Problem:
Score : 200 points

Problem Statement

Snuke has come to a store that sells boxes containing balls. The store sells the following three kinds of boxes:

Red boxes, each containing R red balls

Green boxes, each containing G green balls

Blue boxes, each containing B blue balls

Snuke wants to get a total of exactly N balls by buying r red boxes, g green boxes and b blue boxes.
How many triples of non-negative integers (r,g,b) achieve this?

Constraints

All values in input are integers.

1 \leq R,G,B,N \leq 3000

Input

Input is given from Standard Input in the following format:

R G B N

Output

Print the answer.

Sample Input 1

1 2 3 4

Sample Output 1

4

Four triples achieve the objective, as follows:

(4,0,0)

(2,1,0)

(1,0,1)

(0,2,0)

Sample Input 2

13 1 4 3000

Sample Output 2

87058

Solution in C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Diagnostics;
using System.IO;
using System.Linq;

namespace MyProject
{
    class Program
    {
        static void Main(string[] args)
        {
#if Local
            var sw = new Stopwatch();
            sw.Start();
            Console.SetIn(new StreamReader("input.in"));
#endif

            var solver = new Solver();
            solver.Solve();
#if Local
            Console.WriteLine($"{sw.ElapsedMilliseconds}ms");
#endif
        }
    }

    class Solver
    {
        private int R;
        private int G;
        private int B;

        private Dictionary<int, int> gbNumTable = new Dictionary<int, int>();
        private Dictionary<int, int> bNumTable = new Dictionary<int, int>();

        private int GetGBNum(int gbNum)
        {
            if (gbNumTable.ContainsKey(gbNum))
            {
                return gbNumTable[gbNum];
            }

            var answer = 0;
            for (int j = 0; j * this.G <= gbNum; j++)
            {
                var bNum = gbNum - (j * this.G);
                if (bNum == 0)
                {
                    answer++;
                    continue;
                }

                answer += this.GetBNum(bNum);
            }

            this.gbNumTable[gbNum] = answer;
            return answer;
        }

        private int GetBNum(int bNum)
        {
            if (bNumTable.ContainsKey(bNum))
            {
                return bNumTable[bNum];
            }

            var answer = 0;
            for (int k = 0; k * this.B <= bNum; k++)
            {
                var num = bNum - (k * this.B);
                if (num == 0)
                {
                    answer++;
                }
            }

            this.bNumTable[bNum] = answer;
            return answer;
        }

        public void Solve()
        {
            var inputs = Console.ReadLine().Split().Select(x => int.Parse(x)).ToArray();
            this.R = inputs[0];
            this.G = inputs[1];
            this.B = inputs[2];
            var N = inputs[3];

            var answer = 0;
            for (int i = 0; i * R <= N; i++)
            {
                var gbNum = N - (i * R);
                if (gbNum == 0)
                {
                    answer++;
                    continue;
                }

                answer += this.GetGBNum(gbNum);
            }

            Console.WriteLine(answer.ToString());
        }
    }
}