A child is running up a staircase with N steps, and can hop either 1 step,2steps,3 steps at a time. Count how many possible ways the child can run up

 

A child is running up a staircase with N steps, and can hop either 1 step,2steps,3 steps at a time. Count how many possible ways the child can run up the stairs.

 

 class Upstaircase
    {
        static void Main(string[] args)
        {
            /* Enter your code here. Read input from STDIN. Print output to STDOUT */

            //string line1 = System.Console.ReadLine().Trim();

            System.Console.WriteLine(Upstaircase.countWaysDP(2,new int[100]));
            System.Console.WriteLine(Upstaircase.countWaysDP(3, new int[100]));
            System.Console.WriteLine(Upstaircase.countWaysDP(4, new int[100]));
            System.Console.WriteLine(Upstaircase.countWaysDP(5, new int[100]));
            System.Console.WriteLine(Upstaircase.countWaysDP(36, new int[100]));
            System.Console.WriteLine(Upstaircase.countWaysDP(38, new int[100]));
            Console.Read();

        }
　　　　　　//O(3^n). exponential
        public static int countWays(int n)
        {
            if (n<0)
            {
                return 0;
            }
            else if (n==0)
            {
                return 1;
            }
            else
            {
                return countWays(n - 1) + countWays(n - 2) + countWays(n - 3);
            }

        }
        //DP: dynamic programing.   up to 37 will overflowed.  Using Long type is just delay but not resolve it.
        public static int countWaysDP(int n,int[] map)
        {
            if (n < 0)
            {
                return 0;
            }
            else if (n == 0)
            {
                return 1;
            }
            else if (map[n] > 0)
            {
                return map[n];
            }
            else
            {
                map[n] = countWaysDP(n - 1, map) + countWaysDP(n - 2,map) + countWaysDP(n - 3,map);
                return map[n];
            }

        }