added staircase problem

staircase.cpp

@@ -0,0 +1,39 @@
+
+//Using Memoization
+long helper(int n,long *arr)
+{
+    if(n<=1)
+        return 1;
+    if(n==2)
+        return 2;
+    if(arr[n]!=-1)
+        return arr[n];
+    arr[n]= helper(n-1,arr)+helper(n-2,arr)+helper(n-3,arr);
+    return arr[n];
+}
+
+
+
+
+long staircase(int n)
+{
+    long *arr=new long[n+1];
+    for(int i=0;i<=n;i++)
+        arr[i]=-1;
+    return helper(n,arr);
+
+}
+
+
+//Using DP
+long staircase(int n)
+{
+    long *arr=new long[n+1];
+  	arr[0]=arr[1]=1;
+    arr[2]=2;
+    for(int i=3;i<=n;i++)
+    {
+        arr[i]=arr[i-1]+arr[i-2]+arr[i-3];
+    }	
+    return arr[n];
+}