Fibonacci number - jump stairs

A description of the subject

We all know that Fibonacci number, and now asked to enter an integer n, you output the n-th Fibonacci number Fibonacci sequence of item (from 0, the first 0 is 0).

    def Fibonacci(self, n):
        res = [0, 1]
        while len(res) <= n:
            res.append(res[-1]+res[-2])
        return res[n]

　　

Title Description two

A frog can jump on a Class 1 level, you can also hop on level 2. The frog jumped seeking a total of n grade level how many jumps (the order of different calculation different results).

# -*- coding:utf-8 -*-
class Solution:
    def jumpFloor(self, number):
        a = [0, 1, 2]
        while len(a) <=number:
            a.append(a[-1] + a[-2])
        return a[number]

The 3 title

A frog can jump on a Class 1 level, you can also hop on level 2 ...... n It can also jump on stage. The frog jumped seeking a total of n grade level how many jumps.

Analysis:
Because the n steps, the first step there are n kinds of jump method: 1 skip, skip 2 to n stages hop
skip 1, the remaining level n-1, the remaining jumps is f (n-1 )
skip 2, the remaining n-2 stage, the remaining jumps is F (n-2)
so that f (n) = f (n -1) + f (n-2) + ... + f ( 1)
since f (n-1) = f (n-2) + f (n-3) + ... + f (1)

Therefore, f (n) = 2 * f (n-1)

    def jumpFloorII(self, number):
        if number <= 1:
            return number
        return 2 * self.jumpFloorII(number - 1)