Pascals Triangle in Python using Dynamic Programming and Memoization

# pascals triangle using dynamic programming

memo = dict()

def triangle(n=3):

    result = [[1] * (i + 1) for i in range(n)]

    for i in range(n):

        for j in range(1, i):

            result[i][j] =  pascals(i - 1, j - 1) + pascals(i - 1, j)

    return result

def pascals(n, k):

    global memo

    if (k <= 0 or k == n):

        return 1

    else:

        if (n, k) in memo :

            return memo[ (n, k) ]

        else:

            memo[ (n, k) ] = (pascals(n - 1, k - 1) + pascals(n - 1, k))        

        return memo[ (n , k) ]

if __name__ == '__main__':

    triangle(20)