No70. Climbing Stairs(Python)

題目：

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：

    當n=1時，有一種路徑；當n=2時，有兩種路徑；當n=3時，有三種路徑。當n=4時，有五種，n=5時有八種。可見，n的當前項等於前兩項相加之和。應該把每項的值存放在list集合中，首先先對list集合的數值進行初始化，對第一項和第二項賦值爲1，從第三項開始的每一項都等於前兩項相加之和。最後，返回list集合中的最後一項。

代碼：

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]