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This article mainly explains "how the Python algorithm solves the staircase problem". The content of the explanation is simple and clear, and it is easy to learn and understand. Please follow the editor's train of thought to study and learn "how to solve the staircase problem with Python algorithm".

There is a staircase with N steps. You can climb one or two steps at a time.

Given N, write a function that returns the number of ways to climb the stairs. The order of steps is important.

For example, if N is 4, there are five ways:

1,1,1,1

2,1,1

1,2,1

1,1,2

2,2

What if instead of being allowed to climb 1 or 2 steps at a time, you can use any number in the positive integer X set to climb the stairs? For example, if X = {1 ~ 3 ~ 5}, it means climbing 1 ~ 3 or 5 stairs at a time.

Solution

It's always a good idea to start with some test cases. Let's start with a small case and see if we can find some pattern.

N = 1, 1 way to climb the building: [1]

N = 2Jing two ways to climb the building: [1Jing 1], [2]

N = 3Jing three ways to climb the building: [1Jing 2], [1JI Jol 1], [2Jing 1]

N = 4, there are five ways to climb the building: [1magin 1pyrrine 2], [2magent2], [1mem2pence1], [1min1jingljin1], [2mage1pjen1]

Did you notice anything? See N = 3, the number of methods to climb 3 stairs is 3, based on N = 1 and N = 2. What's the relationship?

The two ways to climb N = 3 are to first reach N = 1, then climb 2 steps, or reach N = 2 and then climb 1 step. So f (3) = f (2) + f (1).

Is this true for N = 4? Yes, this is also true. Because we can only climb four steps when we reach the third step and then climb one more step, or two steps after the second step. So f (4) = f (3) + f (2).

So the relation is as follows: F (n) = f (n-1) + f (n-2), and f (1) = 1 and f (2) = 2. This is the Fibonacci series.

Def fibonacci (n): if n

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