# A Contribution to the Computational Theory of Big Game Hunting: The Dijkstra Method

*Steven Pemberton*

In [1], several methods are propounded for the hard problem of
catching a lion in the Sahara Desert.

However, due to an unfortunate case of bad timing, several important
methods were overlooked. We include here, for historical completeness,
one of them.

## The Dijkstra Method

The way the problem reached me was: catch a wild lion in the Sahara
Desert. Another way of stating the problem is:

Axiom 0: Sahara ∈ deserts

Axiom 1: Lion ∈ Sahara

Axiom 2: ¬(Lion ∈ cage)

We observe the following invariant:

P1: C(L) ∨ ¬(C(L))

where C(L) means: the value of "L" is in the cage.

Establishing C initially is trivially accomplished with the statement

;cage := {}

**Note 0.**

This is easily implemented by opening the door to the cage and
shaking out any lions that happen to be there initially.

**(End of note 0.)**

The obvious program structure is then:

;cage:={}
;do NOT (C(L)) ->
;"approach lion under invariance of P1"
;if P(L) ->
;"insert lion in cage"
[] not P(L) ->
;skip
;fi
;od

where P(L) means: the value of L is within arm's reach.

**Note 1.**

Axiom 1 ensures that the loop terminates.

**(End of note 1.)**

**Exercise 0.**

Refine the step "Approach lion under invariance of P1".

**(End of exercise 0.)**

**Note 2.**

The program is robust in the sense that it will lead to abortion if
the value of L is "tiger".

**Remark 0.**

This may be a new sense of the word "robust" for you.

**(End of remark 0.)**

**(End of note 2.)**

**Note 3.**

From observation we can see that the above program leads to the
desired goal. It goes without saying that we therefore do not have to
run it.

**(End of note 3.)**

**References.**

**(End of references.)**

**(End of Method.)**

[1] H. Petard, A Contribution to the Mathematical Theory of Big Game Hunting,
Princeton, N. J., in American Mathematical Monthly, August, 1938