Leetcode - Climbing Stairs

[题目]

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] 一维动态规划入门题

 

public class Solution {
    // O(n)空间
    public int climbStairs0(int n) {
        if (n <= 0)
            return 0;
        if (n == 1)
            return 1;
        int[] dp = new int[n + 1];
        dp[1] = 1;
        dp[2] = 2;
        for (int i = 3; i <= n; i++)
            dp[i] = dp[i - 1] + dp[i - 2]; //递推关系式
        return dp[n];
    }
    
     // O(1)空间
     public int climbStairs(int n) {
        if (n <= 0)
            return 0;
        int[] dp = {1, 1, 1};
        for (int i = 2; i <= n; i++) {
            dp[2] = dp[1] + dp[0];
            dp[0] = dp[1];
            dp[1] = dp[2];
        }
        return dp[2];
     }
}