Programming Assignment 5  (Chapter 9) - Recursive Thinking

Adapted from Data Structures and Other Objects Using C++

by Michael Main and Walter Savitch

The Assignment:

You will implement and test four short recursive functions. With the proper use of recursion, none of these function should require more than a dozen lines of code.

Purposes:

Ensure that you can write and test small recursive functions.

Before Starting:

Read all of Chapter 9, especially Sections 9.1 and 9.3.

Due Date:

Thursday, April 08, 2010. If you have problems, late work will be accepted on Friday with no penalties. Late work may be submitted on  Saturday  or Sunday with 5% penalty per day. No work will be accepted after Sunday.

How to Turn In:

Pack your files in a WinZip file (Windows) or tar file (Unix). Attach the file in your email with "CSC212 Assignment 5" in your message Subject line, send it to Wai Khoo ( WKhoo@gc.cuny.edu )

Files that you must write and turn in:

rec_fun.cxx: This file should contain the implementations of the four functions described below. You might also want to put the functions prototypes in a separate file rec_fun.h and write a test program that includes rec_fun.h.

1. One Binary Number

  void binary_print(ostream& outs, unsigned int n);

  n=0  Output:0
  n=4  Output:100
  n=27 Output:11011

2. Triangle Pattern

  void triangle(ostream& outs, unsigned int m, unsigned int n)
  // Precondition: m <= n
  // Postcondition: The function has printed a pattern of 2*(n-m+1) lines
  // to the output stream outs. The first line contains m asterisks, the next 
  // line contains m+1 asterisks, and so on up to a line with n asterisks.
  // Then the pattern is repeated backwards, going n back down to m.
  /* Example output:
     triangle(cout, 3, 5) will print this to cout:
     ***
     ****
     *****
     *****
     ****
     ***
  */

3. Pow Function (Project 13, page 452)

    double pow(double x, int n);
    // Precondition: If x is zero, then n must be positive.
    // Postcondition: The value returned is x raised to the power n.

Hint: use the formula x^2n = x^n  x^n

4.  Repeated and Indented Sentences (Project 1, page 450)

Write a  function that produces output like the following:

This was written by calling number 1.
  This was written by calling number 2.
    This was written by calling number 3.
      This was written by calling number 4.
      This was ALSO written by calling number 4.
    This was ALSO written by calling number 3.
  This was ALSO written by calling number 2.
This was ALSO written by calling number 1.

In the above example, the recursion stopped when it reached four levels deep, but your function should be capable of continuing any specific level with the following function prototype.

     void indented_sentences(size_t m, size_t n);
// precondition: m <=n;
//postcondition: print out the above pattern by calling number from m to n