70.Climbing Stairs

【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

假設你正在爬樓梯。需要n步你才能到達樓頂。

每次你可以爬1 或2 個台階。你有多少種不同的方法可以爬到樓頂呢？

注意：給定n是一個正整數。

【思路】

費式數列

【解法】

☆JAVA

    public int climbStairs(int n) {
        int[] a = new int[n + 1];
        a[0] = 1;
        a[1] = 1;
        for (int i = 2; i <= n; ++i) {
            a[i] = a[i - 1] + a[i - 2];
        }
        return a[n];
    }