Python Program to Print Pascal Triangle

You can print Pascal's Triangle in Python by using nested loops and calculating each value with row[i] = row[i] + row[i-1] inside a loop; for example, use for i in range(n): row = [1] + [row[j] + row[j+1] for j in range(len(row)-1)] + [1] to generate each row.

Examples

Input5

Output1 1 1 1 2 1 1 3 3 1 1 4 6 4 1

Input1

Output1

Input0

Output

How to Think About It

To print Pascal's Triangle, start with the first row as [1]. Each next row is built by adding pairs of adjacent numbers from the previous row, with 1 at both ends. Repeat this process for the number of rows you want.

Algorithm

1

Get the number of rows to print.

2

Start with the first row as a list containing only 1.

3

Print the current row.

4

Create the next row by adding adjacent pairs from the current row, and add 1 at the start and end.

5

Repeat steps 3-4 until all rows are printed.

Code

python

def print_pascals_triangle(n):
    row = []
    for i in range(n):
        row = [1] + [row[j] + row[j+1] for j in range(len(row)-1)] + [1] if row else [1]
        print(' '.join(map(str, row)))

print_pascals_triangle(5)

Output

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

Dry Run

Let's trace printing 5 rows of Pascal's Triangle through the code

1

Start with empty row

row = []

2

First iteration (i=0)

row is empty, so row = [1] Print: 1

3

Second iteration (i=1)

row = [1] + [] + [1] = [1, 1] Print: 1 1

4

Third iteration (i=2)

row = [1] + [1+1] + [1] = [1, 2, 1] Print: 1 2 1

5

Fourth iteration (i=3)

row = [1] + [1+2, 2+1] + [1] = [1, 3, 3, 1] Print: 1 3 3 1

6

Fifth iteration (i=4)

row = [1] + [1+3, 3+3, 3+1] + [1] = [1, 4, 6, 4, 1] Print: 1 4 6 4 1

Iteration	Row Values
0	[1]
1	[1, 1]
2	[1, 2, 1]
3	[1, 3, 3, 1]
4	[1, 4, 6, 4, 1]

Why This Works

Step 1: Initialize first row

The first row of Pascal's Triangle is always [1], which starts the pattern.

Step 2: Build next rows

Each new row is created by adding pairs of adjacent numbers from the previous row, with 1 added at the start and end.

Step 3: Print rows

Print each row as a space-separated string to display the triangle shape.

Alternative Approaches

Using factorial formula

python

from math import factorial

def print_pascals_triangle(n):
    for i in range(n):
        row = [str(factorial(i)//(factorial(j)*factorial(i-j))) for j in range(i+1)]
        print(' '.join(row))

print_pascals_triangle(5)

This uses the mathematical formula for combinations but is less efficient for large n due to factorial calculations.

Using recursion

python

def pascal_row(n):
    if n == 0:
        return [1]
    prev = pascal_row(n-1)
    return [1] + [prev[i] + prev[i+1] for i in range(len(prev)-1)] + [1]

def print_pascals_triangle(n):
    for i in range(n):
        print(' '.join(map(str, pascal_row(i))))

print_pascals_triangle(5)

This uses recursion to generate each row but can be slower and use more memory for large n.

Complexity: O(n^2) time, O(n) space

Time Complexity

The program prints n rows, each with up to n elements, so it runs in O(n^2) time due to nested loops.

Space Complexity

Each row stores up to n elements, so space complexity is O(n). The program reuses the row list each iteration.

Which Approach is Fastest?

The iterative approach with list comprehension is fastest and simplest; factorial-based methods are slower due to expensive calculations.

Approach	Time	Space	Best For
Iterative with list comprehension	O(n^2)	O(n)	Most efficient and readable
Factorial formula	O(n^3)	O(1)	Mathematical clarity but slower
Recursive	O(n^2)	O(n^2)	Conceptual clarity but uses more memory