100 question _ 23 jump steps

A step has a total of N levels. If you can skip 1 level at a time, you can also skip 2 levels. Calculate and analyze the total number of hops in totalAlgorithmTime complexity.

 

First, consider the simplest situation. If there is only one level, there is obviously only one method to skip. If there are two steps, there are two ways to skip: one is to skip level 1 each time, and the other is to skip level 2 at a time. Now let's discuss the general situation. We regard the jump Method for n-level steps as a function of N and record it as F (n ). When N> 2, there are two different options for the first hop: one is the first hop with only one level. At this time, the number of hops equals to the number of hops for the next n-1 level step, that is F (n-1); another option is the first jump level 2, at this time the number of Jump method is equal to the number of the next step of the N-2 level, that is, F (n-2 ). Therefore, F (n) = f (n-1) + (F-2) of different hops at N-level steps ).

To sum up, get the recursive formula:

From this perspective, we can see that this is actually the Fibonacci series. We have discussed it before. Please click here to view details.