我将c#示例移植到Objective-c，并没有在响应中看到它:

//Usage
NSMutableArray* numberList = [[NSMutableArray alloc] init];
NSMutableArray* partial = [[NSMutableArray alloc] init];
int target = 16;
for( int i = 1; i<target; i++ )
{ [numberList addObject:@(i)]; }
[self findSums:numberList target:target part:partial];


//*******************************************************************
// Finds combinations of numbers that add up to target recursively
//*******************************************************************
-(void)findSums:(NSMutableArray*)numbers target:(int)target part:(NSMutableArray*)partial
{
    int s = 0;
    for (NSNumber* x in partial)
    { s += [x intValue]; }

    if (s == target)
    { NSLog(@"Sum[%@]", partial); }

    if (s >= target)
    { return; }

    for (int i = 0;i < [numbers count];i++ )
    {
        int n = [numbers[i] intValue];
        NSMutableArray* remaining = [[NSMutableArray alloc] init];
        for (int j = i + 1; j < [numbers count];j++)
        { [remaining addObject:@([numbers[j] intValue])]; }

        NSMutableArray* partRec = [[NSMutableArray alloc] initWithArray:partial];
        [partRec addObject:@(n)];
        [self findSums:remaining target:target part:partRec];
    }
}

这是R中的一个解

subset_sum = function(numbers,target,partial=0){
  if(any(is.na(partial))) return()
  s = sum(partial)
  if(s == target) print(sprintf("sum(%s)=%s",paste(partial[-1],collapse="+"),target))
  if(s > target) return()
  for( i in seq_along(numbers)){
    n = numbers[i]
    remaining = numbers[(i+1):length(numbers)]
    subset_sum(remaining,target,c(partial,n))
  }
}

Javascript版本:

function subsetSum(numbers, target, partial) { var s, n, remaining; partial = partial || []; // sum partial s = partial.reduce(function (a, b) { return a + b; }, 0); // check if the partial sum is equals to target if (s === target) { console.log("%s=%s", partial.join("+"), target) } if (s >= target) { return; // if we reach the number why bother to continue } for (var i = 0; i < numbers.length; i++) { n = numbers[i]; remaining = numbers.slice(i + 1); subsetSum(remaining, target, partial.concat([n])); } } subsetSum([3,9,8,4,5,7,10],15); // output: // 3+8+4=15 // 3+5+7=15 // 8+7=15 // 5+10=15

PHP版本，灵感来自Keith Beller的c#版本。

bala的PHP版本不适合我，因为我不需要对数字进行分组。我想要一个更简单的实现，只有一个目标值和一个数字池。这个函数也会删除任何重复的条目。

编辑25/10/2021:添加精度参数以支持浮点数(现在需要bcmath扩展)。

/**
 * Calculates a subset sum: finds out which combinations of numbers
 * from the numbers array can be added together to come to the target
 * number.
 *
 * Returns an indexed array with arrays of number combinations.
 *
 * Example:
 *
 * <pre>
 * $matches = subset_sum(array(5,10,7,3,20), 25);
 * </pre>
 *
 * Returns:
 *
 * <pre>
 * Array
 * (
 *   [0] => Array
 *   (
 *       [0] => 3
 *       [1] => 5
 *       [2] => 7
 *       [3] => 10
 *   )
 *   [1] => Array
 *   (
 *       [0] => 5
 *       [1] => 20
 *   )
 * )
 * </pre>
 *
 * @param number[] $numbers
 * @param number $target
 * @param array $part
 * @param int $precision
 * @return array[number[]]
 */
function subset_sum($numbers, $target, $precision=0, $part=null)
{
    // we assume that an empty $part variable means this
    // is the top level call.
    $toplevel = false;
    if($part === null) {
        $toplevel = true;
        $part = array();
    }

    $s = 0;
    foreach($part as $x)
    {
        $s = $s + $x;
    }

    // we have found a match!
    if(bccomp((string) $s, (string) $target, $precision) === 0)
    {
        sort($part); // ensure the numbers are always sorted
        return array(implode('|', $part));
    }

    // gone too far, break off
    if($s >= $target)
    {
        return null;
    }

    $matches = array();
    $totalNumbers = count($numbers);

    for($i=0; $i < $totalNumbers; $i++)
    {
        $remaining = array();
        $n = $numbers[$i];

        for($j = $i+1; $j < $totalNumbers; $j++)
        {
            $remaining[] = $numbers[$j];
        }

        $part_rec = $part;
        $part_rec[] = $n;

        $result = subset_sum($remaining, $target, $precision, $part_rec);
        if($result)
        {
            $matches = array_merge($matches, $result);
        }
    }

    if(!$toplevel)
    {
        return $matches;
    }

    // this is the top level function call: we have to
    // prepare the final result value by stripping any
    // duplicate results.
    $matches = array_unique($matches);
    $result = array();
    foreach($matches as $entry)
    {
        $result[] = explode('|', $entry);
    }

    return $result;
}

例子:

$result = subset_sum(array(5, 10, 7, 3, 20), 25);

这将返回一个包含两个数字组合数组的索引数组:

3, 5, 7, 10
5, 20

浮点数示例:

// Specify the precision in the third argument
$result = subset_sum(array(0.40, 0.03, 0.05), 0.45, 2);

这将返回一个匹配项:

0.40, 0.05

Perl版本(前导答案):

use strict;

sub subset_sum {
  my ($numbers, $target, $result, $sum) = @_;

  print 'sum('.join(',', @$result).") = $target\n" if $sum == $target;
  return if $sum >= $target;

  subset_sum([@$numbers[$_ + 1 .. $#$numbers]], $target, 
             [@{$result||[]}, $numbers->[$_]], $sum + $numbers->[$_])
    for (0 .. $#$numbers);
}

subset_sum([3,9,8,4,5,7,10,6], 15);

结果:

sum(3,8,4) = 15
sum(3,5,7) = 15
sum(9,6) = 15
sum(8,7) = 15
sum(4,5,6) = 15
sum(5,10) = 15

Javascript版本:

const subsetSum = (numbers, target, partial = []， sum = 0) => { If (sum < target) 数字。forEach((num, i) => subsetSum(数字。Slice (i + 1)， target, partial.concat([num])， sum + num)); Else if (sum == target) console.log(的总和(% s) = % s, partial.join(),目标); ｝ subsetSum([3、9、8、4、5、7、10、6],15);

Javascript一行实际返回结果(而不是打印它):

const subsetSum = (n, t, p = [], s = 0, r = []) = > (s < t ? n.forEach ((l i) = > subsetSum (n.slice (i + 1), t,[……p、l], s + l r)): s = = t ? r.push (p): 0, r); console.log (subsetSum([3、9、8、4、5、7、10、6],15));

我最喜欢的是带有回调的一行语句:

const subsetSum = (n, t,辛西娅·布雷齐尔,p =黑铝,s = 0) = > s & lt; t ? n.forEach ((l, i) = > subsetSum (n.slice (i + 1)、t、辛西娅·布雷齐尔,黑... p, l铝,s + l)): s = = t ?辛西娅·布雷齐尔(p): 0; 子集（[3,9,8,4,5,7,10,6]，15,console.log）；

我想我应该用这个问题的答案，但我不能，所以这是我的答案。它使用的是《计算机程序的结构和解释》中答案的修改版本。我认为这是一个更好的递归解，应该更能取悦纯粹主义者。

我的答案是用Scala(如果我的Scala很烂，我很抱歉，我刚刚开始学习)。findsumcombination的疯狂之处在于对递归的原始列表进行排序和惟一，以防止欺骗。

def findSumCombinations(target: Int, numbers: List[Int]): Int = {
  cc(target, numbers.distinct.sortWith(_ < _), List())
}

def cc(target: Int, numbers: List[Int], solution: List[Int]): Int = {
  if (target == 0) {println(solution); 1 }
  else if (target < 0 || numbers.length == 0) 0
  else 
    cc(target, numbers.tail, solution) 
    + cc(target - numbers.head, numbers, numbers.head :: solution)
}

使用它:

 > findSumCombinations(12345, List(1,5,22,15,0,..))
 * Prints a whole heap of lists that will sum to the target *