parameters[3];
if ($owed <= 0){
//NOTE: check for new option with least change OR if same as previous option check which uses the least coins paid
if ($owed > $best[0] || ($owed == $best[0] && (array_sum($result) < array_sum($best[1])))){
//NOTE: add extra zeros to end if needed
while (count($result) < 4){
$result[] = 0;
}
$best = [$owed,$result];
}
continue;
}
// skip if we have none of this coin
if ($inventory[$i] == 0){
$result[] = 0;
$stack[] = [$i + 1,$owed,$have,$result];
continue;
}
// minimum needed of this coin
$need = $owed - $have + $inventory[$i] * $coin_value[$i];
if ($need < 0){
$min = 0;
} else {
$min = ceil($need / $coin_value[$i]);
}
// add to stack
for ($j=$min; $j<=$inventory[$i]; $j++){
$stack[] = [$i + 1,$owed - $j * $coin_value[$i],$have - $inventory[$i] * $coin_value[$i],array_merge($result,[$j])];
if ($owed - $j * $coin_value[$i] < 0){
break;
}
}
}
return $best;
}
这是我的测试代码：
$start = microtime(true);
$inventory = [0,1,3,4];
$price = 12;
echo "\n";
echo json_encode(leastChange($inventory,$price));
echo "\n";
$inventory = [0,1,4,0];
$price = 12;
echo "\n";
echo json_encode(leastChange($inventory,$price));
echo "\n";
$inventory = [0,1,4,0];
$price = 6;
echo "\n";
echo json_encode(leastChange($inventory,$price));
echo "\n";
$inventory = [0,1,4,0];
$price = 7;
echo "\n";
echo json_encode(leastChange($inventory,$price));
echo "\n";
$inventory = [1,3,3,10];
$price=39;
echo "\n";
echo json_encode(leastChange($inventory,$price));
echo "\n";
$inventory = [1,3,3,10];
$price=45;
echo "\n";
echo json_encode(leastChange($inventory,$price));
echo "\n";
//stress test
$inventory = [25,25,25,1];
$price=449;
echo "\n";
echo json_encode(leastChange($inventory,$price));
echo "\n";
$time_elapsed = microtime(true) - $start;
echo "\n Time taken: $time_elapsed \n";
结果：
[0,[0,1,2,1]]
[0,[0,0,4,0]]
[0,[0,0,2,0]]
[-1,[0,1,1,0]]
[0,[1,3,3,5]]
["error","Insufficient Funds"]
[-1,[25,25,25,0]]
Time taken: 0.0046839714050293
当然，这个时间是以微秒为单位的，因此它在几分之一秒内执行！