pascal_triangle.py

# Pascal's Triangle.
#
# Each entry is the sum of the two entries above it.
# Row n contains the binomial coefficients C(n,0)...C(n,n).
# Built using dynamic programming — each row derived from the previous.

def generate(n):
    triangle = [[1] * (i + 1) for i in range(n + 1)]
    for i in range(2, n + 1):
        for j in range(1, i):
            triangle[i][j] = triangle[i - 1][j - 1] + triangle[i - 1][j]
    return triangle


def display(triangle):
    n = len(triangle) - 1
    width = len(str(triangle[n][n // 2]))
    for i, row in enumerate(triangle):
        padding = ' ' * (n - i) * ((width + 1) // 2)
        print(padding + ' '.join(str(x).center(width) for x in row))


if __name__ == '__main__':
    while True:
        try:
            n = int(input('Enter a non-negative integer: '))
            if n < 0:
                raise ValueError
            break
        except ValueError:
            print('Incorrect input, try again.')

    triangle = generate(n)
    print()
    display(triangle)