【动态规划】第N个泰波那契数

题目链接：https://leetcode.cn/problems/n-th-tribonacci-number/description/

class Solution {
public:
    int tribonacci(int n) 
    {
        /*时空复杂度都是O(n)*/
        // 处理边界情况
        if (n == 0) return 0;
        if (n == 1 || n == 2) return 1;
        // 1.创建 dp 表
        vector<int> dp(n + 1);
        // 2.初始化
        dp[0] = 0, dp[1] = dp[2] = 1;
        // 3.填表
        for (int i = 3; i < n + 1; ++i)
            dp[i] = dp[i - 1] + dp[i - 2] + dp[i - 3];
        // 4.返回值
        return dp[n];
    }
};

class Solution {
public:
    int tribonacci(int n) {
        // 处理边界情况
        if (n == 0) return 0;
        if (n == 1 || n == 2) return 1;
        
        int a = 0, b = 1, c = 1, d = 0;
        for (int i = 3; i <= n; ++i)
        {
            d = a + b + c;
            // 滚动操作
            a = b; b = c; c = d;
        }
        return d;
    }
};