No70. Climbing Stairs(Python)

题目：

You are climbing a stair case. It takes n steps to reach to the top.

Each time you can either climb 1 or 2 steps. In how many distinct ways can you climb to the top?

Note: Given n will be a positive integer.

Example 1:

Input: 2
Output: 2
Explanation: There are two ways to climb to the top.
1. 1 step + 1 step
2. 2 steps

Example 2:

Input: 3
Output: 3
Explanation: There are three ways to climb to the top.
1. 1 step + 1 step + 1 step
2. 1 step + 2 steps
3. 2 steps + 1 step

思路：

    当n=1时，有一种路径；当n=2时，有两种路径；当n=3时，有三种路径。当n=4时，有五种，n=5时有八种。可见，n的当前项等于前两项相加之和。应该把每项的值存放在list集合中，首先先对list集合的数值进行初始化，对第一项和第二项赋值为1，从第三项开始的每一项都等于前两项相加之和。最后，返回list集合中的最后一项。

代码：

class Solution(object):
    def climbStairs(self,n):
        con = [0]*(n+1)
        con[0] = 1
        con[1] = 1
        i = 2
        while i<= n:
            con[i] = con[i-2]+con[i-1]
            i = i+1
        return con[-1]