Just for a laugh, imagine that you are Papa Gump and you have the following problem: you’ve got a child on the way and you need to come up with a name. You’ve got a list of about twenty names you and Mama Gump like, and you really think you want the first name to be Forrest. Now, being from the South, naturally, you want at least three or four middle names, and you’re pretty dead set on one or two of them, but not sure of the order that will sound best, or what other names to use to fill out those four middle names.

How to make a list of all the possibilities?

Now, I am not a mathematician, and someone might want to check my
math, but in general, the number of permutations of a set of items
will be . For twenty names, that will be over
permutations. Let’s say you want three middle names: that’s four
given names (the middle name plus the first name). According to
Wolfram MathWorld^{1}, the number of -length subsets of a set of
cardinality is . With and that still
gives possible names for the little tyke, which as you might
imagine, is more than Mama and Papa Gump want to check.

Looking at several implementations of permutation generators written
in Common Lisp I quickly found that most are too slow to solve this
problem well. But the Alexandria┫ library has `map-permutations`

which does not return a list of permutations (which would be a
prohibitively large list). Instead it simply applies a function to
each permutation as it is generated and then moves on to the next.

So first we will load Alexandria. I will do it using Quicklisp, naturally, since it is, as the name implies, quick:

```
(ql:quickload "alexandria")
```

Next, let’s define some variables with nil values as default. Most benighted people only cough up a paltry two names to give their kids, so we’ll make that the default, though it’s a case that doesn’t really require this program:

(defvar *number-of-given-names* 2)

We don’t need to operate on the last name, but we’ll need to print it with the output—after all, you have to consider the whole name when checking the rhythm and the way it rolls off the tongue:

(defvar *last-name* 'nil)

Here will be the list of names. Just defining it here.

(defvar *names-list* nil)

Any names that we are sure we want included, but not sure where.

(defvar *required-names-list* nil)

Maybe you’ve already decided on a first name:

(defvar *required-first-name* nil)

Ok, so now, let’s write the main function using `map-permutations`

from Alexandria. `map-permutations`

takes a function to apply to
each permutation, and a list to permute.

(defun permute-names (n list) (alexandria:map-permutations #'permute-names-function list :length n))

Naturally, we need to write the function `permute-names-function`

.
What we want to do is just print the permutation if it
qualifies—that is, if it has the required first name and has any
other required names; and then we want to tack the last name to the
end:

[Edit: Why did I put `add-last-name`

both inside and outside
`print-if`

? I have no idea. I think I had it wrong the first time,
it didn’t do anything, and when I corrected it, I forgot to remove the
old one. Should I remove the incorrect one? Of course.]

(defun permute-names-function (p) (add-last-name (print-if #'filter-permutation-predicate (add-last-name p *last-name*))))

So let’s write this predicate. It is really just a shell for the two
other predicates. If both return `t`

then this will return `t`

.

I wrote it to either take arguments or to use the global values. Here we will be using the global values:

(defun filter-permutation-predicate (p &optional required-names-list required-first-name) (if (and (permutation-has-required-names-p p (or *required-names-list* required-names-list)) (permutation-has-required-first-name-p p (or *required-first-name* required-first-name))) p nil))

So, let’s write our two predicates. One returns `t`

if the
permutation begins with our required first name. If we hand it `nil`

as an argument, then it will always return `t`

. This way we don’t
have to have a required first name. There might be a more elegant
way to do that, but there it is anyway:

(defun permutation-has-required-first-name-p (p &optional name) (if name (equal name (car p)) t))

Then the other predicate, which returns `t`

if the permutation
contains any of the required names somewhere in them:

(defun permutation-has-required-names-p (p &optional required-names-list) (if (null required-names-list) t (if (member (car required-names-list) p) (permutation-has-required-names-p p (cdr required-names-list)) nil)))

So now we’re done except for the function that adds the last name to the output:

(defun add-last-name (p &optional last-name) (if last-name (append p (list last-name)) p))

Oh, almost forgot—we need a function that prints it:

(defun print-if (predicate &rest x) (if (apply predicate x) (print x)))

Now, let’s try it.

First, let’s set our variables:

CL-USER> (setq *last-name* 'gump) GUMP CL-USER> (setq *number-of-given-names* 4) 4 CL-USER> (setq *names-list* '(joe bob bill forrest gus bubba bub doug ray hunter pootie billy cooter chuck wilbur cletus amos jethro buddy vernon)) (JOE BOB BILL FORREST GUS BUBBA BUB DOUG RAY HUNTER POOTIE BILLY COOTER CHUCK WILBUR CLETUS AMOS JETHRO BUDDY VERNON) CL-USER> (length *names-list*) 20 CL-USER> (setq *required-names-list* '(cooter cletus)) (COOTER CLETUS) CL-USER> (setq *required-first-name* 'forrest) FORREST

Now let’s run it.

CL-USER> (permute-names *number-of-given-names* *names-list*) ((FORREST JOE COOTER CLETUS GUMP)) ((FORREST COOTER JOE CLETUS GUMP)) ((FORREST CLETUS COOTER JOE GUMP)) ((FORREST COOTER CLETUS JOE GUMP)) ((FORREST CLETUS JOE COOTER GUMP)) ((FORREST JOE CLETUS COOTER GUMP)) ((FORREST BOB COOTER CLETUS GUMP)) ((FORREST COOTER BOB CLETUS GUMP)) ((FORREST CLETUS COOTER BOB GUMP)) ((FORREST COOTER CLETUS BOB GUMP)) ((FORREST CLETUS BOB COOTER GUMP)) ((FORREST BOB CLETUS COOTER GUMP)) ((FORREST BILL COOTER CLETUS GUMP)) ((FORREST COOTER BILL CLETUS GUMP)) ((FORREST CLETUS COOTER BILL GUMP)) ((FORREST COOTER CLETUS BILL GUMP)) ((FORREST CLETUS BILL COOTER GUMP)) ((FORREST BILL CLETUS COOTER GUMP)) ((FORREST GUS COOTER CLETUS GUMP)) ((FORREST COOTER GUS CLETUS GUMP)) ((FORREST CLETUS COOTER GUS GUMP)) ((FORREST COOTER CLETUS GUS GUMP)) ((FORREST CLETUS GUS COOTER GUMP)) ((FORREST GUS CLETUS COOTER GUMP)) ((FORREST BUBBA COOTER CLETUS GUMP)) ((FORREST COOTER BUBBA CLETUS GUMP)) ((FORREST CLETUS COOTER BUBBA GUMP)) ((FORREST COOTER CLETUS BUBBA GUMP)) ((FORREST CLETUS BUBBA COOTER GUMP)) ((FORREST BUBBA CLETUS COOTER GUMP)) ((FORREST BUB COOTER CLETUS GUMP)) ((FORREST COOTER BUB CLETUS GUMP)) ((FORREST CLETUS COOTER BUB GUMP)) ((FORREST COOTER CLETUS BUB GUMP)) ((FORREST CLETUS BUB COOTER GUMP)) ((FORREST BUB CLETUS COOTER GUMP)) ((FORREST DOUG COOTER CLETUS GUMP)) ((FORREST COOTER DOUG CLETUS GUMP)) ((FORREST CLETUS COOTER DOUG GUMP)) ((FORREST COOTER CLETUS DOUG GUMP)) ((FORREST CLETUS DOUG COOTER GUMP)) ((FORREST DOUG CLETUS COOTER GUMP)) ((FORREST RAY COOTER CLETUS GUMP)) ((FORREST COOTER RAY CLETUS GUMP)) ((FORREST CLETUS COOTER RAY GUMP)) ((FORREST COOTER CLETUS RAY GUMP)) ((FORREST CLETUS RAY COOTER GUMP)) ((FORREST RAY CLETUS COOTER GUMP)) ((FORREST HUNTER COOTER CLETUS GUMP)) ((FORREST COOTER HUNTER CLETUS GUMP)) ((FORREST CLETUS COOTER HUNTER GUMP)) ((FORREST COOTER CLETUS HUNTER GUMP)) ((FORREST CLETUS HUNTER COOTER GUMP)) ((FORREST HUNTER CLETUS COOTER GUMP)) ((FORREST POOTIE COOTER CLETUS GUMP)) ((FORREST COOTER POOTIE CLETUS GUMP)) ((FORREST CLETUS COOTER POOTIE GUMP)) ((FORREST COOTER CLETUS POOTIE GUMP)) ((FORREST CLETUS POOTIE COOTER GUMP)) ((FORREST POOTIE CLETUS COOTER GUMP)) ((FORREST BILLY COOTER CLETUS GUMP)) ((FORREST COOTER BILLY CLETUS GUMP)) ((FORREST CLETUS COOTER BILLY GUMP)) ((FORREST COOTER CLETUS BILLY GUMP)) ((FORREST CLETUS BILLY COOTER GUMP)) ((FORREST BILLY CLETUS COOTER GUMP)) ((FORREST COOTER CHUCK CLETUS GUMP)) ((FORREST CHUCK COOTER CLETUS GUMP)) ((FORREST CLETUS CHUCK COOTER GUMP)) ((FORREST CHUCK CLETUS COOTER GUMP)) ((FORREST CLETUS COOTER CHUCK GUMP)) ((FORREST COOTER CLETUS CHUCK GUMP)) ((FORREST COOTER WILBUR CLETUS GUMP)) ((FORREST WILBUR COOTER CLETUS GUMP)) ((FORREST CLETUS WILBUR COOTER GUMP)) ((FORREST WILBUR CLETUS COOTER GUMP)) ((FORREST CLETUS COOTER WILBUR GUMP)) ((FORREST COOTER CLETUS WILBUR GUMP)) ((FORREST COOTER CLETUS AMOS GUMP)) ((FORREST CLETUS COOTER AMOS GUMP)) ((FORREST AMOS CLETUS COOTER GUMP)) ((FORREST CLETUS AMOS COOTER GUMP)) ((FORREST AMOS COOTER CLETUS GUMP)) ((FORREST COOTER AMOS CLETUS GUMP)) ((FORREST COOTER CLETUS JETHRO GUMP)) ((FORREST CLETUS COOTER JETHRO GUMP)) ((FORREST JETHRO CLETUS COOTER GUMP)) ((FORREST CLETUS JETHRO COOTER GUMP)) ((FORREST JETHRO COOTER CLETUS GUMP)) ((FORREST COOTER JETHRO CLETUS GUMP)) ((FORREST COOTER CLETUS BUDDY GUMP)) ((FORREST CLETUS COOTER BUDDY GUMP)) ((FORREST BUDDY CLETUS COOTER GUMP)) ((FORREST CLETUS BUDDY COOTER GUMP)) ((FORREST BUDDY COOTER CLETUS GUMP)) ((FORREST COOTER BUDDY CLETUS GUMP)) ((FORREST COOTER CLETUS VERNON GUMP)) ((FORREST CLETUS COOTER VERNON GUMP)) ((FORREST VERNON CLETUS COOTER GUMP)) ((FORREST CLETUS VERNON COOTER GUMP)) ((FORREST VERNON COOTER CLETUS GUMP)) ((FORREST COOTER VERNON CLETUS GUMP)) (JOE BOB BILL FORREST GUS BUBBA BUB DOUG RAY HUNTER POOTIE BILLY COOTER CHUCK WILBUR CLETUS AMOS JETHRO BUDDY VERNON) CL-USER>

(The list in the last line of the output is the return value of the function.)

So, now Papa Gump only has about a hundred possibilities to consider. And congratulations! Good luck with your new baby!

By the way, how did Papa Gump know it was going to be a boy?

Footnotes: