Printing a Right Triangle (Half Pyramid) | Simple Shape Patterns in C

The Right Triangle, often referred to as a Half Pyramid, is a quintessential pattern in C programming. Mastering this shape is a critical milestone, as it introduces the concept of dynamic loop boundaries, where the inner loop's behavior is directly dictated by the outer loop's iteration.

What You Will Learn

In this tutorial, we will walk through the implementation of a C program that prints a right triangle of stars. You will learn how to structure nested loops to create a pattern that expands linearly with each row.

Prerequisites:

• A solid understanding of nested for loops.

• Familiarity with the printf function.

Final Output:

If we choose a triangle height of 5, the output will appear as follows:

*

**
***
****
*****

Deconstructing the Pattern: The Logic

1. The Visual Representation

The right triangle is characterized by a "staircase" effect.

• Row 1: 1 star.

• Row 2: 2 stars.

• Row 3: 3 stars.

• Row 4: 4 stars.

• Row 5: 5 stars.

2. Problem Statement

The objective is to print a pattern of symbols where the number of stars in each row is equal to the current row number.

3. Pattern Analysis & Logic

• Identifying the Rows: We use an outer loop to control the vertical height, running from i = 1 to n.

• Identifying the Columns: We use an inner loop to print the star symbol horizontally. To create the triangular effect, the inner loop runs from j = 1 to i.

• Algorithm:

  1. Initialize the size n.

  2. Start an outer loop for the rows (from 1 to n).

  3. Inside, start an inner loop for the columns (from 1 to i).

  4. Print the star symbol.

  5. Print a newline character after the inner loop finishes to move to the next row.

The Code Implementation

#include <stdio.h>

int main() {
    int n = 5; // Height of the triangle

    // Outer loop for rows
    for (int i = 1; i <= n; i++) {
        
        // Inner loop for columns, dependent on row number i
        for (int j = 1; j <= i; j++) {
            printf("*"); // Print the star symbol
        }
        
        // Move to the next line after each row
        printf("\n"); 
    }

    return 0;
}

Explanation:

• int n = 5;: We define the total height of our triangle.

• for (int i = 1; i <= n; i++): The outer loop manages the rows.

• for (int j = 1; j <= i; j++): This is the core logic. By limiting the inner loop to $i$, we ensure that each row contains exactly $i$ stars.

• printf("\n");: This ensures that the program moves to a new line after printing the required number of stars for the current row.

Sample Output and Analysis

User Input:

• The code is set for n = 5.

Program Output:

*

**
***
****
*****

Output Analysis: In the first iteration (i=1), the inner loop runs once. In the fifth iteration (i=5), the inner loop runs five times, creating the characteristic right-angled slope.

Complexity Analysis

• Time Complexity: O(n^2), as the inner loop execution increases with each row, resulting in approximately \frac{n(n+1)}{2} operations.

• Space Complexity: O(1), as the logic uses a constant amount of memory.

Conclusion

You have successfully implemented a right triangle pattern by nesting a dynamic loop inside an outer loop. This logic serves as the building block for all pyramid and triangle variations.

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…till the next post, bye-bye & take care