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.

Code

和 Fibonacci Number 一樣的邏輯，只需要注意使用 while 以及 for 時終止條件，以及是 return d 還是 c。

Time Complexity: $O(n)$, Space Complexity: $O(n)$

class Solution {
public:
    int tribonacci(int n) {
        if (n == 0) return 0;
        if (n == 1) return 1;
        if (n == 2) return 1;
        int a = 0;
        int b = 1;
        int c = 1;
        int d;
        for(int i = 3; i <= n; i++) {
            d = a + b + c;
            a = b;
            b = c;
            c = d;
        }
        return d;
    }
};

class Solution {
public:
    int tribonacci(int n) {
        if (n < 2) return n;
        int a = 0, b = 1, c = 1, d = a + b + c;
        while (n-- > 2) {
            d = a + b + c, a = b, b = c, c = d;
        }
        return c;
    }
};

Link

• 1137. N-th Tribonacci Number