1137. N-th Tribonacci Number

The Tribonacci sequence Tn is defined as follows:

T0 = 0, T1 = 1, T2 = 1, and Tn+3 = Tn + Tn+1 + Tn+2 for n >= 0.

Given n, return the value of Tn.

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.

// Dynamic Programming
int tribonacci(int n) { // time: O(n); space: O(n)
    if (n <= 2) return n == 0 ? 0 : 1;
    vector<int> dp(n + 1, 0);
    dp[1] = 1;
    dp[2] = 1;
    for (int i = 3; i <= n; ++i) {
        dp[i] = dp[i - 3] + dp[i - 2] + dp[i - 1]; 
    }
    return dp.back();
}

// Space Optimized Dynamic Programming
int tribonacci(int n) { // time: O(n); space: O(1)
    if (n <= 2) return n == 0 ? 0 : 1;
    int a = 0, b = 1, c = 1, res;
    for (int i = 3; i <= n; ++i) {
        res = a + b + c;
        a = b;
        b = c;
        c = res;
    }
    return res;
}