C++ Program to Check Triangular Number

Posted in C++ Tutorial

Updated on Oct 06, 2024

By Mari Selvan

👁️ 79 - Views

⏳ 4 mins

💬 1 Comment

Photo Credit to CodeToFun

🙋 Introduction

In the realm of programming, various mathematical properties of numbers often pique our interest. One such property is whether a number is a triangular number.

A triangular number or triangle number is the sum of the natural numbers up to a certain value.

In this tutorial, we'll delve into a C++ program to check if a given number is a triangular number.

📄 Example

Let's take a look at the C++ code that checks whether a given number is a triangular number.

isTriangularNumber.cpp

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#include <iostream>
#include <cmath>

// Function to check if a number is a triangular number
bool isTriangularNumber(int num) {
  // Formula to check triangular number
  int n = static_cast < int > (sqrt(2 * num));
  return (n * (n + 1)) / 2 == num;
}

// Driver program
int main() {
  // Replace this value with your desired number
  int number = 10;

  // Check if the number is a triangular number
  if (isTriangularNumber(number)) {
    std::cout << number << " is a triangular number." << std::endl;
  } else {
    std::cout << number << " is not a triangular number." << std::endl;
  }

  return 0;
}

💻 Testing the Program

To test the program with different numbers, simply replace the value of number in the main function.

Output

10 is a triangular number.

Compile and run the program to check if the given number is a triangular number.

🧠 How the Program Works

The program defines a function isTriangularNumber that checks if a given number is a triangular number using the formula.
Inside the main function, replace the value of number with the desired number to check.
The program then calls the isTriangularNumber function and prints whether the number is a triangular number or not.

📏 Between the Given Range

Let's take a look at the C++ code that checks and displays triangular numbers in the range of 1 to 50.

isTriangular.cpp

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#include <iostream>

// Function to check if a number is triangular
bool isTriangular(int num) {
  int sum = 0;
  int i = 1;

  while (sum < num) {
    sum += i;
    ++i;
  }

  return (sum == num);
}

// Function to display triangular numbers in the range 1 to 50
void displayTriangularNumbers() {
  std::cout << "Triangular Numbers in the Range 1 to 50:\n";

  for (int num = 1; num <= 50; ++num) {
    if (isTriangular(num)) {
      std::cout << num << " ";
    }
  }

  std::cout << std::endl;
}

// Driver program
int main() {
  // Call the function to display triangular numbers
  displayTriangularNumbers();

  return 0;
}

💻 Testing the Program

Output

Triangular Numbers in the Range 1 to 50:
1 3 6 10 15 21 28 36 45

Compile and run the program to see the triangular numbers in the range from 1 to 50.

🧠 How the Program Works

The program defines a function isTriangular that checks if a given number is a triangular number using a loop.
Another function displayTriangularNumbers iterates through the numbers from 1 to 50 and calls the isTriangular function to identify and display triangular numbers.
The main function calls displayTriangularNumbers to execute the program.

🧐 Understanding the Concept of Triangular Numbers

Before delving into the code, let's take a moment to understand the concept of triangular numbers.

A triangular number is the sum of the natural numbers up to a certain value, and it can be represented by the formula T_n = n * (n + 1) / 2, where n is a non-negative integer.

For example, T₃ = 1 + 2 + 3 = 6 is a triangular number.