Efficient algorithm to find a combination, which summation is equal to a known number, in a set of number
<p>Let's say there is a set of number</p>

<blockquote>
  <p>1, 2, 3, 4, 5, 6, 7, 8, 9, 10</p>
</blockquote>

<p>I want to find out several combinations in the set of number such that the summation of it equal to a known number, for example, 18. We can find out that 5, 6, 7 is matched (5+6+7=18). </p>

<p>Numbers in a combination cannot be repeated and the number in a set may not be consecutive.</p>

<p>I've wrote a C# program to do that. The program is random to pick up number to form a combination and check whether the summation of combination is equal to a known number. However, the combination the program found may be repeated and it makes the progress not effective.</p>

<p>I am wondering whether there is any efficient algorithm to find out such combination.</p>

<p>Here's part of my code.</p>

<pre><code>        int Sum = 0;
        int c;
        List&lt;int&gt; Pick = new List&lt;int&gt;();
        List&lt;int&gt; Target = new List&lt;int&gt;() {some numbers}

        Target.Sort();

            while (!Target.Contains(Sum))
            {
                if (Sum &gt; Target[Target.Count - 1])
                {
                            Pick.Clear();
                            Sum = 0;

                }
                while (true)
                {
                    if (Pick.IndexOf(c = Math0.rand(0, Set.Count - 1)) == -1)
                    {
                        Pick.Add(c);
                    }

                    //Summation Pick
                    Sum = 0;
                    for (int i = 0; i &lt; Pick.Count; i++)
                        Sum += Set[Pick[i]];

                    if (Sum &gt;= Target[Target.Count - 1])
                        break;
                }


            }

            Result.Add(Pick);
</code></pre>
