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

To try and answer your first question, why it returns 1 instead of 0, say you're looking at a stair with 2 steps in total, the recursive call then becomes:

countWaysDP(2 - 1, map) + countWaysDP(2 - 2, map) + countWaysDP(2 - 3, map);

The second recursive call is the one where n becomes zero, that's when we have found a successful path, because from 2 steps, there's obviously a path of taking 2 steps. Now, if you write as you suggested:

n == 1: return 1 

you would not accept taking two steps from the two stepped stair! What the statement means is that you only count the path if it ends with a single step!