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 (GCC 5.4.1) (judge verdict: Time Limit Exceeded)

#include <stdio.h>

int main(int argc, const char * argv[]) {
    
    int R = 0;
    int G = 0;
    int B = 0;
    int N = 0;

    scanf("%d",&R);
    scanf("%d",&G);
    scanf("%d",&B);
    scanf("%d",&N);
    
    int count=0;
    int r=0;
    int g=0;
    int b=0;
    
    if(R==1){
        r=3000;
    }else if(R==2){
        r=1500;
    }else if(R==3){
        r=1000;
    }else if(R==4){
        r=750;
    }else if(R==5){
        r=600;
    }else{
        for (int i=1; i<=3001; i++) {
            if (i*R > N) {
                r=i-1;
                break;
            }
        }
    }
    
    if(G==1){
        g=3000;
    }else if(G==2){
        g=1500;
    }else if(G==3){
        g=1000;
    }else if(G==4){
        g=750;
    }else if(G==5){
        g=600;
    }else{
        for (int i=1; i<=3001; i++) {
            if (i*G > N) {
                g=i-1;
                break;
            }
        }
    }
 
    if(B==1){
        b=3000;
    }else if(B==2){
        b=1500;
    }else if(B==3){
        b=1000;
    }else if(B==4){
        b=750;
    }else if(B==5){
        b=600;
    }else{
        for (int i=1; i<=3001; i++) {
            if (i*B > N) {
                b=i-1;
                break;
            }
        }
    }
    
    int tmp = 0;
    int TMP = 0;
    if (R < G) {
        tmp = r;
        TMP = R;
        r = g;
        R = G;
        g = tmp;
        G  = TMP;
    }
    if (G < B) {
        tmp = g;
        TMP = G;
        g = b;
        G = B;
        b = tmp;
        B = TMP;
    }
    if (R < G) {
        tmp = r;
        TMP = R;
        r = g;
        R = G;
        g = tmp;
        G  = TMP;
    }


    int valueA=0;
    int valueB=0;
    
    for (int i = 0; i<=r; i++) {
        valueA = i*R;
        if (N == valueA) {
            count++;
            continue;
        }
        for (int j = 0; j<=g; j++) {
            valueB = (valueA + j*G);
            if(valueB > N){
                break;
            }
            if (N == valueB) {
                count++;
                continue;
            }
            for (int k = 0; k<=b; k++) {
                if (N == (valueB + k*B)) {
                    count++;
                    break;
                }
            }
        }
    }
    printf("%d",count);
}