Recursion on staircase

Question

I\'m trying to understand the solution provided in a book to the following question:

\"A child is running up a staircase with n steps and can hop either 1 step, 2 st

Answer 1

Answer 2: A Static method means the function doesn't need any information from the object.

The function just takes an input (in the parameters), processes it and returns something. When you don't see any "this" in a function, you can set it as static.

Non-static methods usually read some properties (this-variables) and/or store values in some properties.

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Answer 1: I converted this to javascript, just to show what happens.

http://jsbin.com/linake/1/edit?html,js,output

I guess this is the point. Recursion often works opposite to what you could expect. It often returns values in the opposite order. For 5 staircases: First it returns n=1; then n=2, ... up to n=5;
n=5 has to wait until n=4 is ready, n=4 has to wait until n=3 is ready, ...

So here is your n=0 and n<0: The first return of the function has n=1; that calls this

map[n] = countWaysDP(n - 1, map) + countWaysDP(n - 2, map) + countWaysDP(n - 3, map)

So that is

map[n] = countWaysDP(0, map) + countWaysDP(-1, map) + countWaysDP(-2, map)

There countWaysDP(0, map) returns 1; the other terms are meaningless, so they return 0. That's why there are these clauses for n==0 and n<0

notice, you can add

+ countWaysDP(n - 4, map)

if you want to see what happens when the child can also jump 4 cases

Also notice: As I said in answer 2, you see this function doesn't require any object. It just processes data and returns something. So, in your case, having this function in your class is useful because your functions are grouped (they 're not just loose functions scattered around your script), but making it static means the compiler doesn't have to carry around the memory of the object (especially the properties of the object).

I hope this makes sense. There are surely people that can give more accurate answers; I'm a bit out of my element answering this (I mostly do javascript).