New update is available. Click here to update.

Solve problems & track your progress

Checkout your overall progress in every topic here

Become

Sensei

in DSA topics

Open the topic and solve more problems associated with it to improve your skills

Check out the skill meter for every topic

See how many problems you are left with to solve for cracking any stage. Score more than zero to get your progress counted.

Problem

Submissions

Tribonacci Sequence

Contributed by

Paritosh Singh

Medium

0/80

0 upvotes

Problem Statement

You are given an integer ‘N’. Your task is to find out the ‘N’th Tribonacci Number. ‘N’th number in the Tribonacci sequence is defined as T_n = T _{n - 1} + T_{n - 2} + T_{n - 3}. Where T₀ = 0, T₁ = 1, T₂= 1. Return the answer in mod of 10⁹ + 7.

For Example :

You are given ‘N’ = 5, Here we know 0th, 1st and 2nd Tribonacci numbers are 0, 1 and 1 respectively. Therefore we can calculate the 3rd number as 0 + 1 + 1 = 2 and 4th number as 1 + 1 + 2 = 4 and 5th number as 1 + 2 + 4 = 7. Hence the answer is 7.

Follow Up :

Can you solve it in logarithmic time?

Detailed explanation ( Input/output format, Notes, Constraints, Images )

Input Format :

The first input line contains a single integer ‘T’ representing the number of test cases.

The first line of each test case contains a single integer ‘N’ representing Tribonacci number to find.

Output Format :

For each test case, print a single integer, representing the ‘N’th Tribonacci Number.

Print a separate line for each test case.

Constraints :

1 ≤ T ≤10
0 ≤ N ≤ 10^5

Time Limit: 1 sec

Note :

You do not need to print anything. It has already been taken care of. Just implement the given function.

Sample Input 1 :

2
5
2

Sample Output 1 :

7
1

Explanation for Sample Input 1:

For the first test case, ‘N’ = 5, Here we know 0th, 1st and 2nd Tribonacci numbers are 0, 1 and 1 respectively. Therefore we can calculate the 3rd number as 0 + 1 + 1 = 2 and 4th number as 1 + 1 + 2 = 4 and 5th number as 1 + 2 + 4 = 7. Hence the answer is 7.

For the second test case, ‘N’ = 2, Here, the second number in the Tribonacci sequence is already defined as 1. Hence the answer is 1.

Sample Input 2 :

2
0
9

Sample Output 2 :

0
81

Auto

Console