switching machines to be able to make an image
svn: r13708
This commit is contained in:
Robby Findler
parent
3ff2184a38
commit
42a5b15831
|
|
@ -9,6 +9,10 @@ scribble ++xref-in setup/xref load-collections-xref --htmls chat-noir-doc.ss
|
|||
|
||||
@title{Chat Noir}
|
||||
|
||||
@author[(link "http://www.eecs.northwestern.edu/~robby" "Robby Findler")
|
||||
(link "http://www.barzilay.org/" "Eli Barzilay")
|
||||
(link "http://www.cs.utah.edu/~mflatt/" "Matthew Flatt")]
|
||||
|
||||
The goal of Chat Noir is to stop the cat from escaping the board. Each
|
||||
turn you click on a circle, which prevents the cat from stepping on
|
||||
that space, and the cat responds by taking a step. If the cat is
|
||||
|
|
@ -28,7 +32,8 @@ project for the introductory programming course at the University of
|
|||
Chicago in the fall of 2008.
|
||||
|
||||
The remainder of this document explains the implementation of
|
||||
the Chat Noir game.
|
||||
the Chat Noir game in a
|
||||
@link["http://www.literateprogramming.com/"]{Literate Programming} style.
|
||||
|
||||
@section{Overview}
|
||||
|
||||
|
|
@ -56,10 +61,10 @@ Each section also comes with a series of test cases that are collected into the
|
|||
|
||||
@chunk[<tests>
|
||||
<test-infrastructure>
|
||||
<breadth-first-search-tests>
|
||||
<world-tests>
|
||||
<board->graph-tests>
|
||||
<cats-path-tests>
|
||||
<world-tests>]
|
||||
<breadth-first-search-tests>
|
||||
<cats-path-tests>]
|
||||
|
||||
Each test case uses either @scheme[test], a simple form that accepts two
|
||||
arguments and compares them with @scheme[equal?], or @scheme[test/set]
|
||||
|
|
@ -259,18 +264,12 @@ blocked, in which case it has no edges at all (even to the boundary).
|
|||
This section describes the implementation of the breadth-first search, leaving
|
||||
details of how the graph connectivity is computed from the board to the next section.
|
||||
|
||||
The code for the breadth-first search is organized into
|
||||
X parts ....
|
||||
|
||||
@chunk[<breadth-first-search>
|
||||
<dist-cell-data-definition>
|
||||
<build-bfs-table>
|
||||
<neighbors>
|
||||
<neighbors-blocked/boundary>
|
||||
<lookup-in-table>]
|
||||
<lookup-in-table>
|
||||
<build-bfs-table>]
|
||||
|
||||
@chunk[<breadth-first-search-tests>
|
||||
<on-boundary?-tests>
|
||||
<lookup-in-table-tests>
|
||||
<build-bfs-table-tests>]
|
||||
|
||||
|
|
@ -285,6 +284,22 @@ and the @tt{n} field is a natural number or @scheme['∞], indicating
|
|||
the distance of the shortest path from the node to some fixed point on
|
||||
the board.
|
||||
|
||||
The function @scheme[lookup-in-table] returns the distance from the fixed
|
||||
point to the given posn, returning @scheme['∞] if the posn is not in the
|
||||
table or if it is mapped to @scheme['∞] in the table.
|
||||
|
||||
@chunk[<lookup-in-table>
|
||||
(define/contract (lookup-in-table t p)
|
||||
(-> (listof dist-cell?) posn?
|
||||
(or/c '∞ natural-number/c))
|
||||
(cond
|
||||
[(empty? t) '∞]
|
||||
[else (cond
|
||||
[(equal? p (dist-cell-p (first t)))
|
||||
(dist-cell-n (first t))]
|
||||
[else
|
||||
(lookup-in-table (rest t) p)])]))]
|
||||
|
||||
The @scheme[build-bfs-table] accepts a world and a cell
|
||||
(indicating the fixed point)
|
||||
and returns a distance map encoding the distance to that cell.
|
||||
|
|
@ -351,7 +366,9 @@ is in @scheme[dist-table]. If it is, we just move on to the
|
|||
next element in the queue. If that node is not in the @scheme[dist-table],
|
||||
then we add all of the neighbors to the queue, in the @scheme[append]
|
||||
expression, and update the @scheme[dist-table] with the distance to
|
||||
this node.
|
||||
this node. Because we always add the new children to the end of the queue
|
||||
and always look at the front of the queue, we are guaranteed that
|
||||
the first time we see a node, it will be with the shortest distance.
|
||||
|
||||
The @scheme[build-bfs-table] function packages up @scheme[bfs]
|
||||
function. It accepts a @scheme[world] and an initial position
|
||||
|
|
@ -377,12 +394,28 @@ it calls the @scheme[bfs] function
|
|||
and then transforms the result, using
|
||||
@scheme[hash-map], into a list of @scheme[cell]s.
|
||||
|
||||
@section{Board to Graph Functions}
|
||||
|
||||
As far as the @scheme[build-bfs-table] function goes,
|
||||
all of the information specific to Chat Noir is
|
||||
encoded in the neighbors function.
|
||||
It accepts a world and returns a function
|
||||
that computes the neighbors of the boundary
|
||||
and of nodes.
|
||||
and of nodes. This section describes how
|
||||
it is implemented.
|
||||
|
||||
@chunk[<board->graph>
|
||||
<neighbors>
|
||||
<neighbors-blocked/boundary>
|
||||
<adjacent>
|
||||
<in-bounds?>
|
||||
<on-boundary?>]
|
||||
|
||||
@chunk[<board->graph-tests>
|
||||
<on-boundary?-tests>
|
||||
<in-bounds?-tests>
|
||||
<adjacent-tests>
|
||||
<neighbors-tests>]
|
||||
|
||||
The neighbors functions accepts a @scheme[world] and then
|
||||
returns a function that computes the neighbors of a @scheme[posn]
|
||||
|
|
@ -408,7 +441,7 @@ and @scheme[(make-posn 0 1)] has four neighbors:
|
|||
(make-posn 0 2)
|
||||
(make-posn 1 2)))]
|
||||
|
||||
as you can see from the pictures of the 7x7 empty board above.
|
||||
as you can see in the earlier pictures of the 7x7 empty board.
|
||||
Also, there are 6 neighbors of the boundary in the 3x3 board:
|
||||
|
||||
@chunk[<neighbors-tests>
|
||||
|
|
@ -420,7 +453,6 @@ Also, there are 6 neighbors of the boundary in the 3x3 board:
|
|||
(make-posn 2 1)
|
||||
(make-posn 2 2)))]
|
||||
|
||||
|
||||
This is the neighbors function. After it accepts the @scheme[world],
|
||||
it builds a list of the blocked cells in the world and a
|
||||
list of the cells that are on the boundary (and not blocked). Then it
|
||||
|
|
@ -461,8 +493,14 @@ we know that @scheme[p] must have been on the boundary, so we add
|
|||
@scheme['boundary] to the result list.
|
||||
|
||||
@chunk[<neighbors-blocked/boundary>
|
||||
(define/contract (neighbors-blocked/boundary blocked boundary-cells size p)
|
||||
(-> (listof posn?) (listof posn?) natural-number/c (or/c 'boundary posn?)
|
||||
(define/contract (neighbors-blocked/boundary blocked
|
||||
boundary-cells
|
||||
size
|
||||
p)
|
||||
(-> (listof posn?)
|
||||
(listof posn?)
|
||||
natural-number/c
|
||||
(or/c 'boundary posn?)
|
||||
(listof (or/c 'boundary posn?)))
|
||||
|
||||
(cond
|
||||
|
|
@ -485,20 +523,8 @@ we know that @scheme[p] must have been on the boundary, so we add
|
|||
(cons 'boundary in-bounds)]))]))]
|
||||
|
||||
|
||||
@section{Board to Graph Functions}
|
||||
|
||||
There are three functions that build the basic graph structure
|
||||
from a board.
|
||||
|
||||
@chunk[<board->graph>
|
||||
<adjacent>
|
||||
<in-bounds?>
|
||||
<on-boundary?>]
|
||||
|
||||
@chunk[<board->graph-tests>
|
||||
<in-bounds?-tests>
|
||||
<adjacent-tests>
|
||||
<neighbors-tests>]
|
||||
There are the three functions that build the basic graph structure
|
||||
from a board as used by @scheme[neighbors].
|
||||
|
||||
The first function is @scheme[adjacent]. It consumes a
|
||||
@scheme[posn] and returns six @scheme[posn]s that
|
||||
|
|
@ -506,7 +532,9 @@ indicate what the neighbors are, without consideration
|
|||
of the size of the board (or the missing corner pieces).
|
||||
|
||||
For example, these are the @scheme[posn]s that are adjacent
|
||||
to @scheme[(make-posn 0 1)].
|
||||
to @scheme[(make-posn 0 1)]; note that the first and the third
|
||||
are not on the board and do not show up in
|
||||
@scheme[neighbors] function example above.
|
||||
|
||||
@chunk[<adjacent-tests>
|
||||
(test (adjacent (make-posn 0 1))
|
||||
|
|
@ -574,33 +602,11 @@ of the two corners that have been removed.
|
|||
(not (equal? p (make-posn 0 0)))
|
||||
(not (equal? p (make-posn 0 (- board-size 1))))))]
|
||||
|
||||
|
||||
|
||||
@chunk[<lookup-in-table>
|
||||
;; lookup-in-table : distance-map posn -> number or '∞
|
||||
;; looks for the distance as recorded in the table t,
|
||||
;; if not found returns a distance of '∞
|
||||
(define (lookup-in-table t p)
|
||||
(cond
|
||||
[(empty? t) '∞]
|
||||
[else (cond
|
||||
[(equal? p (dist-cell-p (first t)))
|
||||
(dist-cell-n (first t))]
|
||||
[else
|
||||
(lookup-in-table (rest t) p)])]))]
|
||||
|
||||
@chunk[<lookup-in-table-tests>
|
||||
|
||||
(test (lookup-in-table empty (make-posn 1 2)) '∞)
|
||||
(test (lookup-in-table (list (make-dist-cell (make-posn 1 2) 3))
|
||||
(make-posn 1 2))
|
||||
3)
|
||||
(test (lookup-in-table (list (make-dist-cell (make-posn 2 1) 3))
|
||||
(make-posn 1 2))
|
||||
'∞)]
|
||||
|
||||
@section{The Cat's Path}
|
||||
|
||||
Once we have a breadth-first search all sorted out, we can use it to build a function that
|
||||
determines where the shortest paths from the cat's current position to the boundary are.
|
||||
|
||||
@chunk[<cats-path>
|
||||
<on-cats-path?>
|
||||
<+/f>]
|
||||
|
|
@ -609,11 +615,58 @@ of the two corners that have been removed.
|
|||
<on-cats-path?-tests>
|
||||
<+/f-tests>]
|
||||
|
||||
The function @scheme[on-cats-path?] accepts a world and returns a predicate
|
||||
on the @scheme[posn]s in the world. The predicate indicates if the given
|
||||
@scheme[posn] is on the shortest path.
|
||||
|
||||
For example, in a world of size @scheme[7] with the cat at
|
||||
@scheme[(make-posn 2 2)], the circles with white centers
|
||||
are on the shortest path to the boundary:
|
||||
|
||||
@schemeblock[(render-world
|
||||
(make-world (empty-board 7)
|
||||
(make-posn 2 2)
|
||||
'playing
|
||||
7
|
||||
false
|
||||
true))]
|
||||
|
||||
So we can formulate two test cases using this world, one
|
||||
in the white circles and one not:
|
||||
|
||||
@chunk[<on-cats-path?-tests>
|
||||
(test ((on-cats-path? (make-world (empty-board 7)
|
||||
(make-posn 2 2)
|
||||
'playing
|
||||
7
|
||||
false
|
||||
true))
|
||||
(make-posn 1 0))
|
||||
true)
|
||||
(test ((on-cats-path? (make-world (empty-board 7)
|
||||
(make-posn 2 2)
|
||||
'playing
|
||||
5
|
||||
false
|
||||
true))
|
||||
(make-posn 4 4))
|
||||
false)]
|
||||
|
||||
The computation of the shortest path to the boundary proceeds by computing
|
||||
two distance maps; the distance map to the boundary and the distance map
|
||||
to the cat. Then, a node is on one of the shortest paths if the distance
|
||||
to the cat plus the distance to the boundary is equal to the distance from
|
||||
the cat to the boundary.
|
||||
|
||||
The code is essentially that, plus two other special cases. Specifically if the
|
||||
``h'' key is not pressed down, then we just consider no cells to be on that shortest
|
||||
path. And if the distance to the cat is @scheme['∞], then again no nodes are on the
|
||||
path. The second situation happens when the cat is completely boxed in and has
|
||||
lost the game.
|
||||
|
||||
@chunk[<on-cats-path?>
|
||||
;; on-cats-path? : world -> posn -> boolean
|
||||
;; returns true when the posn is on the shortest path
|
||||
;; from the cat to the edge of the board, in the given world
|
||||
(define (on-cats-path? w)
|
||||
(define/contract (on-cats-path? w)
|
||||
(-> world? (-> posn? boolean?))
|
||||
(cond
|
||||
[(world-h-down? w)
|
||||
(let ()
|
||||
|
|
@ -632,35 +685,8 @@ of the two corners that have been removed.
|
|||
[else
|
||||
(lambda (p) false)]))]
|
||||
|
||||
@chunk[<on-cats-path?-tests>
|
||||
(test ((on-cats-path? (make-world (empty-board 5) (make-posn 1 1)
|
||||
'playing 5 (make-posn 0 0) true))
|
||||
(make-posn 1 0))
|
||||
true)
|
||||
(test ((on-cats-path? (make-world (empty-board 5) (make-posn 1 1)
|
||||
'playing 5 (make-posn 0 0) false))
|
||||
(make-posn 1 0))
|
||||
false)
|
||||
(test ((on-cats-path? (make-world (empty-board 5) (make-posn 1 1)
|
||||
'playing 5 (make-posn 0 0) true))
|
||||
(make-posn 2 1))
|
||||
false)
|
||||
(test ((on-cats-path?
|
||||
(make-world (list
|
||||
(make-cell (make-posn 0 1) true)
|
||||
(make-cell (make-posn 1 0) true)
|
||||
(make-cell (make-posn 1 1) false)
|
||||
(make-cell (make-posn 1 2) true)
|
||||
(make-cell (make-posn 2 0) true)
|
||||
(make-cell (make-posn 2 1) true)
|
||||
(make-cell (make-posn 2 2) true))
|
||||
(make-posn 1 1)
|
||||
'cat-lost
|
||||
3
|
||||
(make-posn 0 0)
|
||||
true))
|
||||
(make-posn 0 1))
|
||||
false)]
|
||||
Finally, the helper function @scheme[+/f] is just like @scheme[+], except that
|
||||
it returns @scheme['∞] if either argument is @scheme['∞].
|
||||
|
||||
@chunk[<+/f>
|
||||
(define (+/f x y)
|
||||
|
|
@ -670,14 +696,6 @@ of the two corners that have been removed.
|
|||
[else
|
||||
(+ x y)]))]
|
||||
|
||||
@chunk[<+/f-tests>
|
||||
(test (+/f '∞ '∞) '∞)
|
||||
(test (+/f '∞ 1) '∞)
|
||||
(test (+/f 1 '∞) '∞)
|
||||
(test (+/f 1 2) 3)]
|
||||
|
||||
|
||||
|
||||
@section{Tests}
|
||||
|
||||
@chunk[<test-infrastructure>
|
||||
|
|
@ -734,6 +752,15 @@ of the two corners that have been removed.
|
|||
(printf "passed ~s tests\n" test-count)
|
||||
(flush-output))]
|
||||
|
||||
@chunk[<lookup-in-table-tests>
|
||||
(test (lookup-in-table empty (make-posn 1 2)) '∞)
|
||||
(test (lookup-in-table (list (make-dist-cell (make-posn 1 2) 3))
|
||||
(make-posn 1 2))
|
||||
3)
|
||||
(test (lookup-in-table (list (make-dist-cell (make-posn 2 1) 3))
|
||||
(make-posn 1 2))
|
||||
'∞)]
|
||||
|
||||
@chunk[<build-bfs-table-tests>
|
||||
(test/set (build-bfs-table
|
||||
(make-world (empty-board 3) (make-posn 1 1)
|
||||
|
|
@ -981,6 +1008,52 @@ of the two corners that have been removed.
|
|||
(test (in-bounds? (make-posn 10 0) 11) true)
|
||||
(test (in-bounds? (make-posn 0 10) 11) false)]
|
||||
|
||||
@chunk[<on-cats-path?-tests>
|
||||
(test ((on-cats-path? (make-world (empty-board 5)
|
||||
(make-posn 1 1)
|
||||
'playing
|
||||
5
|
||||
(make-posn 0 0)
|
||||
true))
|
||||
(make-posn 1 0))
|
||||
true)
|
||||
(test ((on-cats-path? (make-world (empty-board 5)
|
||||
(make-posn 1 1)
|
||||
'playing
|
||||
5
|
||||
(make-posn 0 0)
|
||||
false))
|
||||
(make-posn 1 0))
|
||||
false)
|
||||
|
||||
(test ((on-cats-path? (make-world (empty-board 5) (make-posn 1 1)
|
||||
'playing 5 (make-posn 0 0) true))
|
||||
(make-posn 2 1))
|
||||
false)
|
||||
(test ((on-cats-path?
|
||||
(make-world (list
|
||||
(make-cell (make-posn 0 1) true)
|
||||
(make-cell (make-posn 1 0) true)
|
||||
(make-cell (make-posn 1 1) false)
|
||||
(make-cell (make-posn 1 2) true)
|
||||
(make-cell (make-posn 2 0) true)
|
||||
(make-cell (make-posn 2 1) true)
|
||||
(make-cell (make-posn 2 2) true))
|
||||
(make-posn 1 1)
|
||||
'cat-lost
|
||||
3
|
||||
(make-posn 0 0)
|
||||
true))
|
||||
(make-posn 0 1))
|
||||
false)]
|
||||
|
||||
|
||||
@chunk[<+/f-tests>
|
||||
(test (+/f '∞ '∞) '∞)
|
||||
(test (+/f '∞ 1) '∞)
|
||||
(test (+/f 1 '∞) '∞)
|
||||
(test (+/f 1 2) 3)]
|
||||
|
||||
@section{Everything Else}
|
||||
|
||||
|
||||
|
|
|
|||
Loading…
Reference in New Issue
Block a user