Leetcode Climbing Stairs 爬樓梯

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?

分析：

這道題屬于動态規劃裡可能解個數的題。按照分析動态規劃問題的方法進行分析：

1. 每個狀态f[n]代表上到第n個台階的所有可能個數

2. 每次隻能上1台或2台，所有f[n] = f[n-1] + f[n-2]，即上一台到n還是上兩台到n

3. 開始的狀态f[1] = 1，f[2] = 2

4. 結果為上到第n台的f[n]

Java代碼實作：

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