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

Here's some Python code to get you started: it just prints all the possible expressions, without worrying too much about redundancy. You'd need to modify it to evaluate expressions and compare to the target number, rather than simply printing them.

The basic idea is: given a set S of numbers, partition S into two subsets left and right in all possible ways (where we don't care about the order or the elements in left and right), such that left and right are both nonempty. Now for each of these partitions, find all ways of combining the elements in left (recursively!), and similarly for right, and combine the two resulting values with all possible operators. The recursion bottoms out when a set has just one element, in which case there's only one value possible.

Even if you don't know Python, the expressions function should be reasonably easy to follow; the splittings function contains some Python oddities, but all it does is to find all the partitions of the list l into left and right pieces.

def splittings(l):
    n = len(l)
    for i in xrange(2**n):
        left = [e for b, e in enumerate(l) if i & 2**b]
        right = [e for b, e in enumerate(l) if not i & 2**b]
        yield left, right

def expressions(l):
    if len(l) == 1:
        yield l[0]
    else:    
        for left, right in splittings(l):
            if not left or not right:
                continue
            for el in expressions(left):
                for er in expressions(right):
                    for operator in '+-*/':
                        yield '(' + el + operator + er + ')'

for x in expressions('1234'):
    print x