Question

I have a coding/maths problem that I need help translating into C#. It’s a poker chip calculator that takes in the BuyIn, the number of players and the total amount of chips for each colour (there are x amount of colours) and their value.

It then shows you every possible combination of chips per person to equal the Buy In. The user can then pick the chipset distribution they would like to use. It’s best illustrated with a simple example.

• BuyIn: $10
• Number of Players: 1
• 10 Red Chips, $1 value
• 10 Blue Chips, $2 value
• 10 Green Chips, $5 value

So, the possible combinations are:

R/B/G

• 10/0/0
• 8/1/0
• 6/2/0
• 5/0/1
• 4/3/0
• 2/4/0
• 1/2/1

etc.

I have spent a lot of time trying to come up with an algorithm in C#/.NET to work this out. I am stumbling on the variable factor – there’s usually only 3 or 4 different chips colours in a set, but there could be any amount. If you have more than one player than you have to count up until TotalChips / NumberOfPlayers.

I started off with a loop through all the chips and then looping from 0 up to NumberOfChips for that colour. And this is pretty much where I have spent the last 4 hours… how do I write the code to loop through x amount of chips and check the value of the sum of the chips and add it to a collection if it equals the BuyIn? I need to change my approach radically methinks…

Can anyone put me on the right track on how to solve this please? Pseudo code would work – thank you for any advice!

The below is my attempt so far – it’s hopeless (and wont compile, just an example to show you my thought process so far) – Might be better not to look at it as it might biased you on a solution…

   private void SplitChips(List<ChipSuggestion> suggestions)
    {

        decimal valueRequired = (decimal)txtBuyIn.Value;
        decimal checkTotal = 0;
        ChipSuggestion suggestion;

        //loop through each colour
        foreach (Chip chip in (PagedCollectionView)gridChips.ItemsSource)
        {
                //for each value, loop through them all again
                foreach (Chip currentChip in (PagedCollectionView)gridChips.ItemsSource)
                {
                    //start at 0 and go all the way up
                    for (int i = 0; i < chip.TotalChipsInChipset; i++)
                    {
                        checkTotal = currentChip.ChipValue * i;

                        //if it is greater than than ignore and stop
                        if (checkTotal > valueRequired)
                        {
                            break;
                        }
                        else
                        {
                            //if it is equal to then this is a match
                            if (checkTotal == valueRequired)
                            {
                                suggestion = new ChipSuggestion();
                                suggestion.SuggestionName = "Suggestion";

                                chipRed.NumberPerPlayer = i;
                                suggestion.Chips.Add(chipRed);

                                chipBlue.NumberPerPlayer = y;
                                suggestion.Chips.Add(chipBlue);

                                chipGreen.NumberPerPlayer = 0;
                                suggestion.Chips.Add(chipGreen);

                                //add this to the Suggestion
                                suggestions.Add(suggestion);
                                break;
                            }


                    }
                }
            }
        }
    }

Answer 1

Here’s an implementation that reads the number of chips, the chips (their worth and amount) and the buyin and displays the results in your example format. I have explained it through comments, let me know if you have any questions.

class Test
{
    static int buyIn; 
    static int numChips;
    static List<int> chips = new List<int>(); // chips[i] = value of chips of color i
    static List<int> amountOfChips = new List<int>(); // amountOfChips[i] = number of chips of color i

    static void generateSolutions(int sum, int[] solutions, int last)
    {
        if (sum > buyIn) // our sum is too big, return
            return;

        if (sum == buyIn) // our sum is just right, print the solution
        {
            for (int i = 0; i < chips.Count; ++i)
                Console.Write("{0}/", solutions[i]);
            Console.WriteLine();

            return; // and return
        }

        for (int i = last; i < chips.Count; ++i) // try adding another chip with the same value as the one added at the last step. 
                                                 // this ensures that no duplicate solutions will be generated, since we impose an order of generation
            if (amountOfChips[i] != 0)
            {
                --amountOfChips[i]; // decrease the amount of chips
                ++solutions[i]; // increase the number of times chip i has been used

                generateSolutions(sum + chips[i], solutions, i); // recursive call

                ++amountOfChips[i]; // (one of) chip i is no longer used
                --solutions[i]; // so it's no longer part of the solution either
            }
    }

    static void Main()
    {
        Console.WriteLine("Enter the buyin:");
        buyIn = int.Parse(Console.ReadLine());
        Console.WriteLine("Enter the number of chips types:");
        numChips = int.Parse(Console.ReadLine());
        Console.WriteLine("Enter {0} chips values:", numChips);
        for (int i = 0; i < numChips; ++i)
            chips.Add(int.Parse(Console.ReadLine()));

        Console.WriteLine("Enter {0} chips amounts:", numChips);
        for (int i = 0; i < numChips; ++i)
            amountOfChips.Add(int.Parse(Console.ReadLine()));

        int[] solutions = new int[numChips];

        generateSolutions(0, solutions, 0);
    }
} 

Enter the buyin:
10
Enter the number of chips types:
3
Enter 3 chips values:
1
2
5
Enter 3 chips amounts:
10
10
10
10/0/0/
8/1/0/
6/2/0/
5/0/1/
4/3/0/
3/1/1/
2/4/0/
1/2/1/
0/5/0/
0/0/2/