2019-11-02 12:07:41 +08:00
|
|
|
|
# 10.3 跳台阶
|
|
|
|
|
|
|
|
|
|
|
|
[NowCoder](https://www.nowcoder.com/practice/8c82a5b80378478f9484d87d1c5f12a4?tpId=13&tqId=11161&tPage=1&rp=1&ru=/ta/coding-interviews&qru=/ta/coding-interviews/question-ranking&from=cyc_github)
|
|
|
|
|
|
|
|
|
|
|
|
## 题目描述
|
|
|
|
|
|
|
|
|
|
|
|
一只青蛙一次可以跳上 1 级台阶，也可以跳上 2 级。求该青蛙跳上一个 n 级的台阶总共有多少种跳法。
|
|
|
|
|
|
|
2019-11-02 17:33:10 +08:00
|
|
|
|
<div align="center"> <img src="https://cs-notes-1256109796.cos.ap-guangzhou.myqcloud.com/9dae7475-934f-42e5-b3b3-12724337170a.png" width="380px"> </div><br>
|
2019-11-02 12:07:41 +08:00
|
|
|
|
|
|
|
|
|
|
## 解题思路
|
|
|
|
|
|
|
|
|
|
|
|
当 n = 1 时，只有一种跳法：
|
|
|
|
|
|
|
2019-11-02 17:33:10 +08:00
|
|
|
|
<div align="center"> <img src="https://cs-notes-1256109796.cos.ap-guangzhou.myqcloud.com/72aac98a-d5df-4bfa-a71a-4bb16a87474c.png" width="250px"> </div><br>
|
2019-11-02 12:07:41 +08:00
|
|
|
|
|
|
|
|
|
|
当 n = 2 时，有两种跳法：
|
|
|
|
|
|
|
2019-11-02 17:33:10 +08:00
|
|
|
|
<div align="center"> <img src="https://cs-notes-1256109796.cos.ap-guangzhou.myqcloud.com/1b80288d-1b35-4cd3-aa17-7e27ab9a2389.png" width="300px"> </div><br>
|
2019-11-02 12:07:41 +08:00
|
|
|
|
|
|
|
|
|
|
跳 n 阶台阶，可以先跳 1 阶台阶，再跳 n-1 阶台阶；或者先跳 2 阶台阶，再跳 n-2 阶台阶。而 n-1 和 n-2 阶台阶的跳法可以看成子问题，该问题的递推公式为：
|
|
|
|
|
|
|
2019-11-02 17:33:10 +08:00
|
|
|
|
<div align="center"> <img src="https://cs-notes-1256109796.cos.ap-guangzhou.myqcloud.com/508c6e52-9f93-44ed-b6b9-e69050e14807.jpg" width="350px"> </div><br>
|
2019-11-02 12:07:41 +08:00
|
|
|
|
|
|
|
|
|
|
```java
|
|
|
|
|
|
public int JumpFloor(int n) {
|
|
|
|
|
|
if (n <= 2)
|
|
|
|
|
|
return n;
|
|
|
|
|
|
int pre2 = 1, pre1 = 2;
|
|
|
|
|
|
int result = 0;
|
|
|
|
|
|
for (int i = 2; i < n; i++) {
|
|
|
|
|
|
result = pre2 + pre1;
|
|
|
|
|
|
pre2 = pre1;
|
|
|
|
|
|
pre1 = result;
|
|
|
|
|
|
}
|
|
|
|
|
|
return result;
|
|
|
|
|
|
}
|
|
|
|
|
|
```
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
2019-11-02 17:33:10 +08:00
|
|
|
|
<div align="center"><img width="320px" src="https://cs-notes-1256109796.cos.ap-guangzhou.myqcloud.com/githubio/公众号二维码-2.png"></img></div>
|
