Python Program to Print Pascal’s Triangle Pattern

Introduction

Pascal’s Triangle is a triangular array of binomial coefficients. Each entry in Pascal’s Triangle is the sum of the two directly above it. This pattern is an excellent exercise for understanding loops and mathematical operations in Python.

Problem Statement

Create a Python program that:

• Accepts the number of rows for Pascal’s Triangle.
• Prints Pascal’s Triangle in a triangular format.

Example:

• Input: rows = 5
• Output:

      1
     1 1
    1 2 1
   1 3 3 1
  1 4 6 4 1
  

Solution Steps

1. Input the Number of Rows: The user specifies how many rows of Pascal’s Triangle to generate.
2. Use Nested Loops: The outer loop handles the rows, and the inner loop handles printing the elements in Pascal’s Triangle.
3. Calculate Pascal's Triangle Values: Each value in Pascal’s Triangle is computed using the binomial coefficient formula C(n, k) = n! / (k! * (n - k)!).
4. Display Pascal’s Triangle: Print the values in a triangular format, with spaces for alignment.

Python Program

# Step 1: Define a function to calculate the factorial of a number
def factorial(n):
    if n == 0 or n == 1:
        return 1
    else:
        fact = 1
        for i in range(2, n + 1):
            fact *= i
        return fact

# Step 2: Define a function to calculate binomial coefficient C(n, k)
def binomial_coefficient(n, k):
    return factorial(n) // (factorial(k) * factorial(n - k))

# Step 3: Input the number of rows for Pascal’s Triangle
rows = int(input("Enter the number of rows: "))

# Step 4: Outer loop to print each row of Pascal's Triangle
for i in range(rows):
    # Print leading spaces for alignment
    print(" " * (rows - i), end="")
    
    # Print the elements of Pascal's Triangle using binomial coefficient
    for j in range(i + 1):
        print(binomial_coefficient(i, j), end=" ")
    
    # Move to the next line after each row
    print()

Explanation

Step 1: Define the Factorial Function

• The function factorial() calculates the factorial of a number n, which is used to compute the binomial coefficients.

Step 2: Define the Binomial Coefficient Function

• The function binomial_coefficient(n, k) calculates the binomial coefficient using the formula C(n, k) = n! / (k! * (n - k)!). This is how we compute each element in Pascal’s Triangle.

Step 3: Input Number of Rows

• The program asks the user to input how many rows of Pascal’s Triangle to generate.

Step 4: Print Pascal’s Triangle

• The outer loop controls the number of rows printed.
  • Leading spaces are printed to align the triangle.
  • The inner loop calculates and prints each element in the row using the binomial_coefficient() function.

Output Example

For rows = 5, the output will be:

     1
    1 1
   1 2 1
  1 3 3 1
 1 4 6 4 1

For rows = 6, the output will be:

     1
    1 1
   1 2 1
  1 3 3 1
 1 4 6 4 1
1 5 10 10 5 1

Conclusion

This Python program prints Pascal’s Triangle using nested loops and the binomial coefficient formula. The program aligns the output in a triangular format using spaces and prints each element of Pascal’s Triangle using a combination of factorial and binomial coefficient calculations. This exercise helps in practicing loops, functions, and mathematical operations in Python.