Showing posts with label htpd 150 scheme. Show all posts
Showing posts with label htpd 150 scheme. Show all posts

Tuesday, 3 July 2012

Exercise 174: Equip your program from exercise 173 with food.


Exercise 174: Equip your program from exercise 173 with food 

At any point in time, the box should contain one piece of food. To keep things simple, a piece of food is of the same size as worm segment. When the worm’s head is located at the same position as the food, the worm eats the food, meaning the worm’s tail is extended by one segment. As the piece of food is eaten, another one shows up at a different location.
Your program should place the food randomly within the box. To do so properly, you need a design technique that you haven’t seen before—so-called generative recursion—so we provide function definitions:

; Posn -> Posn
; ???
(define (food-create p)
  (food-check-create p (make-posn (random MAX) (random MAX))))
; Posn Posn -> Posn
; generative recursion
; ???
(define (food-check-create p candidate)
  (if (equal? p candidate) (food-create p) candidate))
The code for the exercise can be downloaded here

Generative recursion is defined by wikipedia as recursion that creates an entirely new object.

The function food-check-create creates a random object (via food-create) and then checks to make sure it's not in the same position as the posn passed in.  This is  to ensure that the food does not appear directly under the snakes head thus prematurely ending the game.


The function as supplied does not ensure that the food does not appear under the snake body - however that shouldn't matter too much as this will not end the game due to the collision detection only checking the worms head - it would just seem a bit funny to watch.

In my answer below, I have modified this function somewhat. This is due to the nature of the error collision I have used in checking for food collisions. I am checking the co-ordinates of the food and of the snake and determining a collision has occurred if the x and y co-ordinates are the same. This is an issue because if the co-ordinates are out by 1-20 pixels, the snake would appear to touch (or overlap) the food and pass right over it.

Therefore I have locked the food generation to appear on only x and y co-ordinates that the snake can appear on. I could have also fixed this in the food-collision method, but this would have mean the snake could still only partially intersect the food. It would work, but still look funny (and this is not how snake games are meant to work!)

Whilst I was writing this final stage of this question, I finally recall the the posn structure and realise I probably should have been using them all along (instead of the structure I called segments). This would be a minor thing to change, but I will leave them called segments as this makes the code easier to read and makes it consistant with the answers I have already created.




; Constants


(define WORM-SIZE 10)
(define WORM-MOVE (* WORM-SIZE 2))
(define WIDTH 800)  ; width of the game
(define HEIGHT 500) ; height of the game
(define SEGMENT (circle WORM-SIZE "solid" "red"))
(define FOOD (circle WORM-SIZE "solid" "black"))


; these structs will hold the current list of worm segments, the direction
; the worm is travelling in, and our world object
(define-struct segment(x-pos y-pos))
(define-struct direction(x y))


; worm is a list of worm segments
; direction is the direction the worm is travelling
; segment is our current food segment
(define-struct world(worm direction segment))


(define WORM (list (make-segment 100 100)
                   (make-segment 100 80)
                   (make-segment 100 60)) )      


; To save repeating these directions in tests and code, we'll define them here
(define DOWN  (make-direction 0 1))
(define UP    (make-direction 0 -1))
(define RIGHT (make-direction  1 0))
(define LEFT  (make-direction -1 0))


; Functions





This first function food-create is one of the supplied functions. I have changed the dimensions for the allowed positions for the food segment. This is because we need to make sure the food is in a position that our worm can travel over completely. (Currently this is multiples of 20). If we don't do this, the food could be off by for example 5 pixels, so we could travel over it and not trigger a collision



; Posn -> Posn
; Creates a new item of food at anywhere on the screen *except* for the 
; point defined by posn p. (eg the current snake position)

(define (food-create p)
  (food-check-create
   p 
   (make-segment (* (random (/ WIDTH WORM-MOVE)) WORM-MOVE)
                 (* (random (/ HEIGHT WORM-MOVE)) WORM-MOVE))))



; Posn Posn -> Posn
; checks that the candidate and p are at different points on the screen.
; If they are at the same point, create a new candiate by recursing into
; food-create, otherwise return the new candidate (which will then be returned
; via food-create)
(define (food-check-create p candidate)
  (if (equal? p candidate) (food-create p) candidate))




; draw worm in its current location on the screen. Instead of simply drawing 
; a single dot on the screen, we need to recurse down our list of worm 
; segments drawing each one at a time
(define (draw-worm background worm)
  (cond [(empty? worm) background]
        [else (place-image
               SEGMENT
               (segment-x-pos (first worm)) (segment-y-pos (first worm))
               (draw-worm background (rest worm))
              )]))




; This is a new method for question 174.
; This draws the food on to the background of our world
; Returns a new image.
(define (draw-food background food)
  (place-image FOOD (segment-x-pos food) (segment-y-pos food) background) )


; function to determine if we have collided with a food block
; returns true if the worm's segment is on top of the food
(define (worm-hit-food? segment food)
  (cond ((and (= (segment-x-pos segment) (segment-x-pos food))
              (= (segment-y-pos segment) (segment-y-pos food))) true)
        (else false)))




; This is a new function for question 174. It grows the worm one segment.
; To do this we just append a segment in the existing foods position
; on to the worm. Another way to do this would be to append at the end of 
; the list.
; This method was simpler though (but doesn't look quite as good)
(define (grow-worm worm food)
 (cons (make-segment (segment-x-pos food) (segment-y-pos food)) worm  ))
       


; This is a new function for question 174. This method will check if we are
; in the same location as a food item, and if so, eat it. (and make the worm
; grow longer)
; returns a world state with either nothing changed, or a longer worm and
; a new food;
(define (eat-food world)
  (cond ((worm-hit-food? (first (world-worm world)) (world-segment world))
         (make-world  (grow-worm (world-worm world) (world-segment world))
                     (world-direction world)
                     (food-create (first (world-worm world)))))
        (else world)))



; Checks if the snake has collided with either itself, or with the walls
; Returns true in the event of a collision
(define (collision-detected world)
  (or
   (collision-detected-wall (first (move-worm-helper world )))
   (collision-detected-worm (first (move-worm-helper world))  (world-worm world ))))


; Returns true if the worm has collided with itself.
(define (collision-detected-worm segment worm)
  (member? segment worm))


; helper function for collision detection. Operates directly
; on a worm, rather than world object.
(define (collision-detected-wall segment)
 (cond [(> 0        (segment-x-pos segment)) true]  ; exceeding left edge
        [(> 0       (segment-y-pos segment)) true]  ; exceeding top edge
        [(< WIDTH   (segment-x-pos segment)) true]  ; exceeding right edge
        [(< HEIGHT  (segment-y-pos segment)) true]  ; exceeding bottom edge
        [else false]))




; Draw our final scene with the worm departing the board
; Displays a "Game Over" type message. We should probably be calculating the
; width and height of the image to calculate the offsets, but it's simpler just
; to arbitrarily put it somewhere in the bottom right of the screen

(define (final-scene world)
  (draw-worm
   (place-image 
    (text
     (cond  ((collision-detected-wall (first (move-worm-helper world )))
             "worm hit border" )
            (else "worm hit worm"))       
     20 "red")
    (- WIDTH 100)
    (- HEIGHT 50)
    (empty-scene WIDTH HEIGHT))
   (world-worm world)))



; Draws the current world.
(define (show world)
  (draw-food
   (draw-worm (empty-scene WIDTH HEIGHT) (world-worm world))
   (world-segment world)))


; Move the worm in the current direction. Instead of changing the position of
; a single segment, now we add a segment to start of the worm (in the 
; current direction) and get rid of the end of the worm
(define (move-worm worm direction)
   (cons (new-segment (first worm) direction) (remove-last worm))
)


; helper method to DRY up code when calling this from a world object
(define (move-worm-helper world)
  (move-worm (world-worm world) (world-direction world)))


; return a new segment moved in 'direction' from the segment passed in
(define (new-segment segment direction)
    (make-segment  (+ (segment-x-pos segment)
                  (* WORM-MOVE (direction-x direction)))
               (+ (segment-y-pos segment)
                  (* WORM-MOVE (direction-y direction)))))




; remove the last worm segment. this is a pretty unoptimised function. just
; reverse the list, grab the rest of it, and reverse it again to get it the
; correct order.
(define (remove-last worm)
   (reverse (rest (reverse worm))))






; This has changed for question 174 - we now need to check for food 
; collisions on each clock tick.
; On each clock tick, move the world further in time. This is a new function
; that takes part of the responsibily of the old move-worm function. It just
; moves the worm and creates a new world based on it.
(define (progress-world world)
  (eat-food
   (make-world
    (move-worm  (world-worm world)
                (world-direction world))
    (world-direction world)
    (world-segment world))
  ))


; handle keyboard events.
(define (handle-key-events ws ke)
  (cond
    [(string=? "left" ke)  (change-direction ws LEFT)]
    [(string=? "right" ke) (change-direction ws RIGHT)]
    [(string=? "up" ke)    (change-direction ws UP )]
    [(string=? "down" ke)  (change-direction ws DOWN)]
    [else ws]
  ))


; create a new world with the direction the worm is travelling in changed.
(define (change-direction world  direction)
  (make-world (world-worm world) direction  (world-segment world)))




; This is the big bang function that drives the game.
(define (worm-main rate)
  (big-bang (make-world WORM
                        (make-direction 1 0)
                        (make-segment 300 100)
                        )
            (to-draw    show)
            (stop-when  collision-detected final-scene)
            (on-key     handle-key-events)
            (on-tick    progress-world rate) ))


; start the game off!
(worm-main 0.1)




# TESTS


; Test when we move the worm up, a new segment is added to the start and removed
; from the end.
(check-expect (move-worm WORM LEFT)
              (list
               (make-segment (- 100 WORM-MOVE) 100)
               (make-segment 100 100)
               (make-segment 100 80)))


; Check the remove-last function removes the last segment correctly
(check-expect (remove-last WORM)
              (list (make-segment 100 100)
                   (make-segment 100 80)))


; Test that new segment returns a new segment in the correct position
; (as per the current direction)
(check-expect (new-segment  (make-segment 100 100) UP)
              (make-segment 100 (- 100 WORM-MOVE)))






; exceeding the bottom of the screen


;; Test our worm draws as we expect it.
(check-expect (draw-worm (empty-scene 200 200) WORM)
              (place-image SEGMENT 100 100
                           (place-image SEGMENT 100 80
                           (place-image SEGMENT 100 60 (empty-scene 200 200)))))
             


; Test our worm moves in the direction we expect
(check-expect (move-worm (list (make-segment 50 50)) DOWN)
              (list (make-segment 50 70)))
(check-expect (move-worm (list (make-segment 50 50)) UP)
              (list (make-segment 50 30)))
(check-expect (move-worm (list (make-segment 50 50)) LEFT)
              (list (make-segment 30 50)))
(check-expect (move-worm  (list (make-segment 50 50)) RIGHT)
              (list (make-segment 70 50)))

Tuesday, 18 October 2011

Exercise 150 - Transposing a Matrix


Mathematics teachers may have introduced you to matrix calculations by now. Numeric programs deal with those, too. Here is one possible data representation for matrices:

; A Matrix is one of:
; – empty
;; – (cons LN Matrix)
; An LN is one of:
; – empty
;; – (cons Number LN)
; interp. a matrix is a list of rows, a row is a list of numbers
; constraint: all rows are of the same length

Study it and translate the two-by-two matrix consisting of the numbers 11, 12, 21, 22 into this data representation.


They don't make it 100% clear how this should translate to a matrix (eg horizontally or vectically), but common sense would be to divide it into two horizontal rows

(require racket/base)

(define MATRIX (list (list 11 12)
(list 21 22)))

; define an extra couple of Matrix's to use for testing.
(define MATRIX2 (list (list 11 12)
(list 21 22)
(list 31 32)))

(define MATRIX3 (list (list 11 12 13)
(list 21 22 23)
(list 31 32 33)))


Study it and translate the two-by-two matrix consisting of the numbers 11, 12, 21, 22 into this data representation.
The following function implements the important mathematical operation of transposing the entries in a matrix. To transpose means to mirror the entries along the diagonal, that is, the line from the top-left to the bottom-right.

; Matrix -> Matrix
; transpose the items on the given matrix along the diagonal
;(check-expect (transpose mat1) tam1)
(define (transpose lln)
  (cond
    [(empty? (first lln)) empty]
    [else (cons (first* lln) (transpose (rest* lln)))]))


The definition assumes two auxiliary functions:
first*, which consumes a matrix and produces the first column as a list of numbers;;
rest*, which consumes a matrix and removes the first column. The result is a matrix.

Even though you lack definitions for these functions, you should be able to understand how transpose works. You should also understand that you cannot design this ;function with the design recipes you have seen so far. Explain why.

Design the two “wish list” functions. Then complete the design of the transpose with some test cases. 

I am not at all sure how transpose works at this point! (My maths-fu is weak). From reading the code, it seems to work thru a list of lists of numbers, taking the first column and then creating a new list by adding this first column back onto the start of the matrix (which has just had the first column removed!
(An example here would have gone a long way.)
Even if this is transposing the colums, it seems it would be working in complete columns, so I'm not sure how it could ever produce a diagonal transposition.
To confound things further, they say "You cannot design this function". then without explaining anything further, they tell us to go design this function!

I'm not sure if i'm meant to be able to do this or not, but we'll have a try... If we can run the code and it does what they say, perhaps seeing it in process may make things clearer!

The function first* is not too hard - it's the standard recursive scheme function. If the matrix is empty, return empty, otherwise build up a new list consisting of the first number in the list, and the result of calling this on the *rest* of the rows in the matrix

;first* consumes a matrix and produces the first column as a 
;list of numbers
; Matrix -> LN
(define (first* lln)
  (cond ((empty? lln) empty)
        ((cons? lln) (cons (first (first lln)) 
                           (first* (rest lln))))))  

(check-expect (first* MATRIX) (list 11 21))
(check-expect (first* MATRIX2) (list 11 21 31))

This is basically the inverse of first* - this time we want to grab the rest of each list and return that.

;Matrix -> Matrix
(define (rest* lln)
  (cond ((empty? lln) empty)
        ((cons?  lln) (cons (rest (first lln))
                            (rest* (rest lln))))))

(check-expect (rest* MATRIX) (list (list 12) 
                                   (list 22)))
(check-expect (rest* MATRIX2) (list (list 12) 
                                    (list 22) 
                                    (list 32)))
(check-expect (rest* MATRIX3) (list (list 12 13)
                                    (list 22 23) 
                                    (list 32 33)))



Now to test the transposing - in theory, this function should turn our matrix from this:
; 11 12 13
; 21 22 23
; 31 32 32

into this:

; 11 21 31
; 12 22 32
; 13 23 33


(check-expect (transpose MATRIX3) (list (list 11 21 31)
                                        (list 12 22 32)
                                        (list 13 23 33)))

The test passes, so the transpose function does what it is meant to – but why?!?! 

Let's add a  debugging method to try and work out what's going on.
(define (print-matrix mat)
  (cond ((empty? mat) 
         (fprintf (current-output-port) " *** \n"))
        (else (fprintf (current-output-port) 
                       " ~a\n" 
                       (first mat))
              (print-matrix (rest mat)))))


If you put this into the (transpose) function, you can see that transpose does rip the matrix apart into columns. Once the columns have been removed, these get cons'd together horizontally (as rows) to become the new Matrix. This automatically 'mirrors' each half along the diagonal without needing to work on diagonal sections of the matrix.

For example, originally if you had:
; (list (list 2 5)
;       (list 8 9))
This would get ripped into the two colums (list 2 8) and (list 8 9) and then assembled as;
; (list (list 2 8)
;       (list 8 9))