Lab 10 Color Changing Graphs
Purpose: Practice working with graphs.
Working with Nodes
; A Node is a (make-node Nat Color [List-of Nat]) (define-struct node [id color neighbors]) ; - where id is the unique identifier for the given node ; - color is the node's current color ; - and neighbors is a list of the ids of nodes this one is connected to ; A Graph is a [List-of Node]
Exercise 1 Finish the data design for the above data definitions.
Exercise 2 Design the function can-reach-in-time? which takes a Graph, the IDs of two nodes in the Graph, and a natural number. It determines whether you can get from the node with the first ID to the node with the second ID in the given number of steps. A step is when you move from a node to its neighbor.
Moody Graphs
In this section we will design a program that displays a graph and changes the color of its nodes on every clock tick. Each node will become the same color as the majority of their neighbors.
Step 1: What stays the same?
For your convenience we have provided some constants to use below. You can modify them or add to them if you find that you need to keep track of something else.
(require 2htdp/image) (define WIDTH 500) (define HEIGHT 500) (define MARGIN-SIZE 25) (define GRAPH-SIZE (- WIDTH (* MARGIN-SIZE 2))) (define OFFSET (+ MARGIN-SIZE (/ GRAPH-SIZE 2))) (define BACKGROUND (empty-scene WIDTH HEIGHT)) (define FONT-SIZE 15) (define NODE-SIZE 20)
Step 2: What changes?
Luckily, we already have a data definition to work with! What a crazy random happenstance. We will use a Graph to keep track of the state of the world.
Step 3: Which handlers do we need?
Exercise 3 Write down the signatures and purpose statements for the handler functions you need. This is your "wishlist" of functions that you will need to create.
Step 4: Main Function
Now that we’ve decided on our handler functions, we can put together our main function which will call big-bang. Recall that we write this function first because in this course we follow a top down programming approach. That means larger functions go at the top of our program and smaller functions go underneath.
(require 2htdp/universe) ; moody-graph : Graph -> Graph ; Draw the graph and change its nodes to have the color of the majority of their neighbors (define (moody-graph graph) (big-bang graph [to-draw draw-graph] [on-tick update-graph 0.5]))
Step 5: Design your handlers
The to-draw function is a long one and doesn’t really further the purpose of this lab so we provide it for you below. Please copy the code into your file so that your program will run.
; draw-graph : Graph -> Image ; Draw all the nodes in the graph and their connections (check-expect (draw-graph '()) BACKGROUND) (check-expect (draw-graph GRAPH-12) (place-image (overlay (text "1" FONT-SIZE "white") (circle NODE-SIZE "solid" "purple")) 475 250 (place-image (overlay (text "2" FONT-SIZE "white") (circle NODE-SIZE "solid" "green")) 25 250 (add-line BACKGROUND 475 250 25 250 "black")))) (define (draw-graph all-nodes) (local [(define node-coordinates (find-node-coordinates (length all-nodes)))] (draw-nodes-as-dots all-nodes node-coordinates (draw-all-connections all-nodes node-coordinates)))) ; find-node-coordinates : Nat -> [List-of Posn] ; Produce coordinates for the given number of nodes (check-expect (find-node-coordinates 0) empty) (check-expect (find-node-coordinates 2) (list (make-posn 475 250) (make-posn 25 250))) (define (find-node-coordinates num-nodes) (build-list num-nodes (λ (index) (get-coordinates-at-index index num-nodes)))) ; get-coordinates-at-index : Nat Nat -> Posn ; Find the coordinates for a node at the given index in a list of the given length (check-expect (get-coordinates-at-index 10 20) (make-posn 25 250)) (check-expect (get-coordinates-at-index 7 8) (make-posn 409 91)) (define (get-coordinates-at-index index total) (make-posn (inexact->exact (round (+ (* (cos (* (/ index total) 2 pi)) 1/2 GRAPH-SIZE) OFFSET))) (inexact->exact (round (+ (* (sin (* (/ index total) 2 pi)) 1/2 GRAPH-SIZE) OFFSET))))) ; draw-nodes-as-dots : [List-of Node] [List-of Posn] Image -> Image ; Draw each of the nodes as a dot on the given image (check-expect (draw-nodes-as-dots '() '() (circle 2 "solid" "blue")) (circle 2 "solid" "blue")) (check-expect (draw-nodes-as-dots GRAPH-12 (list (make-posn 30 40) (make-posn 70 20)) BACKGROUND) (place-image (overlay (text "1" FONT-SIZE "white") (circle NODE-SIZE "solid" "purple")) 30 40 (place-image (overlay (text "2" FONT-SIZE "white") (circle NODE-SIZE "solid" "green")) 70 20 BACKGROUND))) (define (draw-nodes-as-dots all-nodes all-coordinates bg-img) (foldr (λ (n c sofar) (draw-circle c (node-id n) (node-color n) sofar)) bg-img all-nodes all-coordinates)) ; draw-circle : Posn Nat Color Image -> Image ; Draw a circle of the given color at the given position on the given background (check-expect (draw-circle (make-posn 30 40) 7 "red" (empty-scene 200 300)) (place-image (overlay (text "7" FONT-SIZE "white") (circle NODE-SIZE "solid" "red")) 30 40 (empty-scene 200 300))) (check-expect (draw-circle (make-posn 0 0) 100 "purple" BACKGROUND) (place-image (overlay (text "100" FONT-SIZE "white") (circle NODE-SIZE "solid" "purple")) 0 0 BACKGROUND)) (define (draw-circle p id color bg) (place-image (overlay (text (number->string id) FONT-SIZE "white") (circle NODE-SIZE "solid" color)) (posn-x p) (posn-y p) bg)) ; draw-all-connections : [List-of Node] [List-of Posn] -> Image ; Draw the lines between each node and its neighbors (check-expect (draw-all-connections '() '()) BACKGROUND) (check-expect (draw-all-connections GRAPH-12 (list (make-posn 1 2) (make-posn 30 40))) (add-line BACKGROUND 1 2 30 40 "black")) (define (draw-all-connections all-nodes all-coordinates) (local [; get-neighbor-coordinates : Node -> [List-of Posn] ; Get the coordinates of all of this node's neighbors (define (get-neighbor-coordinates n) (map (λ (id) (get-coordinates-for-node id all-nodes all-coordinates)) (node-neighbors n)))] (foldr (λ (n c sofar) (draw-connections c (get-neighbor-coordinates n) sofar)) BACKGROUND all-nodes all-coordinates))) ; get-coordinates-for-node : Nat [List-of Node] [List-of Posn] -> Posn ; Get the coordinates for the node with the given ID (check-error (get-coordinates-for-node 10 '() '())) (check-expect (get-coordinates-for-node 8 GRAPH-789 (list (make-posn 1 2) (make-posn 30 40) (make-posn 100 100))) (make-posn 30 40)) (define (get-coordinates-for-node id all-nodes all-coordinates) (cond [(empty? all-nodes) (error (string-append "Could not find node with ID " (number->string id)))] [(cons? all-nodes) (if (same-id? id (first all-nodes)) (first all-coordinates) (get-coordinates-for-node id (rest all-nodes) (rest all-coordinates)))])) ; draw-connections : Posn [List-of Posn] Image -> Image ; Draw lines from the given position to each of the coordinates in the list (check-expect (draw-connections (make-posn 1 2) empty (circle 5 "solid" "red")) (circle 5 "solid" "red")) (check-expect (draw-connections (make-posn 40 30) (list (make-posn 30 40) (make-posn 100 100)) BACKGROUND) (add-line (add-line BACKGROUND 40 30 30 40 "black") 40 30 100 100 "black")) (define (draw-connections p to-connect bg) (foldr (λ (p2 sofar) (line-between p p2 sofar)) bg to-connect)) ; line-between : Posn Posn Image -> Image ; Add a line between the two coordinates to the given image (check-expect (line-between (make-posn 1 2) (make-posn 30 40) BACKGROUND) (add-line BACKGROUND 1 2 30 40 "black")) (check-expect (line-between (make-posn 100 100) (make-posn 0 0) (empty-scene 700 200)) (add-line (empty-scene 700 200) 100 100 0 0 "black")) (define (line-between p1 p2 img) (add-line img (posn-x p1) (posn-y p1) (posn-x p2) (posn-y p2) "black"))
Now we will design the function that updates the graph as time goes by. At each tick we want each node in the graph to become the color shared by the majority of its neighbors. We will break this down into smaller steps in the following exercises.
Exercise 4 Consider the data definition given below:
(define-struct count [element times]) ; A [Count X] is a (make-count X Nat) ; and represents a count of the number of times an element has been seen in a list Design the function count-all-colors which, given a [List-of Color], produces a [List-of [Count Color]] which contains the count of how many times each color appeared in the given list.
Exercise 5 Now design the function majority-color which takes a [List-of Node] and produces the Color that is most common. If there are no Nodes in the list your function should produce false.
Exercise 6 Design the function get-neighbor-nodes which takes a Graph and a Node and produces all the nodes in the graph that are neighbors of the given node.
Exercise 7 Now use the above functions to define update-graph which takes a Graph and produces a Graph where each node in the original graph now has the majority color of its neighbors. If it has no neighbors, the color of the node should remain unchanged.
Lab Quiz
If we were to have a lab quiz it would look like this:
; A Person has a name and a list of their friends. ; Friends can be mutual, but they don't have to be. ; Create a data definition for a Person. Then provide two examples ; of people who are friends with each other.