.. _random-numbers-a-histogram:

A histogram
-----------

It is often useful to take the data from the previous tables and store
them for later access, rather than just print them. What we need is a
way to store 10 integers. We could create 10 integer variables with
names like ``how_many_ones``, ``how_many_twos``, etc. But that would require
a lot of typing, and it would be a real pain later if we decided to
change the range of values.

A better solution is to use a vector with size 10. That way we can
create all ten storage locations at once and we can access them using
indices, rather than ten different names. Here’s how:

::

   std::size_t num_values = 100000;
   int upper_bound = 9;
   std::vector<int> numbers = make_vector (num_values, upper_bound);
   std::vector<std::size_t> histogram (static_cast<std::size_t>(upper_bound) + 1);

   for (std::size_t i = 0; i < histogram.size(); ++i) {
     histogram[i] = how_many (numbers, static_cast<int>(i));
   }

.. index::
   single: histogram

I called the vector **histogram** because that’s a statistical term for
a vector of numbers that counts the number of appearances of a range of
values.

The tricky thing here is that I am using the loop variable in two
different ways. First, it is an argument to ``how_many``, specifying
which value I am interested in. Second, it is an index into the
histogram, specifying which location I should store the result in.

We are making a major assumption with our histogram:
we assume we will remember that each index position in histogram
also corresponds to the value counted.
In other words, index position ``0`` stores the count
for how many times the value ``0`` was randomly generated.
The value ``0`` is not explicitly stored anywhere -
it is *implied* from the position.

If we reorder the data in the histogram, our results are invalid.


.. tb-group::
   :name: self_check

   .. tb-tab:: Q1

      .. tb-choice::
         :name: histogram_1

         Which of the following statements are true about using vectors to store data?

         - [ ] Vectors require more typing than using individual variables to store data.

           Incorrect! Vectors require less typing than using individual varaibles to store data.
         - [x] Vectors create multiple storage locations at once under the same name.

           Correct!
         - [ ] Once you store something in a vector, you cannot change its value.

           Incorrect! The values of vector elements can always be changed.
         - [x] Each storage location of a vector is accessed by indexing.

           Correct!