Triangular Number

Compute the nth triangular number efficiently.

triangular formula math

A triangular number T(n) counts the number of dots that can form an equilateral triangle with n dots on a side. It is defined as T(n) = 1 + 2 + ... + n. For example, T(1)=1, T(2)=3, T(3)=6.

Write a function `triangular_number(n)` that takes a non-negative integer n and returns the nth triangular number.

You must implement the function exactly with this signature.

Constraints

0 <= n <= 10^6

The expected time complexity is O(1). The result fits within Python's integer range.

Example

>>> triangular_number(1)
1
>>> triangular_number(2)
3
>>> triangular_number(3)
6
>>> triangular_number(10)
55
>>> triangular_number(0)
0

10 points ~10 min

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Hints

Recall the formula for the sum of the first n natural numbers.

Use integer arithmetic; n*(n+1)//2 works for all non-negative integers.

The formula gives O(1) time, which is ideal for large n.

Test Results

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