Project P9 Graphs

1. Project P9Graphs CS1050: Understanding and Constructing Proofs Spring 2006 Jarek Rossignac

2. Objectives • Learn how to represent, display, and traverse graphs. • Learn how to compute a vertex spanniging tree • Learn how to compute the topological distance between two nodes

3. Graph editor To Load a graph: click in the graphic window and press "l". To add an edge: click the start point and drag to the end point These will be snapped to existing points if close enough. To move a point, click and drag it while pressing the space bar To toggle the display of point numbers: press "n" To resize and recenter: press "f" When run locally in Processing To save the graph: press "s" To make a picture: press "i"

4. Assignment P9, individual • Modify the code as indicated to compute the Vertex Spanning Tree with vertex 0 as root and set the color of its edges and vertices to not 0. • Post on your PPP: • the image showing the result of your algorithm on the graph provided • the piece of the code that computes the coloring of the VST edges and vertices (with comments) • a discussion of its time complexity • a link to your source code • the applet to run your source codeyour source code

5. Compute spanning tree by growing • Start from seed and grow by layers

6. 18 points col[0]=1 (141,518) col[1]=2 (43,216) col[2]=3 (300,30) col[3]=3 (556,216) col[4]=2 (458,518) col[5]=2 (298,443) col[6]=2 (169.0,381.0) col[7]=3 (150.0,280.0) col[8]=3 (409.0,398.0) col[9]=3 (292.0,317.0) col[10]=4 (278.0,203.0) col[11]=4 (401.0,259.0) col[12]=4 (404.0,183.0) col[13]=4 (315.0,130.0) col[14]=4 (182.0,185.0) col[15]=5 (457.0,321.0) col[16]=6 (481.0,257.0) col[17]=5 (217.0,126.0) 30 edges col[0]=1 (0,1) col[1]=1 (1,2) col[2]=0 (2,3) col[3]=1 (3,4) col[4]=1 (4,0) col[5]=1 (0,5) col[6]=1 (6,0) col[7]=0 (6,5) col[8]=1 (7,6) col[9]=1 (8,5) col[10]=1 (6,9) col[11]=0 (5,9) col[12]=0 (8,4) col[13]=0 (7,9) col[14]=0 (8,9) col[15]=1 (9,10) col[16]=0 (10,7) col[17]=1 (9,11) col[18]=0 (10,11) col[19]=0 (11,8) col[20]=0 (11,12) col[21]=1 (12,3) col[22]=1 (2,13) col[23]=0 (13,12) col[24]=0 (13,10) Colors of points and edges col[25]=0 (10,14) col[26]=1 (11,15) col[27]=1 (15,16) col[28]=1 (14,17) col[29]=1 (14,7)

7. Declarations int vn =5; // initial number of vertices int en =5; // initial number of edges int cap=128; // max nuber of edges and vertices pt[] P = new pt [cap]; // points edge[] E = new edge[cap]; // edges int [] colEdge = new int[cap]; // colors of edges int [] colVert = new int[cap]; // colors of points int mj=10; // user-controlled limit on depth of vertex spanning tree

8. Set up void setup() { size(600, 600); // window size PFont font = loadFont("Courier-14.vlw"); textFont(font, 12); for (int i=0; i<cap; i++) { // clear vertices, edges, colors P[i]=new pt(0,0); E[i]=new edge(0,0); colEdge[i]=0; colVert[i]=0;}; for (int i=0; i<vn; i++) { P[i].setFromValues(-sin((i+0.5)*TWO_PI/vn)* (width*0.45)+width/2.0,cos((i+0.5)*TWO_PI/vn)* (height*0.45)+height/2.0);}; for (int i=0; i<vn; i++) {E[i].setFromValues(i,in(i)); }; VST(); // vertex-spanning-tree }

9. VST void VST() { // colors of edges and points in VSY // insert your code here // my placeholder code just to have something (please delete) for (int i=0; i<vn; i++) {colVert[i]=0;}; // resets vertex colors for (int i=0; i<en; i++) {colEdge[i]=0;}; // resets edge colors colVert[0]=1; // seeds the VST root at vertex for (int i=0; i<en; i++) { if(i%2==1) { colEdge[i]=1; colVert[E[i].s]=1; colVert[E[i].e]=1;};}; // changes colors of odd edges and their vertices }

10. Edge class class edge{ int s,e; edge (int ps, int pe) {s = ps; e = pe;}; edge makeCopy() {return(new edge(s,e));}; void setFromValues(int ps, int pe) {s = ps; e = pe;}; void show() { line(P[s].x,P[s].y,P[e].x,P[e].y);}; void write() {println("("+s+","+e+")");}; }

11. Results