java
class Solution {
    public int tribonacci(int n) {
        if (n == 0) return 0;
        if (n == 1 || n == 2) return 1;

        int[] dp = new int[n + 1];
        dp[0] = 0;
        dp[1] = 1;
        dp[2] = 1;

        for (int i = 3; i <= n; i++) {
            dp[i] = dp[i - 1] + dp[i - 2] + dp[i - 3];
        }

        return dp[n];
    }
}

java
class Solution {
    public int rob(int[] nums) {
        if (nums == null || nums.length == 0) {
            return 0;
        }
        if (nums.length == 1) {
            return nums[0];
        }
        
        int n = nums.length;
        int[] dp = new int[n];
        dp[0] = nums[0];
        dp[1] = Math.max(nums[0], nums[1]);
        
        for (int i = 2; i < n; i++) {
            dp[i] = Math.max(dp[i - 1], dp[i - 2] + nums[i]);
        }
        
        return dp[n - 1];
    }

}

java
class Solution {
    public int minimumTotal(List<List<Integer>> triangle) {
        int n = triangle.size();
        int[] dp = new int[n];
        
        // 初始化dp数组为三角形的最后一行
        for (int i = 0; i < n; i++) {
            dp[i] = triangle.get(n - 1).get(i);
        }
        
        // 从三角形的倒数第二行开始向上计算
        for (int i = n - 2; i >= 0; i--) {
            for (int j = 0; j <= i; j++) {
                // 状态转移方程
                dp[j] = Math.min(dp[j], dp[j + 1]) + triangle.get(i).get(j);
            }
        }
        
        // dp[0] 就是从顶部到底部的最小路径和
        return dp[0];
    }
}