CS 1005, C Term 2000
Introduction to Programming
Solution to the Practice Problems for Test 1

  1. a) Circle all syntactically correct C++ statements among the following. 
       int k;    (circled)

   bool IsEven(int n);    (circled)

   k-;  <-- incorrect. Closest match is k--; (decrements k by one)

   if (k==1) {    (circled)
      k += 1;     (circled)
   }

    b) State two advantages of using functions in program design. 

       Functions allow one to decompose a complex program into smaller,
   more easily understandable pieces.

   Functions allow code reuse. A function is defined only once,
   but it can be called (used) multiple times in a program.

  2. Using the function IsPrime whose specification is given here: 
       bool IsPrime(int n)
   // Returns true if n>1 and the only divisors of n are 1 and n
   // Returns false otherwise
   (function body not shown)
    fill in the main() function below so that it prints all prime numbers between 1 and 10,000 to the console output cout. A prime number is an integer p for which the function invocation IsPrime(n) returns true. Consecutive numbers should be separated by spaces in the output. 
       One possibility:
   (important point: there should *not* be any commas in 10000 below)

   int main() {
      for (int i=2; i<=10000; i++) {
         if (IsPrime(i))
            cout << i << " ";
      }
      return 0;
   }

   Another possibility:

   int main() {
      int i=2;
      while (i<=10000) {
         if (IsPrime(i))
            cout << i << " ";
         i++;
      }
      return 0;
}

  3. For each of the following program segments, state what output is produced. 
    a) int i=12;
   cout << i%5;     output:  2

b) int j=9;
   cout << ++j;     output:  10

c) int k=1;
   while (k/4 < 2) 
      k*=3;
   cout << k;       output:  9
 
d) bool flag=false;
   for (int i=1; i<=1000; i++)
      if (i%3 == 0)
         flag = !flag;
   if (flag)
      cout << "true";     
   else if (!flag)
      cout << "false";     output:  true

e) int lambda = 32;
   while (lambda > 0) {
      int k=lambda;
      while (k > 0) {
         cout << "*";
         k /= 2;
      }
      cout << endl;
      lambda /= 3;         output:  ******
   }                                ****
                                    **
                                    *

  4. Circle all incorrect statements in the following C++ program. In each case, give a brief explanation of what errors are associated with the statement. You may assume that the entirety of the program source file is shown below. 
       int main() {
      double x      error: missing final semicolon
      x = 3;        warning, but no error: conversion from int to double 
      y = 4.5;      error: object named y has not been declared
      cout << the value of x+y equals << x+y;  error: missing quotation marks
      return 0.0;   warning, but no error: conversion from double to int 
   }

  5. Examine the function named UFO defined below and state in words what numbers n yield a return value of true when UFO is called with n as its input argument. 
       bool UFO(int n)
   {
      while (n%2 == 0)
         n/=2;
      return (n==1);
   }

   Answer: UFO(n) returns true if n is a power of 2, and returns false 
   otherwise. For example, UFO(32) returns true because 32 equals 2 to 
   the 5th power, while UFO(7) returns false. By the way, UFO stands 
   for "Unidentified Function Object".