Q1) (Greatest Common Divisor) The greatest common divisor (GCD) of two integers is the largest integer that evenly divides each of the two numbers. Write function gcd that returns the greatest common divisor of two integers.

Q1) (Greatest Common Divisor) The greatest common divisor (GCD) of two integers is the largest integer that evenly divides each of the two numbers. Write function gcd that returns the greatest common divisor of two integers.

C++ Programming: From Problem Analysis to Program Design

8th Edition

ISBN:9781337102087

Author:D. S. Malik

Publisher:D. S. Malik

Chapter15: Recursion

Section: Chapter Questions

Problem 12PE

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integer) Write a function that computes the sum of the digits in an integer. Use the following function header:def sumDigits(n):For example, sumDigits(234) returns 9 (Hint: Use the % operator to extract digits, and the // operator to remove the extracted digit. For instance, toextract 4 from 234, use 234 % 10 To remove 4 from 234, use 234 // 10 (=23) Use a loop to repeatedly extract and remove the digits until all the digits are extracted.) Write a test program that prompts the user to enter an integer and displays the sum of all its digits.
Q2) (Perfect Numbers) An integer number is said to be a perfect number if its factors, including 1 (but not the number itself), sum to the number. For example, 6 is a perfect number because 6 = 1 + 2 + 3. Write a function perfect that determines if parameter number is a perfect number. Use this function in a program that determines and prints all the perfect numbers between 1 and 1000. Print the factors of each perfect number to confirm that the number is indeed perfect. Challenge the power of your computer by testing numbers much larger than 1000.
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Assignment Write a program to calculate n! for a given number n and perform the simple calculator operations. The valid operations of the calculator are: + add - sub * mul I div The program must contain a function fact with one input parameter that returns the factorial of a number, a function add that performs the addition of two numbers, a function sub that performs the subtraction of two numbers, a function mul that performs the multiplication of two numbers, a function div that performs the division of two numbers. The program must also check for bad input data. Make sure when you pass parameters you pass the addresses (not the value). • All function return type must be of type void. • Take inputs in main function. • Pass the addresses of the operands and the address of the result to each function. Output must be displayed as follows: 1: Addition 2: Subtraction 3: Multiplication 4: Division 5: Factorial 6: Quit Enter the choice => 1 Enter two numbers => 2, 3 Sum => 5
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3) A function called isMagic is written below, your task is to write two of the helper functions ckRows and ckSDiagonal. ckRows checks the horizontal rows and ckSDiagonal checks the diagonal going from lower left to upper right. Each function returns true when all the individual sums of rows or the diagonal are equal to the magic number and false otherwise. An example magic square is shown, the size may not always be 3. 2 94 // value will be set, but may not be 5 // value will be set, but may not be 5 const int ROWS = 5; const int COLS = 5; bool isMagic(int arr[][COLS], int magic) { return ckRows (arr, magic) && ckcols(arr, magic) &8 | 75 3 ckMDiagonal (arr, magic) && cksDiagonal(arr, magic); 6 1 8 Your solution should be in this box:
1. Square Flower You can have the turtle draw an interesting flower like sha pe by drawing n squares. Each n-square flower is drawn after turning the turtle by some number of degrees between each square. (see Figure 1 for an example) (a) Typel: A 5-square red flower. (b) A 15-square blue flower. Figure 1: Two types of n-square flowers Using the following implementation of draw square() function write a function na med draw flower() that takes a turtle, the number n of squares to draw, the side length and a color as parameters and draws an n-square flower by repeating the function draw square() n times. Test your code by drawing a yellow 21-square flower with side length of 200. def drav aqu ar e (aTurtle, sidelength): f or i in range (4) : aTurtle.forvard (side Length) aTurtle. 1eft (90)
#5.Incorrect gurantee downvote. Euler's totient function, also known as phi-function ϕ(n),counts the number of integers between 1 and n inclusive,which are coprime to n.(Two numbers are coprime if their greatest common divisor (GCD) equals 1)."""def euler_totient(n): """Euler's totient function or Phi function. Time Complexity: O(sqrt(n)).""" result = n for i in range(2, int(n ** 0.5) + 1): if n % i == 0: while n % i == 0: n //= i.
Question 5: (30 marks) In mathematics, a prime number is a natural number greater than 1 that is not a product of two smaller natural numbers, i.e. is it has only two factors 1 and itself. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways of writing it as a product, 1 × 5 or 5 × 1, involve 5 itself. Note that the prime number series is: 2, 3, 4, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, … a. Write a Java method named isPrime that takes a natural number as a parameter and returns the if the given number is prime or not using the following header: Public static boolean isPrime(int num) b. Write a Java class called PrimeNumbers that: o Reads from the user a natural value n (should be less than or equal 200). o Prints a list of the prime numbers from 2 to n and their number and values. o The program has to work EXACTLY as given in the following sample run. Hints: • You should create a single dimension…
3) A function called isMagic is written below, your task is to write two of the helper functions ckRows and ckSDiagonal. ckRows checks the horizontal rows and ckSDiagonal checks the diagonal going from lower left to upper right. Each function returns true when all the individual sums of rows or the diagonal are equal to the magic number and false otherwise. An example magic square is shown, the size may not always be 3. 2 9 4 // value will be set, but may not be 5 // value will be set, but may not be 5 const int ROWS = 5; const int COLS - 5; bool isMagic(int arr[][COLS], int magic) { return ckRows (arr, magic) && ckCols(arr, magic) && 7 5 3 ckMDiagonal(arr, magic) && ckSDiagonal(arr, magic); 6 8 Your solution should be in this box: 1.
//-In python-// def compute_stats():"""Write a function compute_stats, such that given a string of grades as an input parameter,it calls the function get_new_grades (defined in theprevious question) and returns a tuple that containsthe average value of the initial grades andthe average value after running the get_new_grades function.""" pass The code should aslo have if __name__ == "__main__" section.
Python Q1) Write a function get_new_grades, such that given a list of grades as an input parameter,returns a new list where the minimum score isreplaced by 50.Do not modify the initial list! Q2) Write a function compute_stats, such that given a list of grades as an input parameter,it calls the function get_new_grades (defined in the previous questions)and returns a list that contains the average value of the initial list andthe average value of the list from the get_new_grades function.