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

Generally speaking, when you need to do something recursively it helps to start from the "bottom" and think your way up. Consider: You have a set S of n numbers {a,b,c,...}, and a set of four operations {+,-,*,/}. Let's call your recursive function that operates on the set F(S)

• If n is 1, then F(S) will just be that number.
• If n is 2, F(S) can be eight things:
  • pick your left-hand number from S (2 choices)
  • then pick an operation to apply (4 choices)
  • your right-hand number will be whatever is left in the set
• Now, you can generalize from the n=2 case:
  • Pick a number x from S to be the left-hand operand (n choices)
  • Pick an operation to apply
  • your right hand number will be F(S-x)

I'll let you take it from here. :)

edit: Mark poses a valid criticism; the above method won't get absolutely everything. To fix that problem, you need to think about it in a slightly different way:

• At each step, you first pick an operation (4 choices), and then
• partition S into two sets, for the left and right hand operands,
• and recursively apply F to both partitions

Finding all partitions of a set into 2 parts isn't trivial itself, though.