Question

I’m looking for an algorithm to calculate total cost of licenses purchased based on the “FogBugz for your server” pricing scheme (http://www.fogcreek.com/FogBugz/PriceList.html).

Fogbugz pricing is:

• 1 License $299
• 5 License Pack $999
• 10 License Pack $1,899
• 20 License Pack $3,499
• 50 License Pack $7,999

If you ask a quote for let’s say 136 licenses they calculate it as $22,694.

How can I do this in C# or LINQ?

Any help will be appreciated.

Answer 1

The accepted answer, whilst an elegant piece of code from a programmer’s point of view, does not give the best possible price for the customer and therefore might not be an elegant solution from the customer’s point of view. For example when n = 4, the accepted answer gives $1196, but a customer would obviously prefer to choose the 5 license pack and pay just $999 instead.

It is possible to construct an algorithm which can calculate the minimum price possible that the customer can pay to purchase their required number of licenses. One way of doing this is to use dynamic programming. I think something like this might do the trick:

int calculatePrice(int n, Dictionary<int, int> prices)
{

    int[] best = new int[n + prices.Keys.Max()];
    for (int i = 1; i < best.Length; ++i)
    {
        best[i] = int.MaxValue;
        foreach (int amount in prices.Keys.Where(x => x <= i))
        {
            best[i] = Math.Min(best[i],
                best[i - amount] + prices[amount]);
        }
    }
    return best.Skip(n).Min();
}

void Run()
{
    Dictionary<int, int> prices = new Dictionary<int, int> {
        { 1, 299 },
        { 5, 999 },
        { 10, 1899 },
        { 20, 3499 },
        { 50, 7999 }
    };

    Console.WriteLine(calculatePrice(136, prices));
    Console.WriteLine(calculatePrice(4, prices));
}

Output:

22694
999

---

Update Producing a breakdown is a little more complicated, but I definitely think it will be beneficial for your customers. You could do it something like this (assuming printing to the console, although a real program would probably output to a web page):

using System;
using System.Linq;
using System.Collections.Generic;

class Program
{
    static Dictionary<int, int> prices = new Dictionary<int, int> {
            { 1, 299 },
            { 5, 999 },
            { 10, 1899 },
            { 20, 3499 },
            { 50, 7999 }
    };

    class Bundle
    {
        public int Price;
        public Dictionary<int, int> Licenses;
    }

    Bundle getBestBundle(int n, Dictionary<int, int> prices)
    {
        Bundle[] best = new Bundle[n + prices.Keys.Max()];
        best[0] = new Bundle
        {
            Price = 0,
            Licenses = new Dictionary<int, int>()
        };

        for (int i = 1; i < best.Length; ++i)
        {
            best[i] = null;
            foreach (int amount in prices.Keys.Where(x => x <= i))
            {
                Bundle bundle = new Bundle
                {
                     Price = best[i - amount].Price + prices[amount],
                     Licenses = new Dictionary<int,int>(best[i - amount].Licenses)
                };

                int count = 0;
                bundle.Licenses.TryGetValue(amount, out count);
                bundle.Licenses[amount] = count + 1;

                if (best[i] == null || best[i].Price > bundle.Price)
                {
                    best[i] = bundle;
                }
            }
        }
        return best.Skip(n).OrderBy(x => x.Price).First();
    }

    void printBreakdown(Bundle bundle)
    {
        foreach (var kvp in bundle.Licenses) {
            Console.WriteLine("{0,2} * {1,2} {2,-5} @ ${3,4} = ${4,6}",
               kvp.Value,
                kvp.Key,
                kvp.Key == 1 ? "user" : "users",
                prices[kvp.Key],
                kvp.Value * prices[kvp.Key]);
        }

        int totalUsers = bundle.Licenses.Sum(kvp => kvp.Key * kvp.Value);

        Console.WriteLine("-------------------------------");
        Console.WriteLine("{0,7} {1,-5}           ${2,6}",
            totalUsers,
            totalUsers == 1 ? "user" : "users",
            bundle.Price);
    }

    void Run()
    {
        Console.WriteLine("n = 136");
        Console.WriteLine();
        printBreakdown(getBestBundle(136, prices));
        Console.WriteLine();
        Console.WriteLine();
        Console.WriteLine("n = 4");
        Console.WriteLine();
        printBreakdown(getBestBundle(4, prices));
    }

    static void Main(string[] args)
    {
        new Program().Run();
    }
}

Output:

n = 136

 2 * 50 users @ $7999 = $ 15998
 1 * 20 users @ $3499 = $  3499
 1 * 10 users @ $1899 = $  1899
 1 *  5 users @ $ 999 = $   999
 1 *  1 user  @ $ 299 = $   299
-------------------------------
    136 users           $ 22694


n = 4

 1 *  5 users @ $ 999 = $   999
-------------------------------
      5 users           $   999