Climbing Stairs

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?

思路：

簡單的遞推題，由後往前看，到達第n個階梯的方法有兩種，一種是從第n-1個階梯跨一步，一種是從第n-2個階梯一次跨兩步（注意分兩次每次跨一步和上一種情況重複），

所以f(n) = f(n-1)+f(n-2)，代碼如下：

 

 

public class Solution {
    public int climbStairs(int n) {
        if(n == 1||n == 2) {
            return n;
        }
        int a = 1,b = 2,c = 3;
        for(int i = 3;i <= n;i++) {
            c = a + b;
            a = b;
            b = c;
        }
        return c;
    }
}

Python實現：

class Solution(object):
    def climbStairs(self, n):
        """
        :type n: int
        :rtype: int
        """
        if n == 1 or n == 2:
            return n
        a = 1
        b = 2
        n -= 2
        while n > 0:
            t = a + b
            a = b
            b = t
            n -= 1
        return t