GE8161 Problem solving and python programming lab Manual

NEHRU INSTITUTE OF ENGINEERING AND TECHNOLOGY

(Approved by AICTE, New Delhi and affiliated to Anna University)

NAME      : _____________________________________________________ REG. NO. : _____________________________________________________ Branch : _____________________________________________________ SUBJECT CODE & TITLE :

GE 8161 – PROBLEM SOLVING AND PYTHON PROGRAMMING

LABORATORY

CONTENTS

Sl.No.	Date	Name of the Experiment	Page No.	Signature
1		Compute the GCD of two numbers.
2		Find the square root of a number (Newton’s method)
3		Exponentiation (power of a number)
4		Find the maximum of a list of numbers
5(a)		Linear search
5(b)		Binary search
6(a)		Selection sort
6(b)		Insertion sort
7		Merge sort
8		First n prime numbers
9		Multiply matrices
10		Programs that take command line arguments (word count)
11		Find the most frequent words in a text read from a file
12		Simulate elliptical orbits in Pygame
13		Simulate bouncing ball in Pygame

Ex. No. :01
Date:	GCD OF TWO NUMBERS

Aim:

To write a Python program to find GCD of two numbers.

Algorithm:

1.      Define a function named computeGCD()

2.      Find the smallest among the two inputs x and y

3.      Perform the following step till smaller+1

Check if ((x % i == 0) and (y % i == 0)), then assign GCD=i

4.      Print the value of gcd

Program:

def computeGCD(x, y):

if x > y:

smaller = y

else:

smaller = x

for i in range(1, smaller+1):

if((x % i == 0) and (y % i == 0)):

gcd = i

return gcd

       num1 = int(input("Enter first number: "))

num2 = int(input("Enter second number: "))

print("The GCD. of", num1,"and", num2,"is", computeGCD(num1, num2))

Sample output :

        The GCD of 54 and 24 is 6

Result:

Thus the Python program to compute GCD of two numbers is executed successfully and the output is verified.

Ex. No. :02
Date:	SQUARE ROOT OF A NUMBER

Aim:

To write a Python Program to find the square root of a number by Newton’s Method.

Algorithm:

1.      Define a function named newtonSqrt().

2.      Initialize approx as 0.5*n and better as 0.5*(approx.+n/approx.)

3.      Use a while loop with a condition better!=approx to perform the following,

i.  Set approx.=better

ii. Better=0.5*(approx.+n/approx.)

4.      Print the value of approx

Program:

def newtonSqrt(n):

approx = 0.5 * n

better = 0.5 * (approx + n/approx)

while better != approx:

approx = better

better = 0.5 * (approx + n/approx)

return approx

print('The square root is' ,newtonSqrt(81))

Output:

            The square root is 9

Result:

Thus the Python program for finding the square root of a given number by Newton’s Method is executed successfully and the output is verified.

Ex. No. : 03	EXPONENTIATION OF A NUMBER
Date:

Aim:

To write a Python program to find the exponentiation of a number.

Algorithm:

1.        Define a function named power()

2.      Read the values of base and exp

3.      Use ‘if’ to check if exp is equal to 1 or not

 i. if exp is equal to 1, then return base

ii.if exp is not equal to 1, then return (base*power(base,exp-1))

4.      Print the result

Program:

def power(base,exp):

if(exp==1):

return(base)

if(exp!=1):

return(base*power(base,exp-1))

base=int(input("Enter base: "))

exp=int(input("Enter exponential value: "))

print("Result:",power(base,exp))

Output:

Enter base: 7

Enter exponential value: 2

Result:49

Result:

Thus the Python program to find the exponentiation of a number is executed successfully and the output is verified.

Ex. No. :04 Date:

FINDING MAXIMUM FROM A LIST OF NUMBERS

Aim:

To write a Python Program to find the maximum from a list of numbers.

Algorithm:

1.   Create an empty list named l

2.   Read the value of n

3.   Read the elements of the list until n

4.   Assign l[0] as maxno

5.   If l[i]>maxno then set maxno=l[i]

6.   Increment i by 1

7.   Repeat steps 5-6 until i<n

8.   Print the value of maximum number

Program:

l=[]

n=int(input("enter the upper limit"))

for i in range(0,n):

a=int(input("enter the numbers"))

l.append(a)

maxno=l[0]

for i in range(0,len(l)):

if l[i]>maxno:

maxno=l[i]

print("The maximum number is %d"%maxno)

Output:

Enter the upper limt 3

Enter the numbers 6

Enter the numbers 9

Enter the numbers 90

The maximum number is 90

Result:

Thus a Python Program to find the maximum from the given list of numbers is successfully executed and the output is verified.

Ex. No. : 5(a)
Date:	LINEAR SEARCH

Aim:

To write a Python Program to perform Linear Search

Algorithm:

1.      Read n elements into the list

2.      Read the element to be searched

3.      If alist[pos]==item, then print the position of the item

4.      Else increment the position and repeat step 3 until pos reaches the length of the list

Program:

def search(alist,item):

    found=False

    for i in range(n):

        if alist[i]==item:

            found=True

            print("element found in position",i)

    if(found==False):

        print("not found")

a=[]

n=int(input("enter upper limit"))

for i in range(0,n):

    e=int(input("enter the elements"))

    a.append(e)

x=int(input("enter element to search"))

search(a,x)

Output:

enter upper limit3

enter the elements12

enter the elements21

enter the elements41

enter element to search21

element found in position 1

Result:

Thus the Python Program to perform linear search is executed successfully and the output is verified.

EX. No. : 5(b)
Date:	BINARY SEARCH

Aim:

To write a Python Program to perform binary search.

Algorithm:

1.Read the search element

2.Find the middle element in the sorted list

3.Compare the search element with the middle element

i.  if both are matching, print element found

ii. else then check if the search element is smaller or larger than the middle element

4.If the search element is smaller than the middle element, then repeat steps 2 and 3 for the left sublist of the middle element

5.If the search element is larger than the middle element, then repeat steps 2 and 3 for the right sublist of the middle element

6.Repeat the process until the search element if found in the list

7.If element is not found, loop terminates

Program:

def bsearch(alist,item):

    first=0

    last=len(alist)-1

    found=False

    for i in range(n):

        mid=(first+last)//2

        if alist[mid]==item:

            found=True

            print("element found in position",mid)

            break

        elif item<alist[mid]:

                last=mid-1

        else:

            first=mid+mid-1

    if(found==False):

        print('not found')

a=[]

n=int(input("enter upper limit"))

for i in range(0,n):

    e=int(input("enter the elements"))

    a.append(e)

x=int(input("enter element to search"))

bsearch(a,x)

Output:

enter upper limit3

enter the elements12

enter the elements52

enter the elements65

enter element to search52

element found in position 1

Result:

Thus the Python Program to perform binary search is executed successfully and the output is verified

Ex. No. : 6(a)
Date:	SELECTION SORT

Aim:

To write a Python Program to perform selection sort.

Algorithm:

1.      Create a function named selectionsort

2.        Initialise pos=0

3.      If alist[location]>alist[pos] then perform the following till i+1,

4.      Set pos=location

5.      Swap alist[i] and alist[pos]

6.      Print the sorted list

Program:

def selectionSort(alist):

    for i in range(0,n):

        for j in range(i+1,n):

            if alist[j]<alist[i]:

                min = alist[j];

                alist[j] = alist[i];

                alist[i] = min;

alist = []

n=int(input("enter the no of valus in the list"))

for i in range(n):

    alist.append(int(input()))

selectionSort(alist)

print(“Sorted List”,alist)

Output:

enter the no of valus in the list5

52

12

10

45

65

Sorted List [10, 12, 45, 52, 65]

Result:

Thus the Python Program to perform selection sort is successfully executed and the output is verified.

Ex. No. : 6(b) Date:

INSERTION SORT

Aim:

To write a Python Program to perform insertion sort.

Algorithm:

1.      Create a function named insertionsort

2.      Initialise currentvalue=alist[index] and position=index

3.      while position>0 and alist[position-1]>currentvalue, perform the following  till len(alist)

4.      alist[position]=alist[position-1]

5.        position = position-1

6.        alist[position]=currentvalue

7.      Print the sorted list

Program:

def insertionSort(alist):

for index in range(1,len(alist)):

currentvalue = alist[index]

position = index

while position>0 and alist[position-1]>currentvalue:

alist[position]=alist[position-1]

position = position-1

alist[position]=currentvalue

alist = [54,26,93,17,77,31,44,55,20]

insertionSort(alist)

print(alist)

Output:

[17, 20, 26, 31, 44, 54, 55, 77, 93]

Result:

Thus the Python program to perform insertion sort is successfully executed and the output is verified.

Ex. No. : 7 Date:

MERGE SORT

Aim:

To write a Python Program to perform Merge sort.

Algorithm:

1.      Create  a function named  mergesort

2.      Find the mid of the list

3.      Assign lefthalf = alist[:mid] and righthalf = alist[mid:]

4.      Initialise i=j=k=0

5.      while i < len(lefthalf) and j < len(righthalf), perform the following if lefthalf[i] < righthalf[j]:

alist[k]=lefthalf[i]

Increment i

else

alist[k]=righthalf[j]

Increment j

Increment k

6.        while i < len(lefthalf),perform the following alist[k]=lefthalf[i]

7.      while j < len(righthalf), perform the following alist[k]=righthalf[j]

Increment j Increment k

8.      Print the sorted list

Program:

def mergeSort(alist):

if len(alist)>1:

mid = len(alist)//2 lefthalf = alist[:mid] righthalf = alist[mid:] mergeSort(lefthalf) mergeSort(righthalf) i=j=k=0

while i < len(lefthalf) and j < len(righthalf):

    if lefthalf[i] < righthalf[j]:

alist[k]=lefthalf[i]

i=i+1

else:

alist[k]=righthalf[j]

j=j+1

k=k+1

while i < len(lefthalf): alist[k]=lefthalf[i]

    i=i+1

k=k+1

while j < len(righthalf): alist[k]=righthalf[j]

    j=j+1

k=k+1

alist = [54,26,93,17,77,31,44,55,20]

mergeSort(alist)

print(alist)

Output:

[17, 20, 26, 31, 44, 54, 55, 77, 93]

Result:

Thus the Python program to perform merge sort is successfully executed and the output is verified

Ex. No. : 8   Date:

FIRST N PRIME NUMBERS

Aim:

To write a Python program to find first n prime numbers.

Algorithm:

1.      Read the value of  n

2.      for num in range(0,n + 1), perform the following

3.      if num%i is 0 then break else print the value of num

4.      Repeat step 3 for i in range(2,num)

Program:

n = int(input("Enter the upper limit: "))

print("Prime numbers are")

for num in range(0,n + 1):

#  prime numbers are greater than 1 if num > 1:

for i in range(2,num): if (num % i) == 0:

break

else:

print(num)

Output:

Enter the upper limit:10

Prime numbers are

2

3

5

7

Result:

Thus the Python Program to find the first n prime numbers is executed successfully and the output is verified.

Ex. No. : 9 Date:

MATRIX MULTIPLICATION

Aim:

To write a Python program to multiply matrices.

Algorithm:

1.      Define two matrices X  and Y

2.      Create a resultant matrix named ‘result’

3.      for i in range(len(X)):

i. for j in range(len(Y[0])):

a)      for k in range(len(Y))

b)        result[i][j] += X[i][k] * Y[k][j]

4.      for r in result, print the value of r

Program:

X = [[12,7,3],

     [4 ,5,6],

     [7 ,8,9]]

Y = [[5,8,1,2],

     [6,7,3,0],

     [4,5,9,1]]

result = [[0,0,0,0],

      [0,0,0,0],

      [0,0,0,0]]

for i in range(len(X)):

for j in range(len(Y[0])):

for k in range(len(Y)):

result[i][j] += X[i][k] * Y[k][j]

for r in result:

print(r)

Output:

[114, 160, 60, 27]

[74, 97, 73, 14]

[119, 157, 112, 23]

Result:

Thus the Python program to multiply matrices is executed successfully and the output is verified.

Ex. No. :10
Date:	COMMAND LINE ARGUMENTS(WORD COUNT)

Aim:

To write a Python program for command line arguments.

Algorithm:

1.      Add arguments to find the words and lines

2.      Add the filename as argument

3.      Parse the arguments to get the values

4.      Format and print the words and lines

Program:

parser=argparse.ArgumentParser()

parser.add_argument('--words','-w',action='store_true')

parser.add_argument('--lines','-l',action='store_true')

parser.add_argument('filename')

args=parser.parse_args()

if args.words:

print("words {}".format(print_words(args.filename))

elif args.lines:

print("lines {}".format(print_lines(args.filename))

else:

print ("words {}".format(print_words(args.filename))

print("lines {}".format(print_lines(args.filename))

Output:

python main.py –i input.txt

words 23

lines 1

Result:

Thus the Python program for command line arguments is executed successfully and the output is verified.

Ex. No. : 11
Date:	FINDING MOST FREQUENT WORDS IN A TEXT READ FROM A FILE

Aim:

To write a Python program to find the most frequent words in a text read from a file.

Algorithm:

1.      Read the filename

2.      Open the file in read mode

3.      Read each line from the file to count the lowers and words

4.      Read each  line from the file to replace the punctuations

5.      Split each line into words and count them

6.      Print the words and counts

Program:

def main():

filename=raw_input("enter the file").strip()

infile=open(filename,"r")

wordcounts={}

for line in infile:

processLine(line.lower(),wordcounts)

pairs=list(wordcounts.items())

items=[[x,y] for (y,x) in pairs]

items.sort()

for i in range(len(items)-1,len(items)-11,-1):

print(items[i][1]+"\t"+str(items[i][0]))

def processLine(line,wordcounts):

line=replacePunctuations(line)

words=line.split()

for word in words:

if word in wordcounts:

wordcounts[word]+=1

else:

wordcounts[word]=1

def replacePunctuations(line):

for ch in line:

if ch in "~@#$%^&*()_-+=<>?/.,:;!{}[]''":

line=line.replace(ch," ")

return line

main()

Output:

Enter a filename:a.txt

Hi        1

How    1

Are      1

You     1

Result:

Thus the Python program to find the most frequent words in a text read from a file is executed successfully and the output is verified.

Ex. No. : 12
Date:	SIMULATE ELLIPTICAL ORBITS IN PYGAME

Aim:

To write a Python program to simulate elliptical orbits in Pygame.

Algorithm:

1.      Import the required packages

2.      Set up the colours for the elliptical orbits

3.      Define the parameters to simulate elliptical orbits

4.      Display the created orbits

Program:

import math

import random

import pygame

class Particle ():

def __init__ (self, x, y, colour=0x000000):

self.x = x

self.y = y

self.vx = 0

self.vy = 0

self.colour = colour

def apply_gravity (self, target):

dsqd = (self.x - target.x) ** 2 + (self.y - target.y) ** 2

#g = G*m/dsqd * normalized (self - target)

if dsqd == 0:

return

self.vx += -1 / dsqd * (self.x - target.x) / dsqd ** 0.5

self.vy += -1 / dsqd * (self.y - target.y) / dsqd ** 0.5

def update (self):

self.x += self.vx

self.y += self.vy

pygame.init()

window = pygame.display.set_mode ((600, 400))

main_surface = pygame.Surface ((600, 400))

colours = [0x000000, 0x111111, 0x222222, 0x333333, 0x444444, 0x555555, 0x666666, 0x777777, 0x888888, 0x999999, 0xaaaaaa, 0xbbbbbb] + [0xFF0000, 0x00FF00, 0x0000FF, 0xFFFF00, 0xFF00FF, 0x00FFFF, 0x888888, 0xFFFFFF, 0x808000, 0x008080, 0x800080, 0x800000]

#colours = [0xFF0000, 0x00FF00, 0x0000FF, 0xFFFF00, 0xFF00FF, 0x00FFFF, 0x888888,

0xFFFFFF, 0x808000, 0x008080, 0x800080, 0x800000] particles = [Particle (200, 100, colours [i]) for i in range (20)] earth = Particle (200, 200)

for i, p in enumerate (particles):

p.vx = i / 100

while (True):

#   main_surface.fill(0x000000)

pygame.draw.circle (main_surface, 0x00FF00, (earth.x, earth.y), 5, 2)

for p in particles:

p.apply_gravity (earth)

p.update ()

pygame.draw.circle (main_surface, p.colour, (int (p.x), int (p.y)), 5, 2)

window.blit(main_surface, (0, 0))

pygame.display.flip()

Output:

Result:

Thus the Python Program to simulate elliptical orbits using Pygame is executed successfully and the output is verified.

Ex. No. : 13
Date:	SIMULATE BOUNCING BALL USING PYGAME

Aim:

To write a Python program to bouncing ball in Pygame.

Algorithm:

1.      Import the required packages

2.      Define the required variables

3.      Define the screen space to display the  bouncing balls in that space

Program:

import sys

import pygame

pygame.init()

size = width, height = 320, 240

speed = [2, 2]

black = 0, 0, 0

screen = pygame.display.set_mode(size)

ball = pygame.image.load('C:\\Users\\admin\\Desktop//ball.jpg')

ballrect = ball.get_rect()

while 1:

for event in pygame.event.get():

if event.type == pygame.QUIT: sys.exit()

ballrect = ballrect.move(speed)

if ballrect.left < 0 or ballrect.right > width:

speed[0] = -speed[0]

if ballrect.top < 0 or ballrect.bottom > height:

speed[1] = -speed[1]

screen.fill(black)

screen.blit(ball, ballrect)

pygame.display.flip()

Output:

Result:

Thus the Python Program to simulate bouncing ball using Pygame is executed successfully and the output is verified.