optimised pascals triangle with dynamic programming using python

Question

def pascal(row, col):
    if col == 1 or col == row:
        return 1
    else:
        return pascal(row - 1, col) + pascal(row - 1, col - 1)

The above recursive implementation is exponential in terms of time complexity. With the knowledge of Dynamic Programming, how do we write a function fast_pascal(row, col)? The function should take in an integer row and an integer col and return the value in (row, col). Note: row and col starts from 1.

This is what i tried,

def fast_pascal(row,col):
dynamic = [[1]+[1]*(col-1)for i in range(row)]
for row_ind in range(1,row):
    for col_ind in range(1,col):
        dynamic[row_ind][col_ind] = dynamic[row_ind-1][col_ind] + dynamic[row_ind-1][col_ind-1]
return dynamic[row-1][col-1]

The code gives the wrong results. Its supposed to be,

fast_pascal(3,2) == 2
fast_pascal(4,3) == 3
fast_pascal(500,3) == 124251

what is your problem? Do you get error message? Code gives wrong result? — furas, Apr 27 '21 at 06:42

score 0 · Answer 1 · edited Apr 28 '21 at 16:00

0

def fast_pascal(row,col):
    dynamic = [[1]+[0]*(col-1)for i in range(row)]
    for row_ind in range(1,row):
        for col_ind in range(1,col):
            dynamic[row_ind][col_ind] = dynamic[row_ind-1][col_ind] + dynamic[row_ind-1][col_ind-1]
    return dynamic[row-1][col-1]

edited Apr 28 '21 at 16:00

Mateus Junges

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answered Apr 28 '21 at 05:11

raw0804

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optimised pascals triangle with dynamic programming using python

1 Answers1