Question

I’ve got a real problem (it’s not homework, you can check my profile). I need to parse data whose formatting is not under my control.

The data look like this:

6,852:6,100,752

So there’s first a number made of up to 9 digits, followed by a colon.

Then I know for sure that, after the colon:

• there’s at least one valid combination of numbers that add up to the number before the column
• I know exactly how many numbers add up to the number before the colon (two in this case, but it can go as high as ten numbers)

In this case, 6852 is 6100 + 752.

My problem: I need to find these numbers (in this example, 6100 + 752).

It is unfortunate that in the data I’m forced to parse, the separator between the numbers (the comma) is also the separator used inside the number themselves (6100 is written as 6,100).

Once again: that unfortunate formatting is not under my control and, once again, this is not homework.

I need to solve this for up to 10 numbers that need to add up.

Here’s an example with three numbers adding up to 6855:

6,855:360,6,175,320

I fear that there are cases where there would be two possible different solutions. HOWEVER if I get a solution that works “in most cases” it would be enough.

How do you typically solve such a problem in a C-style bracket language?

Answer 1

Recursive implementation (pseudo code):

int total;  // The total read before the colon

// Takes the list of tokens as integers after the colon
// tokens is the set of tokens left to analyse,
// partialList is the partial list of numbers built so far
// sum is the sum of numbers in partialList
// Aggregate takes 2 ints XXX and YYY and returns XXX,YYY (= XXX*1000+YYY)
function getNumbers(tokens, sum, partialList) =
    if isEmpty(tokens)
         if sum = total return partialList
         else return null  // Got to the end with the wrong sum
    var result1 = getNumbers(tokens[1:end], sum+token[0], Add(partialList, tokens[0]))
    var result2 = getNumbers(tokens[2:end], sum+Aggregate(token[0], token[1]), Append(partialList, Aggregate(tokens[0], tokens[1])))
    if result1 <> null return result1
    if result2 <> null return result2
    return null  // No solution overall

You can do a lot better from different points of view, like tail recursion, pruning (you can have XXX,YYY only if YYY has 3 digits)… but this may work well enough for your app.
Divide-and-conquer would make for a nice improvement.