/* seq.h - Matt Mahoney, mmahoney@cs.fit.edu

ANALYSIS

A Seq<T> is a fixed numeric sequence.  The declaration

  Seq<T> s(n, start, step);

defines a sequence of elements with fixed values

  s[0] = start
  s[1] = start + step
  s[2] = start + step*2
  ...
  s[n-1] = start + step*(n-1)

All constructor arguments default as follows:

  step = 1
  start = 0
  n = 0

s.size() returns n.  s.begin() and s.end() return Seq<T>::const_iterator,
input iterators pointing to s[0] and s[n] respectively.
Seq<T>::iterator is a synonym for Seq<T>::const_iterator.  Indexing
out of bounds throws an out_of_range exception.  For example:

  Seq<int> s(4, 10, 2);  // {10, 12, 14, 16}
  cout << s[1];  // 12
  for (Seq<int>::iterator p=s.begin(); p!=s.end(); ++p)
    cout << " " << *p  // 10 12 14 16
  try {
    s[s.size()];  // Error: s[4]
  }
  catch (out_of_range x) {
    cerr << "Index out of bounds\n";
  }

DESIGN

A Seq<T> s is represented by a vector<T> v, such that s[i] == v[i].
The elements are initialized by the constructor and remain fixed.
The iterator types are both vector<T>::const_iterator.

*/

#include <stdexcept>
#include <vector>

template <class T> class Seq {
private:
  std::vector<T> v;  // Precomputed elements
public:
  Seq(int n=0, const T& start=0, const T& step=1): v(n) {
    for (int i=0; i<n; ++i)
      v[i]=start+step*i;
  }
  int size() const {return v.size();}
  const T& operator[](int i) const {
    if (i<0 || i>=int(v.size()))
      throw std::out_of_range("Seq out of range");
    else
      return v[i];
  }
  typedef std::vector<T>::const_iterator const_iterator;
  typedef std::vector<T>::const_iterator iterator;
  iterator begin() const {return v.begin();}
  iterator end() const {return v.end();}
};