QUESTION DESCRIPTION 


Create a logic to print Floyd's triangle upto the given n rows.

Refer Sample Test Cases.

Programming Language need to be used:C++
TEST CASE 1 

INPUT
5
OUTPUT
1
23
456
78910
1112131415

TEST CASE 2 

INPUT
4
OUTPUT
1
23
456
78910

Solution : 

#include <iostream>
using namespace std;

int main()
{
    int n, i,  c, a = 1;
    
     cin >> n;
    
    for (i = 1; i <= n; i++)
    {
        for (c = 1; c <= i; c++)
        {        
            cout << a; 
            a++; 
        }
        cout << endl;
    }    
    return 0;
}

Printing Floyd's Triangle in C++: A Comprehensive Guide

In the world of competitive programming and algorithm design, one of the classic problems is to print Floyd's Triangle. It's a simple but insightful problem that helps beginners get acquainted with loops, variables, and basic logic building in programming. In this blog, we'll explore Floyd's Triangle, its structure, and how to solve the problem using C++. We'll also analyze test cases, break down the solution, and offer detailed explanations for each part of the code.

Table of Contents

  1. Introduction to Floyd's Triangle
  2. Problem Description and Requirements
  3. Understanding the Structure of Floyd's Triangle
  4. Breaking Down the Logic: Step-by-Step Approach
  5. C++ Code Implementation
  6. Explanation of the Code
  7. Sample Test Cases and Analysis
  8. Conclusion

1. Introduction to Floyd's Triangle

Floyd's Triangle is a right-angled triangular array of natural numbers. The numbers are arranged starting from 1 and are filled row by row. The first row has one element, the second row has two elements, and so on. This problem is widely used to help learners understand nested loops and how to manage counters within loops.

A Floyd’s Triangle looks like this:


1
23
456
78910
1112131415

The problem requires us to generate this pattern up to n rows. Each number in the triangle is the next natural number in sequence.

2. Problem Description and Requirements

We are tasked with writing a C++ program that prints Floyd's Triangle up to n rows, where n is a user-input integer. The challenge includes:

  • Taking an integer input n from the user.
  • Generating and printing the triangle with n rows.
  • The triangle should start with the number 1 and fill subsequent numbers in order, row by row.

Constraints:

  • Input n should be a positive integer.
  • The output should display the triangle with consecutive numbers starting from 1.

Output Example:

For n = 5, the output should be:


1
23
456
78910
1112131415

3. Understanding the Structure of Floyd's Triangle

To approach the problem, let’s break down Floyd's Triangle step by step:

  • First row: The first row contains only the number 1.
  • Second row: The second row contains the next two numbers: 2 and 3.
  • Third row: The third row contains three numbers: 4, 5, and 6.
  • Fourth row: The fourth row continues with four numbers: 7, 8, 9, and 10.

We notice that the number of elements in each row corresponds to the row number. For example, row 1 has 1 element, row 2 has 2 elements, and row 3 has 3 elements. This means that for row i, we need to print exactly i numbers.

The numbers are consecutive, starting from 1, and increment by 1 for each element in the triangle. To manage this, we’ll use a counter that increases continuously as we print each number in the triangle.

4. Breaking Down the Logic: Step-by-Step Approach

Steps:

  1. Input Handling: First, we need to accept an integer input n from the user. This represents the number of rows in Floyd's Triangle.
  2. Nested Loop Setup: We'll use two loops. The outer loop will iterate over the rows from 1 to n. The inner loop will print the numbers in each row.
    • Outer loop runs from 1 to n (row numbers).
    • Inner loop prints exactly i numbers in the i-th row.
  3. Counter Management: A counter variable will start at 1 and increment after each number is printed. This ensures consecutive numbers are printed in sequence.
  4. Newline Handling: After each row is printed, we need to move to the next line. This can be achieved by printing a newline character (endl) after each inner loop completes.

5. C++ Code Implementation

Let’s now translate our approach into C++ code. Below is a concise and efficient solution:


#include <iostream>
using namespace std;

int main() {
    int n, i, c, a = 1;  // Declare variables
    
    cin >> n;  // Take input from the user
    
    // Outer loop to control the rows
    for (i = 1; i <= n; i++) {
        // Inner loop to print numbers in each row
        for (c = 1; c <= i; c++) {
            cout << a;  // Print the current number
            a++;  // Increment the counter
        }
        cout << endl;  // Move to the next line after each row
    }
    
    return 0;  // End the program
}

6. Explanation of the Code
Key Sections:
  • Input: The program starts by reading an integer n from the user, which represents the number of rows for Floyd's Triangle.

    cin >> n;

  • Outer Loop (Rows): The outer loop runs from 1 to n. For each iteration of the outer loop, a new row of the triangle is printed.

    for (i = 1; i <= n; i++) {
    // Inner loop and printing logic
}

  • Inner Loop (Columns): The inner loop runs i times for each row. In the first row, it runs once, in the second row, it runs twice, and so on. The inner loop prints consecutive numbers and increases the counter a after each print.

    for (c = 1; c <= i; c++) {
    cout << a;
    a++;
}

  • Newline: After each row is printed, the program moves to the next line using cout << endl;.

    cout << endl;

  • Counter: The variable a keeps track of the current number to be printed. It starts at 1 and increases after every print.

    int a = 1;
7. Sample Test Cases and Analysis
Test Case 1
Input:

5

Output:
1
23
456
78910
1112131415

Explanation:
  • Row 1: 1 number → 1
  • Row 2: 2 numbers → 2 3
  • Row 3: 3 numbers → 4 5 6
  • Row 4: 4 numbers → 7 8 9 10
  • Row 5: 5 numbers → 11 12 13 14 15
Test Case 2
Input:

4

Output:

1
23
456
78910

Explanation:
  • Row 1: 1 number → 1
  • Row 2: 2 numbers → 2 3
  • Row 3: 3 numbers → 4 5 6
  • Row 4: 4 numbers → 7 8 9 10
Edge Case Test
Input:

1

Output:

1

In this case, the input is 1, so only one row is printed with the number 1.
Final 
Printing Floyd's Triangle is an excellent exercise for beginners to learn about loops, nested loops, and controlling variables in a program. The solution we provided is efficient and simple to understand, making it ideal for those new to C++ programming. By understanding the structure of Floyd’s Triangle and breaking down the problem into smaller steps, we were able to solve the problem with ease.
This task also highlights the importance of logic building in programming, and as one progresses, understanding and implementing such problems becomes crucial for more advanced challenges. Keep practicing with more patterns and exercises like this to sharpen your programming skills!