Assignment 1 - Flexible Resizable Array

Create a class that implements a safe resizable array, which can
contain data of any single type. It should be easy and convenient
to use.

+ Use templates so that the data stored in the arrays can be of any type.

+ Provide a "default" (no parameter) constructor that sets the array to
  some reasonable default initial size.

+ Provide another constructor with one int parameter that allows the
  programmer to specify the original size.

    so these would all be possible declarations:

    { Array<int> A;
      Array<string> B, C;
      Array<double> D(100);

+ Provide a destructor that ensures all heap memory is released when
  an Array object is destroyed.

+ Provide set and get methods that allow the programmer to put data into
  and take data from an Array object, e.g.

      cout << B.get(3)     is like     cout << B[3]
      D.set(i, x*y)        is like     D[i] = x*y

+ Make sure your set and get methods check that the index used (3 and i
  in the above examples) are properly in range.

+ Provide a change_size(int newsize) method that changes the size of the
  array, preserving as much of the original data as possible, and carefully
  recycling any heap memory that is no longer needed.

+ Make your set method automatically use the change_size method if ever
  the index used is too big.

+ Provide a get_size() method that returns the current size of the array.

+ Provide a set_default method that makes the Array object remember a
  special default value. Whenever the get method is used with an index
  that is out of bounds, it should return the default value (if one has
  been set) instead of reporting an error.

+ Test it.

Here is a dull example

  { Array<int> Xvals(10);
    Array<double> Yvals;

    cout << "size is " << Xvals.get_size() << "\n";

    for (int i = 0; i < 30; i += 1)
    { int x = i*3+1;
      double y = sin(pi/x);
      Xvals.set(i, x);
      Yvals.set(i, y); }

    cout << "size is " << Xvals.get_size() << "\n";

    for (int i = 0; i <= Xvals.get_size(); i += 1)
      cout << i << ": x = " << Xvals.get(i) << ", sin(pi/x) = " << Yvals.get(i) << "\n"; }

It should produce output a lot like this (not necessarily identical)

  size is 10
  size is 30
  0: x = 1, sin(pi/x) = 1.22461e-16
  1: x = 4, sin(pi/x) = 0.707107
  2: x = 7, sin(pi/x) = 0.433884
  3: x = 10, sin(pi/x) = 0.309017
  4: x = 13, sin(pi/x) = 0.239316
  5: x = 16, sin(pi/x) = 0.19509
  6: x = 19, sin(pi/x) = 0.164595
  7: x = 22, sin(pi/x) = 0.142315
  8: x = 25, sin(pi/x) = 0.125333 
  9: x = 28, sin(pi/x) = 0.111964
  10: x = 31, sin(pi/x) = 0.101168
  11: x = 34, sin(pi/x) = 0.0922684
  12: x = 37, sin(pi/x) = 0.0848059
  13: x = 40, sin(pi/x) = 0.0784591
  14: x = 43, sin(pi/x) = 0.0729953
  15: x = 46, sin(pi/x) = 0.0682424
  16: x = 49, sin(pi/x) = 0.0640702
  17: x = 52, sin(pi/x) = 0.0603785
  18: x = 55, sin(pi/x) = 0.0570888
  19: x = 58, sin(pi/x) = 0.0541389
  20: x = 61, sin(pi/x) = 0.0514788
  21: x = 64, sin(pi/x) = 0.0490677
  22: x = 67, sin(pi/x) = 0.0468723
  23: x = 70, sin(pi/x) = 0.0448648
  24: x = 73, sin(pi/x) = 0.0430222
  25: x = 76, sin(pi/x) = 0.041325
  26: x = 79, sin(pi/x) = 0.0397565 
  27: x = 82, sin(pi/x) = 0.0383027
  28: x = 85, sin(pi/x) = 0.0369515
  29: x = 88, sin(pi/x) = 0.0356923
  Error - index out of bounds.