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If you look at oezis algorithm one drawback is immediately clear: It spends very much time summing up numbers which are already known not to work. (For example if 1 + 2 is already too big, it doesn't make any sense to try 1 + 2 + 3, 1 + 2 + 3 + 4, 1 + 2 + 3 + 4 + 5, ..., too.)

因此，我写了一个改进的版本.它不使用位魔术，而是使所有操作变为手动.缺点是，它要求对输入值进行排序(使用rsort).但这不应该是一个大问题；)

Thus I have written an improved version. It does not use bit magic, it makes everything manual. A drawback is, that it requires the input values to be sorted (use rsort). But that shouldn't be a big problem ;)

function array_sum_parts($vals, $sum){
    $solutions = array();
    $pos = array(0 => count($vals) - 1);
    $lastPosIndex = 0;
    $currentPos = $pos[0];
    $currentSum = 0;
    while (true) {
        $currentSum += $vals[$currentPos];

        if ($currentSum < $sum && $currentPos != 0) {
            $pos[++$lastPosIndex] = --$currentPos;
        } else {
            if ($currentSum == $sum) {
                $solutions[] = array_slice($pos, 0, $lastPosIndex + 1);
            }

            if ($lastPosIndex == 0) {
                break;
            }

            $currentSum -= $vals[$currentPos] + $vals[1 + $currentPos = --$pos[--$lastPosIndex]];
        }
    }

    return $solutions;
}

oezis测试程序的修改版(请参阅末尾)输出:

A modified version of oezis testing program (see end) outputs:

possibilities: 540
took: 3.0897309780121

因此执行仅花费了 3.1秒，而oezis代码在我的计算机上执行了 65秒(是的，我的计算机非常慢).速度快了 20倍！

So it took only 3.1 seconds to execute, whereas oezis code executed 65 seconds on my machine (yes, my machine is very slow). That's more than 20 times faster!

此外，您可能会注意到，我的代码找到了540而不是338的可能性.这是因为我将测试程序调整为使用整数而不是浮点数. 直接进行浮点比较很少是正确的事，这是一个很好的例子，原因:您有时会得到59.959999999999而不是59.96，因此不计算匹配数.因此，如果我使用整数运行oezis代码，它也会发现540种可能性；)

Furthermore you may notice, that my code found 540 instead of 338 possibilities. This is because I adjusted the testing program to use integers instead of floats. Direct floating point comparison is rarely the right thing to do, this is a great example why: You sometimes get 59.959999999999 instead of 59.96 and thus the match will not be counted. So, if I run oezis code with integers it finds 540 possibilities, too ;)

测试程序:

// Inputs
$n = array();
$n[0]  = 6.56;
$n[1]  = 8.99;
$n[2]  = 1.45;
$n[3]  = 4.83;
$n[4]  = 8.16;
$n[5]  = 2.53;
$n[6]  = 0.28;
$n[7]  = 9.37;
$n[8]  = 0.34;
$n[9]  = 5.82;
$n[10] = 8.24;
$n[11] = 4.35;
$n[12] = 9.67;
$n[13] = 1.69;
$n[14] = 5.64;
$n[15] = 0.27;
$n[16] = 2.73;
$n[17] = 1.63;
$n[18] = 4.07;
$n[19] = 9.04;
$n[20] = 6.32;

// Convert to Integers
foreach ($n as &$num) {
    $num *= 100;
}
$sum = 57.96 * 100;

// Sort from High to Low
rsort($n);

// Measure time
$start = microtime(true);
echo 'possibilities: ', count($result = array_sum_parts($n, $sum)), '<br />';
echo 'took: ', microtime(true) - $start;

// Check that the result is correct
foreach ($result as $element) {
    $s = 0;
    foreach ($element as $i) {
        $s += $n[$i];
    }
    if ($s != $sum) echo '<br />FAIL!';
}

var_dump($result);