有n阶楼梯，每次走一步或者两步，问有几种走法到第n阶

最近面试 的时候遇到的，记个笔记。

/**
 * 斐波那契数列
 * //0 1 1 2 3 5 8 13 21 34
 * f(n) = f(n-2)+f(n-1)
 */
public class Fibonaccisequence {
    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        System.out.println("请输入有几阶楼梯:");
        short i = scanner.nextShort();
        Fibonaccisequence fibonaccisequence = new Fibonaccisequence();
        Short kinds = fibonaccisequence.kinds((short) i);

        System.out.println("一共有"+kinds+"种走法");

    }
    
    private Short kinds(short i){
        //f(n)=f(n-1)+f(n-2)
        //将斐波那列数放入一个有序链表中
        List<Short> list = new ArrayList<Short>();
        int m;
        if (list.isEmpty()){
            list.add((short) 0);
            list.add((short) 1);
        }
        //从下标等于2开始循环
        for ( m = 2 ;m<=i+1;m++){
            list.add( (short) (list.get(m - 2) + list.get(m - 1)));
        }
        return list.get(m-1);
    }
}

运行结果：

Connected to the target VM, address: '127.0.0.1:63097', transport: 'socket'
请输入有几阶楼梯:
4
一共有5种走法