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)))

Exercise 173: Re-design your program so that it stops if the worm has run into the walls of the world or into itself.

Re-design your program from exercise 172 so that it stops if the worm has run into the walls of the world or into itself. Display a message like the one in exercise 171 to explain whether the program stopped because the worm hit the wall or because it ran into itself.

Code for this exercise is available here.

Only fairly straight forward changes were required to accomodate this new iteration. Changes needed to be  made to the collision-detection function and the final-scene function.

The collision-detection function now needs to check for both collisions with the wall and collisions with the tail of the worm. By breaking this method into two independent functions; one checking for wall collisions and one checking for tail collisions, I was able to re-use the code for the wall collisions in final-scene function for determining which message to display - either "You have hit the wall", or "You have hit yourself".

Although we have a multi-segmented worm now, the collision detection functions didn't need to be drastically modified as it only needs to check the head of the worm. We can just pop off the first segment and use this to check for collisions. For worm tail collisions we use the member? function as specified in the hint.

For the final-scene function the only change was to determine which message to display. As the collision-detection function only returns true or false we can't use this directly. By calling the indivdiual functions within this method (ie collision-detection-wall) we can determine the method. There is no need to check for collisions with the worm, as if the worm has collided with something and it was not the wall, then it must have collided with itself.

Code

; 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"))                              


; these structs 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))
(define-struct world(worm direction))
(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


; draw worm in its current location on the screen. This function recurses
; down our list of worm segments drawing each one at a time on to the background
; passed in
(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 function has changed for this exercise so that instead of just checking for a collision with the wall, we check for a collision with the worm as well. This is accomplished by calling two separate collision functions - one for the wall, and one for the worm. The reason this has been split up is so that we can use the same function to determine which end of game message should be displayed. This function could be trivially extended to check for collisions with objects in the room.




; Check for collisions with either the walls or the rest of the worm.
; return true if collision detected, false otherwise
(define (collision-detected world)
  (or
   (collision-detected-wall (first (move-worm-helper world )))
   (collision-detected-worm (first (move-worm-helper world)) 
                            (world-worm world ))))





; a helper function for checking for collision with the worm. 
; This works by checking if area the worm would move into is already in the
; list of worm segments
; return true if collision detected, false otherwise
(define (collision-detected-worm segment worm)
  (member? segment worm))


; a helper function for collision detection with the wall
; returns true if a collision is detected, false otherwise
(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]))




The final-scene method also changed for this exercise. To display the correct end of game message we need to determine if we've collided with the worm or the wall.
We can use the collision-detected-wall method to determine if the game finished because we hit the wall. If it didn't finish because of that, it must have finished because we hit the rest of the worm.


; 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. This consists of the snake and the food objects
(define (show world)
  (draw-worm (empty-scene WIDTH HEIGHT) (world-worm world)) )


; Move the worm in the current direction. To move the worm 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.
(define (move-worm-helper world)
  (move-worm (world-worm world) (world-direction world)))


; returns 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))))






; On each clock tick, move the world further in time. It moves the worm
; and creates a new world based on this.
(define (progress-world world)
   (make-world
    (move-worm  (world-worm world)  (world-direction world))
    (world-direction 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))




; This is the big bang function that drives the game.
(define (worm-main rate)
  (big-bang (make-world WORM
                        (make-direction 1 0))
            (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
;(check-expect (collision-detected (make-world
;                                    (make-worm (- WIDTH 10) (+ HEIGHT 10)) RIGHT))
;              true)
;; exceeding the right side of the scren
;(check-expect (collision-detected (make-world
;                                    (make-worm (+ WIDTH 10) (- HEIGHT 10)) RIGHT))
;              true)
;
;; exceeding the top of the screen
;(check-expect (collision-detected (make-world
;                                    (make-worm -10 (- HEIGHT 10)) LEFT))
;              true)
;; exceeding the left side of the screen
;(check-expect (collision-detected (make-world
;                                    (make-worm (- WIDTH 10) -10) LEFT))
;              true)
;
;;in the middle of the screen - should not collide
;(check-expect (collision-detected (make-world
;                                    (make-worm (- WIDTH 10) (- HEIGHT 10)) LEFT))
;              false)
;


;
;; 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)))


; Test our change-direction function changes the direction, but doesn't impact 
; the postion
(check-expect (change-direction (make-world (make-segment 50 50) DOWN) UP)
              (make-world (make-segment 50 50) UP))
(check-expect (change-direction (make-world (make-segment 50 50) DOWN) RIGHT)
              (make-world (make-segment 50 50) RIGHT))          

Exercise 167: Write down the data definition for List-of-words.

Systematically make up examples of Words and List-of-words. Finally, formulate the functional example from above with check-expect.  Instead of working with the full example, you may wish to start with a word of just two letters, say "d" and "e".

 A Word is either
 – empty or
 – (cons 1String Word)

I think this is the correct data definition for a List-of-words. It is either an empty list, or a Word cons'd together with another List-of-words (which may itself be an empty word)

; A List-of-words is either
; - empty or
; (cons Word List-of-words)



For our examples we will create two Words - "word" and "roger".  There is a 1String function we could use to do this but for practice I'm using cons directly.

(define word (cons "w" (cons "o" (cons "r" (cons "d" empty)))))  
(define roger (cons "r" (cons "o" (cons "g" (cons "e" (cons "r" empty))))))


Now an example List-of-words containing these two words:
(define list-of-words (cons word (cons roger empty))) 


For testing this example we will create a 1String for the string "de"
(define de (cons "d" (cons "e" empty)))


Now a check-expect to test all arrangements of the word "de".
This will be failing at this time as we haven't implemented the arrangements function yet.
(check-expect (arrangements de)
              (cons (cons (cons "d" (cons "e" empty))
                    (cons "e" (cons "d" empty)))
                     empty))

Exercise 166: Modify connect-dots so that it consumes an additional Posn structure ...

Exercise 166: Modify connect-dots

Modify connect-dots so that it consumes an additional Posn structure to which the last Posn is connected.
Then modify render-poly to use this new version of connect-dots. Note: this new version is called an accumulator version.

This is perhaps not the ideal way to solve this question but I believe it is doing what has been asked.
It seems a little odd as it is defined as an "accumulator" version which normally means the answer
'accumulates' (or changes) as you recurse up or down the stack. In this case our accumulator remains unchanged and is used simply as a means to draw the link back to the original posn.

When we reach the end of the list of posns instead of returning an empty scene element to draw the rest of the polygon onto, I am returning an image with this last link already drawn in. The rest of the function is exactly the same, with the exception that we are passing our final-posn all the way down the stack.

; NELoP -> Image
; connect the Posns in p
(define (connect-dots p final-posn)
  (cond
    [(empty? (rest p)) (render-line MT final-posn (first p) )]
    [else
      (render-line
  (connect-dots (rest p) final-posn) (first p) (second p) )]))

We need to change the way we call connect-dots to take into account our new function signature. instead of wrapping an additional render-line around the call to connect-dots, we pass back in the first posn in the list so that connect-dots knows where to attach the last posn back to.

; Polygon -> Image
; add the Polygon p into an image in MT
(define (render-polygon p)
  (connect-dots p (first p)))


; check our rendering of a list of triangle is sane
(check-expect
  (render-polygon
    (list (make-posn 20 0) (make-posn 10 10) (make-posn 30 10)))
  (add-line
    (add-line
      (add-line MT 20 0 10 10 "red")
      10 10 30 10 "red")
    30 10 20 0 "red"))




; check our rendering of a square is sane
(check-expect
  (render-polygon
    (list (make-posn 10 10) (make-posn 20 10)
          (make-posn 20 20) (make-posn 10 20)))
  (add-line
    (add-line
      (add-line
        (add-line MT 10 10 20 10 "red")
        20 10 20 20 "red")
      20 20 10 20 "red")
    10 20 10 10 "red"))


The following supporting code is copied directly from the book.



(require 2htdp/image)


; A Polygon is one of:
; – (list Posn Posn Posn)
; – (cons Posn Polygon)


(define MT (empty-scene 50 50))




; A NELoP is one of:
; – (cons Posn empty)
; – (cons Posn NELoP)






; Image Posn Posn -> Image
; draw a red line from Posn p to Posn q into im
(define (render-line im p q )
  (add-line
    im (posn-x p) (posn-y p) (posn-x q) (posn-y q) "red"))


; NELoP -> Posn
; extract the last Posn from p
(define (last p)
  (cond
    [(empty? (rest (rest (rest p)))) (third p)]
    [else (last (rest p))]))