Computer Programming and Software

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lst = []
n=int(input('How many numbers are there? '))

for i in range(n):
    num = float(input('Enter {}th number: '.format(i+1)))
    lst.append(num)
# k=range(n)
# print(k)
maxi=lst[0]
# print(maxi)
for i in range(1,n):
    if (maxi < lst[i]):
        maxi=lst[i]
print('Maximum computed manually is: ', maxi)
print('Maximum number from the list is: ', max(lst))

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# Program to check whether a number is odd or even
n=int(input('Enter your number: '))
if n%2 == 0:
    print('Your entered number', n, 'is even')
else:
    print('Your entered number', n, 'is odd')

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# Program to check if the input year is a leap year or not

year = int(input("Enter a year number of your choice: "))

#if year%400 == 0 or (year %4==0 and year%100!=0):
#    print('The year {} is a leap year.'.format(year))
#else:
#    print('The year {} is not a leap year.'.format(year))

if (year % 4 == 0):
    if (year % 100 == 0):
        if year % 400 == 0:
            print("{} is a leap year".format(year))
        else:
            print("{} is not a leap year".format(year))
    else:
        print("{} is a leap year".format(year))
else:
    print("{} is not a leap year".format(year))

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# Program to find roots of quadratic equation

print('Consider the equation of the form ax^2+bx+c=0')

a=float(input('Enter the non-zero coefficient a of x^2: '))
b=float(input('Enter the coefficient b of x: '))
c=float(input('Enter the constant term c: '))

delta = b**2 - 4 * a * c
d=delta**(0.5)

if (delta<0):
    print('The given quadratic equation {}x^2 + {}x + c =0 has no real roots'.format(a,b,c))
else:
    r1 = (-b+d)/(2*a)
    r2 = (-b-d)/(2*a)
    print('The real roots of given quadratic equation {}x^2 + {}x + {} =0 are {} and {}'.format(a,b,c,r1,r2))

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# Python program to compute n factorial
n = int(input('Enter a non-negative integer: '))
if n<0:
    print('Please enter a non-negative integer.')
elif n==0:
    print('0! = 1')
else:
    i=n
    nfact=1
    for i in range(n,0,-1):
        nfact = nfact * i
    print('{}! = {}'.format(n,nfact))

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# Python program to check whether a number is prime or not
n=int(input('Enter an integer n>2: '))
for i in range(2,int((n**0.5)+1)):
    if n%i==0:
        print("The entered number {} is not prime.".format(n))
        print(i)
        break
else:
    print("The entered number {} is a prime number.".format(n))

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# Python program to list all the prime numbers in a given range
a = int(input('Give the starting point a (> 0) of the range: '))
b = int(input('Give the ending point b (> a) of the range: '))
if b > a > 0:
    if a == 1:
        a1 = 2
    else:
        a1 = a
    print('The prime numbers between {} and {} are the following:'.format(a,b))
    for n in range(a1, b+1):
        test = 0
        for i in range(2, int((n**0.5)+1)):
            if n % i == 0:
                test = 1
                break
#        else:
        if test == 0:
            print(n, end=', ')
else:
    print("Please enter a valid range.")

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# Program to factorize a given number
n = int(input("Enter the number (n > 1) which you want to factorize: "))
lst = [1]
#lst.append(1)
for i in range(2, n+1):
    if n % i == 0:
        lst.append(i)
if len(lst) == 2:
    print("The number {} is prime and it only factors are 1 and {}.".format(n,n))
else:
    print('The factors of {} are the following:'.format(n))
    for p in lst:  # range(len(lst)):
        print(p, end=', ')
# Extending the program to check whether the number is perfect or not
print('')
if n == sum(lst)-n:
    print('The number',n,'is perfect')

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# Program to compute the nth prime number

n = int(input('Enter the value of n to compute the nth prime number: '))
c = 2
x = 5
while c < n:
    for i in range(2,int(x**0.5)+1):
        if x % i == 0:
            break
    else:
        c = c + 1
    x = x + 2
print(n,"th prime number is ",x-2)

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# Program to do various manipulation of numbers
# We check number is perfect or not, palindrome or not, compute sum of digits, sum of squares of digits and reverse the number

n = int(input('Enter the number: '))

sumdiv = 0  # for storing sum of divisors

for i in range(1,int(n/2)+1):
    if n % i == 0:
        sumdiv = sumdiv + i

if sumdiv == n:
    print('The entered number {} is perfect'.format(n))
else:
    print('The entered number {} is Not perfect'.format(n))

num = n  # num will be used for manipulation without disturbing n
sum = 0  # will be used to store the sum of digits of n
sumsq = 0  # will be used to store the sum of squares of digits
rev = 0  # will be used to reverse the number

while num > 0:
    digit = num % 10
    sum = sum + digit
    sumsq = sumsq + (digit**2)
    rev = (rev * 10) + digit
    num = num // 10

if rev == n:
    print('The entered number {} is palindrome'.format(n))
else:
    print('The entered number {} is Not palindrome'.format(n))

print('The sum of digits of {} is {}'.format(n,sum))
print('The sum of the squares of digits of {} is {}'.format(n,sumsq))
print('The entered number {} in the reverse order of its digits is {}'.format(n,rev))

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# Program to find gcd and lcm of two numbers
a = int(input('Enter first positive integer a: '))
b = int(input('Enter second positive integer b: '))

gc = 1

def gcd(x,y):
    global gc
    x1=x
    y1=y
    if x1 % y1 == 0:
        print('GCD of {} and {} computed by recurrence is {}'.format(a,b,y1))
        gc = y1
    else:
        gcd(y1,(x1%y1))


gcd(a, b)

for i in range (min(int(a/2),int(b/2))+1,0,-1):
    if a % i == 0 and b % i == 0:
        print('GCD of {} and {} computed by loop is {}'.format(a,b,i))
        break

print('LCM of {} and {} is {} (using y1)'.format(a,b,int(a*b/gc)))
print('LCM of {} and {} is {} (using i)'.format(a,b,int(a*b/i)))

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# Python Program to compute Euler's phi function for n >= 2

g=1
def gcd(x,y):
    global g
    if x % y == 0:
        g = y
#        return y
    else:
        gcd(y,x%y)

n = int(input('Enter a positive integer: '))
c = 0

for i in range(1,n):
    gcd(n,i)
    if g == 1:
        c = c + 1
print('Euler\'s function of {} is {}'.format(n,c))

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# Python Program to compute the mobius function mu(n)
n = int(input('Enter the value of n: '))
u=1
def is_prime(x):
    for i in range(2,int(x**(0.5))+1):
        if x%i==0:
            return 0
    else:
        return 1

if n <=0:
    print('Enter a valid positive integer n')
elif n==1:
    print('u(1)=1')
else:
    for k in range(2,n+1):
        if is_prime(k)==1 and n%k==0:
            if n%(k*k)==0:
                u=0
                break
            else:
                u = u*(-1)
    print('Mobius function u({})={}'.format(n,u))

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# Python program to compute n terms of fibonacci sequence

def fibo(x):
    if x <= 0:
        print('Enter a positive integer.')
    elif x  == 1:
        return 0
    elif x == 2:
        return 1
    else:
        return fibo(x-1)+fibo(x-2)

n = int(input('Enter the term n: '))

#print(fibo(n))  # To print the nth fibonacci number

#for i in range(1,n+1):  # To print first n fibonacci numbers
#    print(fibo(i))

i = 1
while fibo(i)<= n:  # To print fibonacci numbers upto n
    print(fibo(i))
    i = i + 1

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# Python program to compute the sum of the series e^x, sin x, cos x, sinh x and cosh x upto n terms

import math

x = float(input('Enter the value of x: '))
n = int(input('Enter the number of terms of the series n: '))

#x = y*math.pi/180

def expo(x):
    sumex = 1
    termex = 1
    for m in range(1,n):
        termex = (termex * x)/m
        sumex = sumex + termex
    return sumex

sumcos = 1
termcos = 1
termsin = x
sumsin = termsin

#i=1
#while math.fabs(termcos) > 0.0001:
for i in range(1,n):
    termsin = (termsin * (x**2) * (-1))/((2*i)*(2*i+1))
    sumsin = sumsin + termsin
    termcos = (termcos * (x**2) * (-1))/((2*i-1)*(2*i))
    sumcos = sumcos + termcos
#    i = i + 1

print('')
print('The computed value of e^{} upto {} terms is {}.'.format(x,n,expo(x)))
print('The actual value of e^{} using math module is {}.'.format(x,math.exp(x)))
print('')

print('The computed value of sin({}) upto {} terms is {}.'.format(x,n,sumsin))
print('The actual value of sin({}) using math module is {}.'.format(x,math.sin(x)))
print('')

print('The computed value of cos({}) upto {} terms is {}.'.format(x,n,sumcos))
print('The actual value of cos({}) using math module is {}.'.format(x,math.cos(x)))
print('')

print('The computed value of sinh({}) upto {} terms is {}.'.format(x,n,(expo(x)-expo(-1*x))/2))
print('The actual value of sinh({}) using math module is {}.'.format(x,math.sinh(x)))
print('')

print('The computed value of cosh({}) upto {} terms is {}.'.format(x,n,(expo(x)+expo(-1*x))/2))
print('The actual value of cosh({}) using math module is {}.'.format(x,math.cosh(x)))
print('')