Climbing Stairs

https://leetcode.com/problems/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?

自己的超时程序：

public class Solution {
    private static int[]db;
    public static int climbStairs(int n) {
        db=new int[n+1];
        F(0,n);
        return db[n];
    }
    public static void F(int i,int n){
    db[i]++;
    if(i>=n){return;}
    F(i+1,n);
    if(i>=n-1){return;}
    F(i+2,n);
    }
    public static void main(String[]args){
    System.out.println(climbStairs(44));
    }
}

斐波那契数列求解：

public int climbStairs(int n) {
    // bottom cases
    if(n <= 0) return 0;
    if(n == 1) return 1;
    if(n == 2) return 2;

    int one_step_before = 1;
    int two_steps_before = 2;
    int all_ways = 0;

    for(int i=2; i<n; i++){
        all_ways = one_step_before + two_steps_before;
        one_step_before = two_steps_before;
        two_steps_before = all_ways;
    }
    return all_ways;
}   

动态规划求解：

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