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Write a Program to print Pascal's triangle?

its about Write a Program to print Pascal's triangle


Asked On2019-09-03 18:30:10 by:Annaliya

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Method ( O(n^2) time and O(1) extra space )
This method is based on method 1. We know that ith entry in a line number line is Binomial Coefficient C(line, i) and all lines start with value 1. The idea is to calculate C(line, i) using C(line, i-1). It can be calculated in O(1) time using the following.

# Python3 program for Pascal's Triangle 

# A O(n^2) time and O(1) extra 

# space method for Pascal's Triangle 

  

# Pascal function 

def printPascal(n): 

  

    for line in range(1, n + 1): 

        C = 1; # used to represent C(line, i) 

        for i in range(1, line + 1): 

              

            # The first value in a 

            # line is always 1 

            print(C, end = " "); 

            C = int(C * (line - i) / i); 

        print(""); 

  

# Driver code 

n = 5; 

printPascal(n);


C(line, i)   = line! / ( (line-i)! * i! )
C(line, i-1) = line! / ( (line - i + 1)! * (i-1)! )
We can derive following expression from above two expressions.
C(line, i) = C(line, i-1) * (line - i + 1) / i

So C(line, i) can be calculated from C(line, i-1) in O(1) time

Answerd on:2019-09-04 Answerd By:Tanisha-Garg

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