PHP:数字数组可以加起来为数字吗

Question

这比任何事情都更像是一个谜题。我实际上找到了解决方案，但它太慢了，我以为我失去了互联网连接(见下文)。

问题是:

假设我有一个数字数组，如下所示:

$numbers_array = array(1, 2, 3, 4, 5, 6, 7, 8, 9);

假设我有一些数字，存储在这样的变量中:

$sum = 15;
$sum2 = 24;
$sum3 = 400;

我正在尝试创建一个函数，如果可以将 $numbers_array 中的任何数字加在一起(每个数字仅使用一次)以形成总和，该函数将返回 true:

function is_summable($array_of_nums, $sum_to_check) {
    //What to put here?
}

var_dump(is_summable($numbers_array, $sum));
var_dump(is_summable($numbers_array, $sum2));
var_dump(is_summable($numbers_array, $sum3));

上面应该输出:

bool(true)
bool(true)
bool(false)

因为 7 + 8 = 15，7 + 8 + 9 = 24，但是 1-9 的组合不能创造 200。

这是我极其缓慢的解决方案:

function is_summable($numbers, $sum) {
    //Sort provided numbers and assign numerical keys.
    asort($numbers);
    $numbers = array_values($numbers);

    //Var for additions and var for number of provided numbers.
    $total = 0;
    $numbers_length = count($numbers);

    //Empty var to fill below.
    $code = '';

    //Loop and add for() loops.
    for ($i = 0; $i < $numbers_length; $i++) {
        $code .= 'for ($n' . $i . ' = 0; $n' . $i . ' < ' . $numbers_length . '; $n' . $i . '++) {';

        if ($i != 0) {
            $code .= 'if ($n' . $i . ' != $n' . ($i - 1) . ') {';
        }

        $code .= '$total += intval($numbers[$n' . $i . ']);';
        $code .= 'if ($total == $sum) {';
        $code .= 'return true;';
        $code .= '}';
    }

    //Add ending bracket for for() loops above.
    for ($l = 0; $l < $numbers_length; $l++) {
        $code .= '$total -= intval($numbers[$n' . $i . ']);';
        if ($l != 0) {
            $code .= '}';
        }
        $code .= '}';
    }

    //Finally, eval the code.
    eval($code);

    //If "true" not returned above, return false.
    return false;
}

$num_arr = array(1,2,3,4,5,6,7,8,9);
var_dump(is_summable($num_arr, 24));

http://pastebin.com/1nawuwXK

一如既往，感谢帮助!

Answer 1

您的问题实际上是标准算法问题(如 Jon 提到的背包问题)，更具体地说是 Subset sum problem .它可以在多项式时间内解决(查看 wiki page )。

伪代码:

initialize a list S to contain one element 0.
for each i from 1 to N do
  let T be a list consisting of xi + y, for all y in S
  let U be the union of T and S
  sort U
  make S empty 
  let y be the smallest element of U 
  add y to S 
  for each element z of U in increasing order do
     //trim the list by eliminating numbers close to one another
     //and throw out elements greater than s
    if y + cs/N < z ≤ s, set y = z and add z to S 
if S contains a number between (1 − c)s and s, output yes, otherwise no