Dynamic Programming - Part1

 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!");
         }

     }