1137. N-th Tribonacci Number.md

1137. N-th Tribonacci Number

1. Description

The Tribonacci sequence $T_n$ is defined as follows:

$T_0 = 0$, $T_1 = 1$, $T_2 = 1$, and $T_{n+3} = T_{n} + T_{n+1} + T_{n+2}$ for $n \geq 0$.

Given n, return the value of $T_n$.

Example 1:

Input: n = 4
Output: 4
Explanation:
T_3 = 0 + 1 + 1 = 2
T_4 = 1 + 1 + 2 = 4

Example 2:

Input: n = 25
Output: 1389537

Constraints:

• 0 <= n <= 37
• The answer is guaranteed to fit within a 32-bit integer, ie. answer <= 2^31 - 1.

2. Solutions

Solution 1: Language: Java Dynamic Programming

• Saturday, 26 February, 2022
• Time Complexity: $O(n)$
• Space Complexity: $O(n)$
• Runtime: 0 ms, faster than 100.00% of Java online submissions for N-th Tribonacci Number.
• Memory Usage: 38.8 MB, less than 41.76% of Java online submissions for N-th Tribonacci Number.

class Solution {
    public int tribonacci(int n) {
        int dp[] = new int[n < 3 ? 3 : 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];
    }
}