N-th Tribonacci Number

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The Tribonacci sequence is defined as T(0)=0, T(1)=1, T(2)=1, T(n+3)=T(n)+T(n+1)+T(n+2). Given n, return T(n).

Example 1
Input: n=4 → Output: 4
Example 2
Input: n=25 → Output: 1389537

Solution Approach

Simple DP with three variables. No array needed.

  • Base: t0=0, t1=1, t2=1.
  • For i from 3 to n: next = t0+t1+t2; t0=t1; t1=t2; t2=next.
  • Return t2 (handle n=0 and n=1 separately).
Java
class Solution {
    public int tribonacci(int n) {
        if (n == 0) return 0;
        if (n <= 2) return 1;
        int a = 0, b = 1, c = 1;
        for (int i = 3; i <= n; i++) {
            int next = a + b + c;
            a = b; b = c; c = next;
        }
        return c;
    }
}
  • Time Complexity: O(N)
  • Space Complexity: O(1)