[SOLVED] NYU Homework 7

The function should:

Print a formatted monthly calendar of that month

Return a number 1-7 that represents the day in the week of the last day in that

month.

Formatting Notes:

• •

Example: when calling printMonthCalender(31, 4)it should return 6, and should print:

b. A method for determining if a year is a leap year in the Gregorian calendar system is to check if it is divisible by 4 but not by 100, unless it is also divisible by 400.
For example, 1896, 1904, and 2000 were leap years but 1900 was not.
Write a function that takes in a year as input and return true if the year is a leap year, return false otherwise.

Note: background on leap year https://en.wikipedia.org/wiki/Leap_year c.

• •

The output should include a header line with the days’ names.

Columns should be spaced by a Tab.

The function should use the functions from sections (a) and (b) in order to print a

formatted yearly calendar of that year.

Formatting Note: As the header for each month you should print the months’ name

followed by the year (e.g. March 2016).

Example: Appendix A shows the expected output of the call

printYearCalender(2016, 5).

d. Write program that interacts with the user and your function in (c).

Question 2:

Consider the following definitions:

1. A proper divisors of a positive integer (≥ 2) is any of its divisors excluding the number itself.

   For example, the proper divisors of 10 are: 1, 2 and 5.

2. A perfect number is a positive integer (≥ 2) that is equal to the sum of its proper divisors.

   For example, 6 and 28 are perfect numbers, since:
   6=1+2+3
   28 = 1 + 2 + 4 + 7 + 14
   Background of perfect numbers: https://en.wikipedia.org/wiki/Perfect_number

3. Amicable numbers are two different positive integer (≥ 2), so related that the sum of the proper divisors of each is equal to the other number.
   For example, 220 and 284 are amicable numbers, since:
   284 = 1 + 2 + 4 + 5 + 10 + 11 + 20 + 22 + 44 + 55 + 110

220 = 1 + 2 + 4 + 71 + 142

(proper divisors of 220)

(proper divisors of 284)

Background of amicable numbers: https://en.wikipedia.org/wiki/Amicable_numbers

1. Write a function:

   void analyzeDividors(int num, int& outCountDivs, int& outSumDivs) The function takes as an input a positive integer num (≥ 2), and updates two output parameters with the number of num’s proper divisors and their sum.
   For example, if this function is called with num=12, since 1, 2, 3, 4 and 6 are 12s proper divisors, the function would update the output parameters with the numbers 5 and 16. Note:

2. Use the function you wrote in section (a), to implement the function:

   bool isPerfect(int num)
   This functions is given positive integer num (≥ 2), and determines if it is perfect number or not.

3. Use the functions you implemented in sections (a) and (b), to write a program that reads from the user a positive integer M (≥ 2), and prints:
   • All the perfect numbers between 2 and M.
   • All pairs of amicable numbers that are between 2 and M (both numbers must be in the

     range).
     Note: Pay attention to the running time of your implementation. An efficient algorithm for this part would call analyzeDividors Θ(𝑀) times all together.

Pay attention to the running time of your function. An efficient implementation would

run in Θ”√𝑛𝑢𝑚’.

Question 3:

a. b.

Question 4:

a)E c

b) c) d)

Question 5:

a) b) c) d) e)

Question 6:

a) b)

Question 7:

How many one-to-one functions are there from a set with five elements to sets with the following number of elements?
a) 4
b) 5

c) 6 d) 7

Solve Exercise 8.2.2, section b from the Discrete Math zyBook.

Solve Exercise 8.3.5, sections a-e from the Discrete Math zyBook

Solve the following questions from the Discrete Math zyBook:

xercise 5.1.2, sections b,

Exercise 5.3.2, section a

Exercise 5.3.3, sections b, c

Exercise 5.2.3, sections a, b

Solve the following questions from the Discrete Math zyBook:

Exercise 5.4.2, sections a, b

Exercise 5.5.3, sections a-g

Exercise 5.5.5, section a

Exercise 5.5.8, sections c-f

Exercise 5.6.6, sections a, b

Solve the following questions from the Discrete Math zyBook:

Exercise 5.7.2, sections a, b

Exercise 5.8.4, sections a, b

Appendix A.

The expected output of the call printYearCalender(2016, 5) is: