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.

1.遞歸（超時）

public int climbStairs(int n) {
        if (n<=0) return 0;
        if (n==1) return
 
 1;
        if (n==2) return 2;
        return climbStairs(n-1)+climbStairs(n-2);
    }

2.動態規劃

public int climbStairs(int n) {
        if (n == 0 || n == 1 || n == 2) return n;
        int[] dp = new int[n + 1];
        dp[0] = 0;
        dp[1] = 1;
        dp[2] = 2;
        for (int i = 3; i <= n; i++) {
            dp[i] 
 
= dp[i - 1] + dp[i - 2];
        }
        return dp[n];
    }

[leetcode] 70. Climbing Stairs 解題報告