Generate a Row of Pascal's Triangle in C

Introduction

In this lab, you will learn how to generate a row of Pascal's Triangle using C programming. The lab covers three main steps: reading the row number from the user, computing the binomial coefficients for the row, and printing the row. You will start by creating a program that prompts the user to enter the desired row number, then implement a function to calculate the binomial coefficients, and finally display the row of Pascal's Triangle. By the end of this lab, you will have a solid understanding of number theory and discrete math concepts, as well as practical experience in applying them using C programming.

Skills Graph

Read the Row Number

In this step, you'll learn how to read the row number for generating a row in Pascal's Triangle using C programming. We'll create a program that prompts the user to input the desired row number.

First, let's create a new C file in the project directory:

cd ~/project
nano pascal_triangle.c

Now, add the following code to read the row number:

#include <stdio.h>

int main() {
    int rowNumber;

    printf("Enter the row number for Pascal's Triangle: ");
    scanf("%d", &rowNumber);

    printf("You entered row number: %d\n", rowNumber);

    return 0;
}

Let's compile and run the program:

gcc pascal_triangle.c -o pascal_triangle
./pascal_triangle

Example output:

Enter the row number for Pascal's Triangle: 5
You entered row number: 5

Code Explanation:

• #include <stdio.h> includes the standard input/output library
• scanf() reads an integer input from the user
• printf() displays the entered row number
• The program validates basic user input for the row number

Key Points:

• We use scanf() to read an integer input
• The row number will be used to generate the specific row of Pascal's Triangle
• Input validation will be added in subsequent steps

Compute Binomial Coefficients

In this step, you'll learn how to compute binomial coefficients for generating a specific row of Pascal's Triangle. We'll modify the previous program to calculate the coefficients using a function.

Open the existing file:

cd ~/project
nano pascal_triangle.c

Replace the previous code with the following implementation:

#include <stdio.h>

// Function to compute binomial coefficient
int binomialCoeff(int n, int k) {
    // Base cases
    if (k == 0 || k == n)
        return 1;

    // Recursive calculation using Pascal's Triangle property
    return binomialCoeff(n-1, k-1) + binomialCoeff(n-1, k);
}

int main() {
    int rowNumber;

    printf("Enter the row number for Pascal's Triangle: ");
    scanf("%d", &rowNumber);

    printf("Binomial Coefficients for Row %d:\n", rowNumber);

    // Generate and print coefficients
    for (int k = 0; k < rowNumber; k++) {
        printf("%d ", binomialCoeff(rowNumber - 1, k));
    }
    printf("\n");

    return 0;
}

Compile and run the program:

gcc pascal_triangle.c -o pascal_triangle
./pascal_triangle

Example output:

Enter the row number for Pascal's Triangle: 5
Binomial Coefficients for Row 5:
1 4 6 4 1

Code Explanation:

• binomialCoeff() function calculates binomial coefficients recursively
• Base cases handle the first and last elements of each row
• The function uses the recursive property of Pascal's Triangle
• Nested loop generates coefficients for the specified row

Key Points:

• Binomial coefficients represent the numbers in each row of Pascal's Triangle
• Recursive calculation demonstrates the mathematical relationship
• Time complexity is exponential due to recursive approach

Print the Row

In this step, you'll enhance the Pascal's Triangle program to format and print the row with proper spacing and alignment, making the output visually appealing.

Open the existing file:

cd ~/project
nano pascal_triangle.c

Replace the previous code with the following implementation:

#include <stdio.h>

// Function to compute binomial coefficient
int binomialCoeff(int n, int k) {
    if (k == 0 || k == n)
        return 1;
    return binomialCoeff(n-1, k-1) + binomialCoeff(n-1, k);
}

// Function to print Pascal's Triangle row
void printPascalRow(int rowNumber) {
    // Print leading spaces for alignment
    for (int space = 0; space < rowNumber; space++) {
        printf("   ");
    }

    // Generate and print coefficients
    for (int k = 0; k < rowNumber; k++) {
        int coefficient = binomialCoeff(rowNumber - 1, k);
        printf("%4d ", coefficient);
    }
    printf("\n");
}

int main() {
    int rowNumber;

    printf("Enter the row number for Pascal's Triangle (1-10): ");
    scanf("%d", &rowNumber);

    if (rowNumber < 1 || rowNumber > 10) {
        printf("Please enter a row number between 1 and 10.\n");
        return 1;
    }

    printf("Pascal's Triangle Row %d:\n", rowNumber);

    // Print the specified row
    printPascalRow(rowNumber);

    return 0;
}

Compile and run the program:

gcc pascal_triangle.c -o pascal_triangle
./pascal_triangle

Example output:

Enter the row number for Pascal's Triangle (1-10): 5
Pascal's Triangle Row 5:
            1    4    6    4    1

Code Explanation:

• printPascalRow() function handles row formatting
• Added leading spaces for visual alignment
• Used %4d format specifier for consistent column width
• Added input validation to limit row numbers
• Prints the entire row with proper spacing

Key Points:

• Formatting improves readability of Pascal's Triangle
• Input validation prevents unexpected behavior
• Demonstrates basic formatting techniques in C

Summary

In this lab, you will learn how to read the row number for generating a row in Pascal's Triangle using C programming, and how to compute the binomial coefficients to print the row. First, you will create a program that prompts the user to input the desired row number. Then, you will implement a function to calculate the binomial coefficients using the recursive property of Pascal's Triangle. Finally, you will print the row of Pascal's Triangle based on the computed coefficients. The key points covered in this lab include using scanf() to read user input, implementing a recursive function to calculate binomial coefficients, and printing the generated row.