Generate a number by using a given list of numbers and arithmetic operators

Question

You are given a list of numbers L = [17, 5, 9, 17, 59, 14], a bag of operators O = {+:7, -:3, *:5, /:1} and a number N = 569.

Task

Output an equation that uses all numbers in L on the left-hand side and only the number N on the right-hand side. If this is not possible, output False. Example solution:

59*(17-5)-9*17+14 = 569

Limitations and Clarification

• You may not concatenate numbers ([13,37] may not be used as 1337)
• Only natural numbers and zero will appear in L.
• The order in L doesn't matter.
• You must use all numbers in L.
• Only the operators +,-,*,/ will appear in O.
• O can have more operators than you need, but at least |L|-1 operators
• You may use each operator any number of times up to the value in O.
• All four operations in O are the standard mathematical operations; in particular, / is normal division with exact fractions.

Points

• The less points, the better
• Every character of your code gives you one point

You have to provide an un-golfed version that is easy to read.

Background

A similar question was asked on Stack Overflow. I thought it might be an interesting code-golf challenge.

Computational Complexity

As Peter Taylor said in the comments, you can solve subset sum with this:

1. You have an instance of subset sum (hence a set S of integers and a number x)
2. L := S + [0, ..., 0] (|S| times a zero), N := x, O := {+:|S|-1, *: |S| - 1, /:0, -: 0}
3. Now solve this instance of my problem
4. The solution for subset sum is the numbers of S that don't get multiplied with zero.

If you find an Algorithm that is better than O(2^n), you prove that P=NP. As P vs NP is a Millennium Prize Problem and hence worth 1,000,000 US-Dollar, it is very unlikely that somebody finds a solution for this. So I removed this part of the ranking.

Test cases

The following are not the only valid answers, other solutions exist, and are permitted:

• ([17,5,9,17,59,14], {+:7, -:3, *:5, /:1}, 569)
  => 59 * (17-5)- 9 * 17 + 14 = 569
• ([2,2], {'+':3, '-':3, '*':3, '/':3}, 1)
  => 2/2 = 1
• ([2,3,5,7,10,0,0,0,0,0,0,0], {'+':20, '-':20, '*':20, '/':20}, 16)
  => 5+10-2*3+7+0+0+0+0+0+0+0 = 16
• ([2,3,5,7,10,0,0,0,0,0,0,0], {'+':20, '-':20, '*':20, '/':20}, 15)
  => 5+10+0*(2+3+7)+0+0+0+0+0+0 = 15

Answer 1

Python 2.7 / 478 chars

L=[17,5,9,17,59,14]
O={'+':7,'-':3,'*':5,'/':1}
N=569
P=eval("{'+l+y,'-l-y,'*l*y,'/l/y}".replace('l',"':lambda x,y:x"))
def S(R,T):
 if len(T)>1:
  c,d=y=T.pop();a,b=x=T.pop()
  for o in O:
   if O[o]>0 and(o!='/'or y[0]):
    T+=[(P[o](a, c),'('+b+o+d+')')];O[o]-=1
    if S(R,T):return 1
    O[o]+=1;T.pop()
  T+=[x,y]
 elif not R:
  v,r=T[0]
  if v==N:print r
  return v==N
 for x in R[:]:
  R.remove(x);T+=[x]
  if S(R,T):return 1
  T.pop();R+=[x]
S([(x,`x`)for x in L],[])

The main idea is to use postfix form of an expression to search. For example, 2*(3+4) in postfix form will be 234+*. So the problem become finding a partly permutation of L+O that evalates to N.

The following version is the ungolfed version. The stack stk looks like [(5, '5'), (2, '5-3', (10, ((4+2)+(2*(4/2))))].

L = [17, 5, 9, 17, 59, 14]
O = {'+':7, '-':3, '*':5, '/':1} 
N = 569

P = {'+':lambda x,y:x+y,
     '-':lambda x,y:x-y,
     '*':lambda x,y:x*y,
     '/':lambda x,y:x/y}

def postfix_search(rest, stk):
    if len(stk) >= 2:
        y = (v2, r2) = stk.pop()
        x = (v1, r1) = stk.pop()
        for opr in O:
            if O[opr] > 0 and not (opr == '/' and v2 == 0):
                stk += [(P[opr](v1, v2), '('+r1+opr+r2+')')]
                O[opr] -= 1
                if postfix_search(rest, stk): return 1
                O[opr] += 1
                stk.pop()
        stk += [x, y]
    elif not rest:
        v, r = stk[0]
        if v == N: print(r)
        return v == N
    for x in list(rest):
        rest.remove(x)
        stk += [x]
        if postfix_search(rest, stk):
            return True
        stk.pop()
        rest += [x]
postfix_search(list(zip(L, map(str, L))), [])