N Th Tribonacci Number · Interview Problem

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Leetcode

Easy

Dynamic Programming

Recursion

Math

N Th Tribonacci Number

Compute the $n$ -th Tribonacci number, where each term is the sum of the previous three terms.

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Problem Statement

Problem

The Tribonacci sequence is defined similarly to Fibonacci, but each term depends on the previous three terms.

Let:

$T_0 = 0$
$T_1 = 1$
$T_2 = 1$
For $n \ge 3$ , $T_n = T_{n-1} + T_{n-2} + T_{n-3}$

Given an integer $n$ , return the $n$ -th Tribonacci number.

Goal

Write a function that computes the value of $T_n$ efficiently.

Input Format

One integer $n$

Output Format

Return a single integer: the $n$ -th Tribonacci number

Constraints

$0 \le n \le 37$
The result fits in a 32-bit signed integer

Examples

Sample cases returned by the problem API.

Example 1

Input

n = 4

Output

Explanation

The sequence starts 0, 1, 1, 2, 4, ... so $T_4 = 4$ .

Example 2

Input

n = 25

Output

Explanation

Using the recurrence repeatedly gives $T_{25} = 1389537$ .

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Example 3

Input

n = 0

Output

Explanation

By definition, $T_0 = 0$ .

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