Python Program to Print Pascal Triangle

A Pascal’s Triangle is a triangle of numbers where the sum of the two numbers that are above and to the left and right of a number is equal to that number. It is initiated with a 1 at the top, and each subsequent row consists of one more number than the last row.
Example of how Pascal’s Triangle looks to 5 rows:

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

Structure of Pascal’s Triangle

1. The triangle is symmetrical.
2. The first and last number of any row is 1.
3. Any other number in row n is the sum of the two numbers directly above it in row n-1.

Python Program to Print Pascal’s Triangle

def print_pascals_triangle(n):
    # Initialize an empty list to hold the rows of the triangle
    triangle = []

    for i in range(n):
        # Start each row with a single 1
        row = [1]

        # Fill the row with appropriate values (except the first and last)
        if i > 0:
            for j in range(1, i):
                # Add the two numbers directly above in the triangle
                value = triangle[i - 1][j - 1] + triangle[i - 1][j]
                row.append(value)

            # End each row with a single 1
            row.append(1)

        # Append the completed row to the triangle
        triangle.append(row)

    # Print the triangle
    for row in triangle:
        print(" " * (n - len(row)), end="")  # Add spacing for alignment
        print(" ".join(map(str, row)))


# Input: number of rows for Pascal's triangle
num_rows = int(input("Enter the number of rows for Pascal's Triangle: "))
print_pascals_triangle(num_rows)

Detailed Explanation of the Code

1. Function Definition

def print_pascals_triangle(n):

• The function print_pascals_triangle(n) takes one argument n, which specifies the number of rows in Pascal’s Triangle.

2. Triangle Initialization

triangle = []

• An empty list triangle is created to store all the rows of Pascal’s Triangle.

3. Outer Loop for Rows

for i in range(n):

• This loop iterates n times, where each iteration corresponds to a row in Pascal’s Triangle.

4. Row Initialization

row = [1]

• Each row starts with a 1.

5. Filling the Row

if i > 0:
    for j in range(1, i):
        value = triangle[i - 1][j - 1] + triangle[i - 1][j]
        row.append(value)
    row.append(1)

• For rows after the first row (i > 0), the middle values are calculated as the sum of two values directly above it in the previous row.
• The loop for j in range(1, i) iterates over the indices where the sum needs to be calculated.
• The value is calculated using:

triangle[i - 1][j - 1] + triangle[i - 1][j]

• The row ends with another 1.

6. Adding the Row to the Triangle

triangle.append(row)

• The completed row is added to the triangle.

7. Printing the Triangle

for row in triangle:
    print(" " * (n - len(row)), end="")  # Add spacing for alignment
    print(" ".join(map(str, row)))

• Each row is printed with appropriate spacing for alignment to create the triangular structure.
• The function map(str, row) converts all numbers in the row to strings so they can be joined and printed.

8. Taking User Input

num_rows = int(input("Enter the number of rows for Pascal's Triangle: "))
print_pascals_triangle(num_rows)

• The program asks the user for the number of rows and then calls the function to print Pascal’s Triangle.

Example Output

Input:

Enter the number of rows for Pascal's Triangle: 5

Output:

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

Key Concepts Covered:

1. Nested Loops: In this method, the outer loop computes rows, while the inner one calculates elements of a row.
2. Operations Lists: Appending values to rows of the triangle, retrieving previous rows.
3. String Formatting: It is used for spacing to align the triangle properly.
4. Dynamic Programming: Compute Pascal’s Triangle row by row, using answers to previous rows.