Computing target number from numbers in a set

Question

I\'m working on a homework problem that asks me this:

Tiven a finite set of numbers, and a target number, find if the set can be used to calculate the target number

Answer 1

Well, you didn't mention efficiency so I'm going to post a really brute force solution and let you optimize it if you want to. Since you can have parantheses, it's easy to brute force it using Reverse Polish Notation:

First of all, if your set has n numbers, you must use exactly n - 1 operators. So your solution will be given by a sequence of 2n - 1 symbols from {{your given set}, {*, /, +, -}}

st = a stack of length 2n - 1
n = numbers in your set
a = your set, to which you add *, /, +, -
v[i] = 1 if the NUMBER i has been used before, 0 otherwise

void go(int k)
{
  if ( k > 2n - 1 ) 
  {
    // eval st as described on Wikipedia. 
    // Careful though, it might not be valid, so you'll have to check that it is   
    // if it evals to your target value great, you can build your target from the given numbers. Otherwise, go on.

    return;
  }

  for ( each symbol x in a )
    if ( x isn't a number or x is a number but v[x] isn't 1 )
    {
      st[k] = x;
      if ( x is a number )
        v[x] = 1;

      go(k + 1);
    }
}