Functions and Recursion in Python, Lecture notes of Web Programming and Technologies

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Functions and Recursion in Python

Data and File Structures Laboratory

http://www.isical.ac.in/~dfslab/2020/index.html

Parameter passing

def function1 (x) :

x = 10

return

def function2 (x) :

x = x + 1

return

def function3 (l) :

l = [ 10 ]

return

def function4 (l) :

l[0] = 10

return

def function5 (l) :

l = l + l

print(l)

return

def function6 (l) :

l.extend(l)

return

Parameter passing in Python

Call by reference

Immutable arguments (integers, strings, tuples): passed by value or

reference (doesn’t matter)

Mutable arguments : passed by reference

in place changes reflected in caller

if the name is reassigned, it points to a different object

Parameter passing in Python

Call by reference

Immutable arguments (integers, strings, tuples): passed by value or

reference (doesn’t matter)

Mutable arguments : passed by reference

in place changes reflected in caller

if the name is reassigned, it points to a different object

>>> x = 10

>>> id(x)

>>> y = 10

>>> id(y)

>>> y = y+

>>> id(y)

x = a

x

x = b

x

x = x + 1

x.inplace_operation()

vs.

x now points to a different object

Recursive vs. iterative implementations

def factorial(n) :

# Not recommended!

if n < 0 : return -

prod = 1

while n > 0 :

prod *= n

n = n - 1

return prod

def factorial(n) : # Recursive implementation

if n < 0 : return -1 # Error condition if n == 0 : return 1 # Base case return n * factorial(n-1) # Recursive call

Z curve

Problem statement

Consider a 2-D matrix of size 2 m^ × 2 m. The entries of the matrix are, in row-major order, 1 , 2 , 3 ,... , 22 m. Print the entries of the matrix in Z-curve

order (as shown in the picture below).

Z curve: code

def z_curve(matrix, top_left_row, top_left_column, bottom_right_row, bottom_right_column) :

Base case

if top_left_row == bottom_right_row and top_left_column == bottom_right_column : print("%d" % matrix[top_left_row][top_left_column], end=" ") return

TLC

TLR

BRR

BRC

Z curve: code

def z_curve(matrix, top_left_row, top_left_column, bottom_right_row, bottom_right_column) :

Base case

if top_left_row == bottom_right_row and top_left_column == bottom_right_column : print("%d" % matrix[top_left_row][top_left_column], end=" ") return

TLC BRC

TLR TLR

BRR BRR

TLC BRC

Z curve: code

def z_curve(matrix, top_left_row, top_left_column, bottom_right_row, bottom_right_column) :

Base case

if top_left_row == bottom_right_row and top_left_column == bottom_right_column : print("%d" % matrix[top_left_row][top_left_column], end=" ") return

TLC (TLC + BRC)//2 (TLC + BRC)//2 + 1 BRC

TLR TLR

(TLC + BRC)//2 (TLC + BRC)//2 + 1

BRR BRR

TLC (TLC + BRC)//2 (TLC + BRC)//2 + 1 BRC

Z curve: code

def z_curve(matrix, top_left_row, top_left_column, bottom_right_row, bottom_right_column) :

Base case

if top_left_row == bottom_right_row and top_left_column == bottom_right_column : print("%d" % matrix[top_left_row][top_left_column], end=" ") return

TLC (TLC + BRC)//2 (TLC + BRC)//2 + 1 BRC

TLR TLR

(TLR + BRR)//2 (TLC + BRC)//2 (TLC + BRC)//2 + 1

(TLR + BRR)//2 + 1

BRR BRR

TLC (TLC + BRC)//2 (TLC + BRC)//2 + 1 BRC

Z curve: code

# lower-right sub-square

z_curve(matrix,

(top_left_row + bottom_right_row)//2 + 1,

(top_left_column + bottom_right_column)//2 + 1,

bottom_right_row,

bottom_right_column)

return

Z curve: code

# lower-right sub-square

z_curve(matrix,

(top_left_row + bottom_right_row)//2 + 1,

(top_left_column + bottom_right_column)//2 + 1,

bottom_right_row,

bottom_right_column)

return

N = 2**

i = 1; j = 0

A = [ [ x for x in range(jN+i, jN+i+N) ] for j in range(N) ]

z_curve(A,0,0,N-1,N-1); print()

Permutations: code

def permute(A) :

n = len(A)

if n < 2: return [ A ]

# Need recursion for n >=

permlist = [ ]

for p in permute(A[1:]) :

for position in range(n) :

p.insert(position, A[0])

permlist.append(p.copy())

p.pop(position)

return permlist

Problems – I

1. Towers of Hanoi: see

https://en.wikipedia.org/wiki/Tower_of_Hanoi

CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=

1. Write a recursive function with prototype int C(int n, int r); to

compute the binomial coefficient using the following definition:

( n r

)

=

( n − 1 r

)

( n − 1 r − 1

)

Supply appropriate boundary conditions.