Chapter 7: Advanced Control Flow II

Chapter Goals

• To be able to program loops with the do/while statement
• To learn how to process character, word, and line input
• To learn how to read input from a file through redirection
• To implement approximations and simulations

The do Loop

• Sometimes you want to execute the body of a loop at least once and perform the loop test after the body was executed.
• The do/while loop serves that purpose.

  do
  { statements
  }
  while (condition);

• Example: A simple approximation algorithm to compute square root (ancient Greeks) - the sequence
  
  
  x₀ = a,  x_n+1 = ( x_n + a/x_n ) / 2
  
  converges and has limit square root of a.

  do
  {  xold = xnew;
     xnew = (xold + a / xold) / 2;
  }
  while (fabs(xnew - xold) > EPSILON);

  Stop when two successive approximations differ from each other by a very small amount. We want to enter the loop at least once so that we can compute the difference between two approximations.

  

The do Loop (sqroot.cpp)

The do Loop (Syntax 7.2: do/while Statement)

do statement while (condition);

do x = sqrt(x); while (x >= 10);

Nested Loops

• How can we print a table of values?
• For example, this table tells you the fate of $10,000 invested under various interest rates for a different number of years.

• Here is the pseudocode:

  print table header
  double rate;
  for (rate = RATE_MIN; rate <= RATE_MAX; 
       rate = rate + RATE_INCR)
  {  print table row
  }

• How do we print a table row? You need to program another loop.

  int year;
  for (year = YEAR_MIN; year <= YEAR_MAX;
       year = year + YEAR_INCR)
  {  balance = future_value(initial_balance, rate, year);
     cout << setw(10) << balance;
  }

• It's a good idea to print the table header as a loop as well.

  cout << "Rate     ";
  int year;
  for (year = YEAR_MIN; year <= YEAR_MAX;
       year = year + YEAR_INCR)
  {  cout << setw(2) << year << " years";
  }

• Once everything is put together, we have the loop printing a single row nested in the loop that traverses the interest rates.

Nested Loops (table.cpp)

Nested Loops

• Sometimes the iteration count of the inner loop depends on the outer loop.
• Example: printing a triangle shape.

  []
  [][]
  [][][]
  [][][][]

• To print n rows, use the loop.

  for (int i = 1; i <= n; i++)
  {  print triangle row
  }

• Each row contains i boxes.

  for (int j = 1; j <= i; j++) cout << "[]";
  cout << "\n";

• Putting the two loops together yields

  for (int i = 1; i <= n; i++)
  {  for (int j = 1; j <= i; j++) cout << "[]";
     cout << "\n";
  }

• triangle.cpp
  

Processing Text Input

• When processing text input we need to make a decision - is the input structured as a sequence of characters, words, or lines?
• To input a sequence of word, use the loop

  string word;
  while (cin >> word)
  {  process word
  }

• cin >> word has the same value as cin - it is the same test as !cin.fail().
• To process input one line at a time, use the getline function.

  string line;
  while (getline(cin, line))
  {  process line
  }

• As above, the getline function returns cin, so you can test that cin hasn't yet failed.
• To process input character by character, use the loop

  char ch;
  while (cin.get(ch))
  {  process ch
  }

Processing Text Input (words.cpp)

• You would type text in, and at the end of the input the program would tell you how many words you typed. (You would never want to use such a program!)
• The program makes a lot of sense if input is read from a file.
• To link a file to the input of a program you type

  words < article.txt

  on a command line. The input instructions no longer expect input from the keyboard but from the file article.txt.
• Input redirection on the command line.
• You can redirect also output of this program typing

  words < article.txt > output.txt

Simulations

• In a simulation we generate random events and evaluate their outcomes.
  
• The C++ library has a random number generator, which produces numbers that appear to be random.
• Calling rand() yields a random number between 0 and RAND_MAX (usually 32767, but implementation dependent).
• These numbers actual come from a a very long sequence of numbers computed from fairly simple formulas; they just behave like random numbers. For that reason they are often called pseudorandom numbers.
• The following program produces the exact same output every time the program is run (because the numbers are generated with formulas).

  int main()
  {  int i;
     for (i = 1; i <= 10; i++)
     {  int r = rand();
        cout << r << "\n";
     }
     return 0;
  }

• When you specify a new seed for the random number sequence, the generator generates a new (different) sequence.The seed is set with the srand function.
• By setting the seed based on the time, the random numbers will be different every time you run the program.

  Time now;
  int seed = now.seconds_from(Time(0,0,0));
  srand(seed);

• In actual applications you want to generate random numbers in different ranges, say between a and b.
• For example, to simulate a die roll, you need numbers between a = 1 and b = 6.
• First compute rand() % (b - a + 1) to obtain a random value between 0 and b - a.
• Add that to a to yield a random value between a and b.

  int rand_int(int a, int b)
  {  return a + rand() % (b - a + 1);
  }

Simulations (dice.cpp)

• To generate a random floating-point number, note that the quantity rand() * 1.0 / RAND_MAX is a random floating-point value between 0 and 1.
• The 1.0 ensures that the division is a floating-point number.

  double rand_double(double a, double b)
  {  return a + (b - a) * rand() * (1.0 / RAND_MAX);
  }

Simulations (Buffon Needle Experiment)

• Devised by Comte George-Louis Leclerc de Buffon (1707-1788), a French naturalist.
  
• A needle of length 1 inch is dropped onto paper that is ruled with parallel lines 2 inches apart.
• If the needle drops onto a line, we count it as a hit.
• The quotient tries / hits approximates pi.
• Our program randomly generates the lower point of the needle and an angle.
• The upper point of the needle is given by y_high = y_low + sin(angle).
• If y_high >= 2, we count the needle as a hit.

Simulations (buffon.cpp)

• The point of this program is not to compute pi (after all, we needed the value of pi in the deg2rad function). Rather, the point is to show how to a physical experiment can be simulated on the computer.