Assignment 5

1. Understanding Scope

   Consider the following program:

   #include <iostream>
   #include "simpio.h"
   using namespace std;
   int main()
   {
     int p2n = 1;
     int n = getInteger("n?");
     for (int i = 0; i < n; i++) {
       int tmp = p2n;
       cout << "2^" << i << " = " << tmp << endl;
       p2n = tmp * 2;
     }
     cout << "2^n = " << p2n << endl;
   }
   

   For this program above, what is printed for the following input values of n: 4, 7, 9?

   Now, consider the following program:

   #include <iostream>
   #include "simpio.h"
   using namespace std;
   int main()
   {
     int p2n = 1;
     int n = getInteger("n?");
     for (int i = 0; i < n; i++) {
       int tmp = p2n;
       cout << "2^" << i << " = " << tmp << endl;
       int p2n = tmp * 2;
     }
     cout << "2^" << n << " = " << p2n << endl;
   }
   

   For this program above, what is printed for the following input values of n: 4, 7, 9?

   What is the difference between the two programs? Why are the outputs of the two programs so different?

   Now consider the following program:

   #include <iostream>
   #include "simpio.h"
   using namespace std;
   int main()
   {
     int p2n = 1;
     int n = getInteger("n?");
     for (int i = 0; i < n; i++)
       int p2n = p2n * 2;
     cout << "2^" << n << " = " << p2n << endl;
   }
   

   Notice that there are no curly braces { } in the body of the for loop. What is the output that you get for different input values of n? Explain.

2. DrawBox: Functions with Multiple Arguments

   1. Write a function drawBox(int height, int width) which takes two inputs height and width and draws a box of specified height and width on the console. For example, drawBox(4,5) should draw a structure of the following form:
      

      *****
      *   * 
      *   *
      *****
      

      Think about what additional helper functions you would like to write to facilitate the above operation. For instance, you can write two additional functions drawLine(width) which draws a line of given width, and drawSide(width) which draws (a part of) the sides of the box for a given width, and then call these functions multiple times.
   2. Write a main() function which repeatedly inputs two integers height and width from the user and makes use of the drawBox(height,width) function defined above to draw a box of the corresponding height and width. You should keep doing this until the user enters a non-positive value (i.e., 0 or less) for either height or width in which case you should exit the program.

3. Prime Numbers: Functions with Return Values

   1. Recall that a number is prime if it is not divisible by any number other 1 and itself. Write a function checkPrime(int x) which takes as input a positive integer x, and returns true if the number is prime, and false otherwise. By convention, 1 is not considered to be prime, and your program should correctly handle this special case.
   2. Write a main() function to input a positive integer n from the user, and print all the primes less than equal to n. Specifically, you should make use of checkPrime(x) function written in the part above.