Question

I have an integer collection. I need to get all possibilites that sum of values are equal to X.

I need something like this.

It can be written in: delphi, c#, php, RoR, python, cobol, vb, vb.net

Answer 1

That’s a subset sum problem. And it is NP-Complete.

The only way to implement this would be generate all possible combinations and compare the sum values. Optimization techniques exists though.

Here’s one in C#:

static class Program {     static int TargetSum = 10;     static int[] InputData = new[] { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 };      static void Main()     {         // find all permutations         var permutations = Permute(InputData);          // check each permutation for the sum         foreach (var item in permutations) {              if (item.Sum() == TargetSum) {                  Console.Write(string.Join(' + ', item.Select(n => n.ToString()).ToArray()));                 Console.Write(' = ' + TargetSum.ToString());                 Console.WriteLine();              }         }          Console.ReadKey();     }      static IEnumerable<int[]> Permute(int[] data) { return Permute(data, 0); }      static IEnumerable<int[]> Permute(int[] data, int level)     {         // reached the edge yet? backtrack one step if so.         if (level >= data.Length) yield break;          // yield the first #level elements         yield return data.Take(level + 1).ToArray();          // permute the remaining elements         for (int i = level + 1; i < data.Length; i++) {             var temp = data[level];             data[level] = data[i];             data[i] = temp;              foreach (var item in Permute(data, level + 1))                 yield return item;              temp = data[i];             data[i] = data[level];             data[level] = temp;         }      } }