pascals_triangle_improved.py

# using factorial, reduced the time complexity 
# of program from O(2^N) to O(N)

def factorial(n):
  if n<2:
    return 1
  else:
    return n*factorial(n-1)

def computeCoefficient(col, row):
  return factorial(row)//(factorial(col)*factorial(row-col))

# Recusrive method to create the series
def computePascal(col, row):
  if col == row or col == 0:
    return 1
  else:
    return computeCoefficient(col, row)
    
# Method to create the triangle for `N` row
def printTriangle(num):
  for r in range(num):
    for c in range(r+1):
      print(str(computePascal(c, r)), end=' ')
    print('\n')
    
printTriangle(10)
'''
Output:
1 

1 1 

1 2 1 

1 3 3 1 

1 4 6 4 1 

1 5 10 10 5 1 

1 6 15 20 15 6 1 

1 7 21 35 35 21 7 1 

1 8 28 56 70 56 28 8 1 

1 9 36 84 126 126 84 36 9 1 
'''