NYU - Extended Bridge to CS - Homework 4  - Solved

Question           1:    write    two       versions            of            a              program              that        reads     a              positive               integer n, and        prints    the         first       n             even      numbers.                            

a)      In            the         first,      use         a              while loop.                      

b)     In            the         second, use         a              for       loop.                      

 

Each      section should  interact                with      the         user       exactly as            it             shows   in            the following            example:             Please   enter     a              positive               integer:                3             

2              4             

6              

   

Question 2: 

In this question we will use a simplified version of the Roman Numerals System to represent positive integers. 

 

The digits in this system are I, V, X, L, C, D and M. Each digit corresponds to a decimal value, as showed in the following table: 

 

Roman digit 
I
V
X
L
C
D
M
Decimal value 
1
5
10
50
100
500
1000
 

A number in the simplified Roman numerals system is a sequence of Roman digits, which follow these 2 rules: 

1.       The digits form a monotonically non-increasing sequence. That is the value of each digit is less than or equal to the value of the digit that came before it.  

For example, DLXXVI is a monotonically non-increasing sequence of Roman digits, but XIV is not. 

2.       There is no limit on the number of times that ‘M’ can appear in the number. ‘D’, ‘L’ and ‘V’ can each appear at most one time in the number. 

‘C’, ‘X’ and ‘I’ can each appear at most four times in the number. 

For example: IIII, XVII and MMMMMMDCCLXXXXVII are legal numbers in our simplified Roman numeral system, but IIIII, XIV, VVI and CCXLIII are not. 

Write a program that reads from the user a (decimal) number, and prints it’s representation in the simplified Roman numerals system. 

                

Your      program              should  interact                with      the         user       exactly as            it             shows   in            the following            example:             Enter decimal number:  

147

147 is CXXXXVII 

                

                

                 

Question 3: 

Write a program that reads from the user a positive integer (in a decimal representation), and prints its binary (base 2) representation. 

                

Your      program              should  interact                with      the         user       exactly as            it             shows   in            the following            example:             Enter decimal number:  

76           

The        binary  representation of            76           is             1001100             

 

Implementation Requirements:  

1.       You are supposed to implement the algorithm that converts to base 2. You should not use any string or special cout functionalities to make the conversion.  

2.       You are not allowed to use arrays. 

  

Question 4: 

Write two versions of a program that reads a sequence of positive integers from the user, calculates their geometric mean, and print the geometric mean.  

Notes:  

1.        In mathematics, geometric mean of a dataset {𝑎!, 𝑎", 𝑎# … , 𝑎$} containing positive numbers, is given by:  !&𝑎! ∙ 𝑎" ∙ 𝑎# ∙∙∙ 𝑎$.  

 For example, the geometric mean of 2, 9 and 12 is equal to 6 ("√2 ∙ 9 ∙ 12 = 6). 

2.       In    order    to            calculate             the         n-th       root       of            a              number,              you        should  call        the         pow       function,             located in            the         cmath library.  

 

Your two versions should read the integer sequence in two ways:       a) First read the length of the sequence. For example, an execution would look like: Please enter the length of the sequence: 3 Please enter your sequence:  

1 

2 

3 

The geometric mean is: 1.8171 

 

b) Keep reading the numbers until -1 is entered. For example, an execution would look like: 

Please enter a non-empty sequence of positive integers, each one in a separate line. End your sequence by typing -1: 

1                     2 

3 

-1 

The geometric mean is: 1.8171 

 

 

                                

Question           5:                            

Write a program that asks the user to input a positive integer n, and prints a textual image of an hourglass made of 2n lines with asterisks.  For example if n=4, the program should print: 

******* 

 ***** 

  *** 

   *    * 

  *** 

 ***** 

******* 

                

                

                

Question           6: 

Write    a              program              that        asks       the         user       to            input     a              positive               integer n, and        print      all           of            the         numbers             from     1             to            n             that        have      more     even digits     than       odd        digits.    

For         example,             if             n=30,    the         program              should  print:    

2                     4 

6 

8 

20 

22 

24 26 

28