leetcode : Climbing Stairs

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.

方法1:  动态规划

方法2:  两个变量（最优解）

方法3: 递归， 最差解

动态规划解法：

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

　　

方法二： 两个变量

public class Solution {
    public int climbStairs(int n) {
        if(n == 0 ) {
            return 0;
        }
        if(n == 1){
            return 1;
        }
       
        int a = 0;
        int b = 1;
        int sum = 0;
        for(int i = 1; i <= n; i++) {
            sum = a + b;
            a = b;
            b = sum;
            
        }
        return sum;
    }
}