Dynamic Programming

public static void main(String[] args) {
        //give N, find the number of different ways to write N as the sum of 1, 3, 4
        // 1. subproblem; 2. relation; 3. the begin data
        // 1. d[n]: n value and the ways d[n]
        // 2. d[n] = d[n-1] + d[n-3] + d[n-4] 
        // 3. d[0],d[1],d[2],d[3]
        int n = 5;
        
        if (n <= 3 && n >= 0) {
            switch (n) {
            case 0:
                System.out.println("Ways: "+1);
                break;
            case 1:
                System.out.println("Ways: "+1);
                break;
            case 2:
                System.out.println("Ways: "+1);
                break;
            case 3:
                System.out.println("Ways: "+2);
                break;
            default:
                break;
            }
            
        } else if (n >= 4) {
            //core
            int[] ways = new int[n+1];
            ways[0]=1;ways[1]=1;ways[2]=1;ways[3]=2;
            for (int i = 4; i <= n; i++) {
                ways[i] = ways[i-1] + ways[i-3] + ways[i-4];
            }
            System.out.println("Ways: " + ways[n]);
        } else {
            System.out.println("N should be >= 0!");
        }
        
    }