linear algebra - C# SolverFoundation find maximum combination of lengths -

i have list of brackets need find combination of them 4 brackets, best fits length.

these brackets , example need find out combination of these closest without going on 120 inches.

<?xml version="1.0" encoding="utf-8" ?> <brackets>   <bracket>     <partnumber>f0402583</partnumber>     <length>42.09</length>   </bracket>   <bracket>     <partnumber>f0402604</partnumber>     <length>32.36</length>   </bracket>   <bracket>     <partnumber>f0403826</partnumber>     <length>46.77</length>   </bracket>   <bracket>     <partnumber>f0402566</partnumber>     <length>44.17</length>   </bracket>   <bracket>     <partnumber>f0402289</partnumber>     <length>20.55</length>   </bracket>   <bracket>     <partnumber>f0402612</partnumber>     <length>18.46</length>   </bracket>   <bracket>     <partnumber>f0402606</partnumber>     <length>30.28</length>   </bracket>   <bracket>     <partnumber>f0403828</partnumber>     <length>22.76</length>   </bracket> </brackets> 

i've tried figure out solverfoundation library i'm not math major , have little experience it...using excel solver simplex lp solving method solution 1 30.28" bracket, 1 42.09" bracket, , 1 46.77" bracket comes out 119.14"

here naive solution. have limited understanding of mathematics (most advanced combinatorics , such!), understand challenge. solution runs through possibilities filters valid solution (those total lengths < 120), sorts them length, , outputs first result.

i'm sure if solution require demonstrating understanding of mathematics concept, not way go looking solution - allow check solution.

the runtime of o(n^c).

    public static void main(string[] args)     {         var lengths = new list<decimal>(new decimal[] { 42.09m, 32.36m, 46.77m, 44.17m, 20.55m, 18.46m, 30.28m, 22.76m });          var lst = new list<solution>();          (int = 0; < lengths.count; i++) {              lst.add(new solution(new decimal[] { lengths[i] }));               (int j = 0; j < lengths.count; j++) {                  lst.add(new solution(new decimal[] { lengths[i], lengths[j] }));                  (int k = 0; k < lengths.count; k++) {                      lst.add(new solution(new decimal[] { lengths[i], lengths[j], lengths[k] }));                      (int l = 0; l < lengths.count; l++) {                          lst.add(new solution(new decimal[] { lengths[i], lengths[j], lengths[k], lengths[l] }));                      }                 }             }         }          var validsolution = (from sln in lst                              sln.value <= 120.00m                                 && sln.isvalid                              select sln).orderbydescending(sln => sln.value)                             .first();          console.writeline(validsolution);      } 

and solution class:

public class solution : icomparable<solution> {      public readonly int maxlengths = 4;      public readonly decimal value;      public readonly decimal maxvalue = 120.00m;      public readonly bool isvalid;     public readonly decimal[] lengths;       public solution(decimal[] lengths)     {          this.lengths = lengths;          if (lengths.length > 4)             throw new argumentexception("too many lengths.");          foreach (var dec in lengths) {             if (dec <= 0.00m)                 throw new argumentexception();              value += dec;          }         isvalid = value < 120.00m;      }             public int compareto(solution other)     {         if (this.value > other.value) return 1;          else if (this.value == other.value) return 0;          else return -1;      }      public override string tostring()     {         var value = string.format("[solution] lengths:");         foreach (var d in lengths) {              value += d + ", ";          }         value += this.value;          return value.tostring();      } }