Since Emacs is designed to be flexible and work with all kinds of terminals, including character-only terminals, the graph will need to be made from one of the typewriter symbols. An asterisk will do; as we enhance the graph-printing function, we can make the choice of symbol a user option.

We can call this function `graph-body-print`

; it will take a
`numbers-list`

as its only argument. At this stage, we will not
label the graph, but only print its body.

The `graph-body-print`

function inserts a vertical column of
asterisks for each element in the `numbers-list`

. The height of
each line is determined by the value of that element of the
`numbers-list`

.

Inserting columns is a repetitive act; that means that this function can
be written either with a `while`

loop or recursively.

Our first challenge is to discover how to print a column of asterisks. Usually, in Emacs, we print characters onto a screen horizontally, line by line, by typing. We have two routes we can follow: write our own column-insertion function or discover whether one exists in Emacs.

To see whether there is one in Emacs, we can use the `M-x apropos`
command. This command is like the `C-h a` (`command-apropos`

)
command, except that the latter finds only those functions that are
commands. The `M-x apropos` command lists all symbols that match
a regular expression, including functions that are not interactive.

What we want to look for is some command that prints or inserts
columns. Very likely, the name of the function will contain either
the word “print” or the word “insert” or the word “column”.
Therefore, we can simply type `M-x apropos RET
print\|insert\|column RET` and look at the result. On my system, this
command once took quite some time, and then produced a list of 79
functions and variables. Now it does not take much time at all and
produces a list of 211 functions and variables. Scanning down the
list, the only function that looks as if it might do the job is

`insert-rectangle`

.
Indeed, this is the function we want; its documentation says:

insert-rectangle: Insert text of RECTANGLE with upper left corner at point. RECTANGLE's first line is inserted at point, its second line is inserted at a point vertically under point, etc. RECTANGLE should be a list of strings. After this command, the mark is at the upper left corner and point is at the lower right corner.

We can run a quick test, to make sure it does what we expect of it.

Here is the result of placing the cursor after the
`insert-rectangle`

expression and typing `C-u C-x C-e`
(`eval-last-sexp`

). The function inserts the strings
‘`"first"`’, ‘`"second"`’, and ‘`"third"`’ at and below
point. Also the function returns `nil`

.

(insert-rectangle '("first" "second" "third"))first second thirdnil

Of course, we won’t be inserting the text of the
`insert-rectangle`

expression itself into the buffer in which we
are making the graph, but will call the function from our program. We
shall, however, have to make sure that point is in the buffer at the
place where the `insert-rectangle`

function will insert its
column of strings.

If you are reading this in Info, you can see how this works by
switching to another buffer, such as the `*scratch*` buffer,
placing point somewhere in the buffer, typing `M-:`, typing the
`insert-rectangle`

expression into the minibuffer at the prompt,
and then typing `RET`. This causes Emacs to evaluate the
expression in the minibuffer, but to use as the value of point the
position of point in the `*scratch*` buffer. (`M-:` is the
key binding for `eval-expression`

. Also, `nil`

does not
appear in the `*scratch*` buffer since the expression is
evaluated in the minibuffer.)

We find when we do this that point ends up at the end of the last inserted line—that is to say, this function moves point as a side-effect. If we were to repeat the command, with point at this position, the next insertion would be below and to the right of the previous insertion. We don’t want this! If we are going to make a bar graph, the columns need to be beside each other.

So we discover that each cycle of the column-inserting `while`

loop must reposition point to the place we want it, and that place
will be at the top, not the bottom, of the column. Moreover, we
remember that when we print a graph, we do not expect all the columns
to be the same height. This means that the top of each column may be
at a different height from the previous one. We cannot simply
reposition point to the same line each time, but moved over to the
right—or perhaps we can…

We are planning to make the columns of the bar graph out of asterisks.
The number of asterisks in the column is the number specified by the
current element of the `numbers-list`

. We need to construct a
list of asterisks of the right length for each call to
`insert-rectangle`

. If this list consists solely of the requisite
number of asterisks, then we will have to position point the right number
of lines above the base for the graph to print correctly. This could
be difficult.

Alternatively, if we can figure out some way to pass
`insert-rectangle`

a list of the same length each time, then we
can place point on the same line each time, but move it over one
column to the right for each new column. If we do this, however, some
of the entries in the list passed to `insert-rectangle`

must be
blanks rather than asterisks. For example, if the maximum height of
the graph is 5, but the height of the column is 3, then
`insert-rectangle`

requires an argument that looks like this:

(" " " " "*" "*" "*")

This last proposal is not so difficult, so long as we can determine
the column height. There are two ways for us to specify the column
height: we can arbitrarily state what it will be, which would work
fine for graphs of that height; or we can search through the list of
numbers and use the maximum height of the list as the maximum height
of the graph. If the latter operation were difficult, then the former
procedure would be easiest, but there is a function built into Emacs
that determines the maximum of its arguments. We can use that
function. The function is called `max`

and it returns the
largest of all its arguments, which must be numbers. Thus, for
example,

(max 3 4 6 5 7 3)

returns 7. (A corresponding function called `min`

returns the
smallest of all its arguments.)

However, we cannot simply call `max`

on the `numbers-list`

;
the `max`

function expects numbers as its argument, not a list of
numbers. Thus, the following expression,

(max '(3 4 6 5 7 3))

produces the following error message;

Wrong type of argument: number-or-marker-p, (3 4 6 5 7 3)

We need a function that passes a list of arguments to a function.
This function is `apply`

. This function applies its first
argument (a function) to its remaining arguments, the last of which
may be a list.

For example,

(apply 'max 3 4 7 3 '(4 8 5))

returns 8.

(Incidentally, I don’t know how you would learn of this function
without a book such as this. It is possible to discover other
functions, like `search-forward`

or `insert-rectangle`

, by
guessing at a part of their names and then using `apropos`

. Even
though its base in metaphor is clear—apply its first argument to
the rest—I doubt a novice would come up with that particular word
when using `apropos`

or other aid. Of course, I could be wrong;
after all, the function was first named by someone who had to invent
it.)

The second and subsequent arguments to `apply`

are optional, so
we can use `apply`

to call a function and pass the elements of a
list to it, like this, which also returns 8:

(apply 'max '(4 8 5))

This latter way is how we will use `apply`

. The
`recursive-lengths-list-many-files`

function returns a numbers’
list to which we can apply `max`

(we could also apply `max`

to
the sorted numbers’ list; it does not matter whether the list is
sorted or not.)

Hence, the operation for finding the maximum height of the graph is this:

(setq max-graph-height (apply 'max numbers-list))

Now we can return to the question of how to create a list of strings
for a column of the graph. Told the maximum height of the graph
and the number of asterisks that should appear in the column, the
function should return a list of strings for the
`insert-rectangle`

command to insert.

Each column is made up of asterisks or blanks. Since the function is
passed the value of the height of the column and the number of
asterisks in the column, the number of blanks can be found by
subtracting the number of asterisks from the height of the column.
Given the number of blanks and the number of asterisks, two
`while`

loops can be used to construct the list:

```
;;; First version.
(defun column-of-graph (max-graph-height actual-height)
"Return list of strings that is one column of a graph."
(let ((insert-list nil)
(number-of-top-blanks
(- max-graph-height actual-height)))
```

```
;; Fill in asterisks.
(while (> actual-height 0)
(setq insert-list (cons "*" insert-list))
(setq actual-height (1- actual-height)))
```

```
;; Fill in blanks.
(while (> number-of-top-blanks 0)
(setq insert-list (cons " " insert-list))
(setq number-of-top-blanks
(1- number-of-top-blanks)))
```

```
;; Return whole list.
insert-list))
```

If you install this function and then evaluate the following expression you will see that it returns the list as desired:

(column-of-graph 5 3)

returns

(" " " " "*" "*" "*")

As written, `column-of-graph`

contains a major flaw: the symbols
used for the blank and for the marked entries in the column are
hard-coded as a space and asterisk. This is fine for a prototype,
but you, or another user, may wish to use other symbols. For example,
in testing the graph function, you may want to use a period in place
of the space, to make sure the point is being repositioned properly
each time the `insert-rectangle`

function is called; or you might
want to substitute a ‘`+`’ sign or other symbol for the asterisk.
You might even want to make a graph-column that is more than one
display column wide. The program should be more flexible. The way to
do that is to replace the blank and the asterisk with two variables
that we can call `graph-blank`

and `graph-symbol`

and define
those variables separately.

Also, the documentation is not well written. These considerations lead us to the second version of the function:

(defvar graph-symbol "*" "String used as symbol in graph, usually an asterisk.")

(defvar graph-blank " " "String used as blank in graph, usually a blank space. graph-blank must be the same number of columns wide as graph-symbol.")

(For an explanation of `defvar`

, see
Initializing a Variable with `defvar`

.)

```
;;; Second version.
(defun column-of-graph (max-graph-height actual-height)
"Return MAX-GRAPH-HEIGHT strings; ACTUAL-HEIGHT are graph-symbols.
```

The graph-symbols are contiguous entries at the end of the list. The list will be inserted as one column of a graph. The strings are either graph-blank or graph-symbol."

(let ((insert-list nil) (number-of-top-blanks (- max-graph-height actual-height)))

` ;; Fill in ``graph-symbols`

.
(while (> actual-height 0)
(setq insert-list (cons graph-symbol insert-list))
(setq actual-height (1- actual-height)))

` ;; Fill in ``graph-blanks`

.
(while (> number-of-top-blanks 0)
(setq insert-list (cons graph-blank insert-list))
(setq number-of-top-blanks
(1- number-of-top-blanks)))
;; Return whole list.
insert-list))

If we wished, we could rewrite `column-of-graph`

a third time to
provide optionally for a line graph as well as for a bar graph. This
would not be hard to do. One way to think of a line graph is that it
is no more than a bar graph in which the part of each bar that is
below the top is blank. To construct a column for a line graph, the
function first constructs a list of blanks that is one shorter than
the value, then it uses `cons`

to attach a graph symbol to the
list; then it uses `cons`

again to attach the top blanks to
the list.

It is easy to see how to write such a function, but since we don’t
need it, we will not do it. But the job could be done, and if it were
done, it would be done with `column-of-graph`

. Even more
important, it is worth noting that few changes would have to be made
anywhere else. The enhancement, if we ever wish to make it, is
simple.

Now, finally, we come to our first actual graph printing function.
This prints the body of a graph, not the labels for the vertical and
horizontal axes, so we can call this `graph-body-print`

.