TriangleCount

SRM 199 · 2004-06-16 · by legakis

SRM 199 · 2004-06-16 · by legakis · Math

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Class Name: TriangleCount

Return Type: int

Method Name: count

Arg Types: (int)

Problem Statement

Given an equilateral triangle with side length N divided into a triangular grid of triangles with side length 1, count the total number of triangles present in the grid. For example, if N is 4:


         /\
        /__\
       /\  /\
      /__\/__\
     /\  /\  /\
    /__\/__\/__\
   /\  /\  /\  /\
  /__\/__\/__\/__\

Here there are ten right-side-up and six up-side-down triangles with a side length of 1, six right-side-up and one up-side-down triangles with a side length of 2, three right-side-up triangles with a side length of 3, and one right-side-up triangle with a side length of 4. The total number of triangles is 27.

Constraints

N will be between 1 and 500, inclusive.

Examples

2
Returns: 5

There are four small triangles and one big triangle.

3
Returns: 13

4
Returns: 27

This is the example from the problem statement.

5
Returns: 48

100
Returns: 256275

Submissions are judged against all 27 archived test cases, of which 5 are shown here. Case numbers match the judge’s.

Coding Area

Language: C++17 · define a public class TriangleCount with a public method int count(int N) · 27 test cases · 2 s / 256 MB per case