CS1050: Understanding and Constructing Proofs
Spring 2006
Programming Project 2
SORTING
Lecture 05, file P2
Due January 31 before class as a link on your PPP
Jarek Rossignac
Jarek Rossignac
http://www.gvu.gatech.edu/~jarek
MAGIC Lab
Georgia Tech, IIC, GVU, 2006
1
Start with the sample P2
• Access the applet at
http://www.gvu.gatech.edu/~jarek/courses/1050/processing/P2/
• Click in the window and hold mouse down to see animation
• It sorts random numbers and then animates the sorting
Jarek Rossignac
http://www.gvu.gatech.edu/~jarek
MAGIC Lab
Georgia Tech, IIC, GVU, 2006
2
Declarations
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PFont fontUsed; // name of font used for writing on the graphic screen
int H=5;
// number of entries in the table
int T[] = new int[H];
// table (array). Will contain integers
int AT[] = new int[H];
// copy of the table for animation
int swaps[][] = new int[H*H+1][2]; // record swaps (pair of indices)
color myRed = color(250,100,100); color myGreen = color(100,250,100);
color myBlue = color(100,100,250); // my colors (R,G,B) in [0,255]
int cw, ch;
// cell width and height
int c=0, mc=150;
// animation counter and max
int w=0, mw=50;
// wait counter and max
int swap=0;
// index to swaps
int swapMax=0;
// counter of th enumber of swaps
float t=0.0;
// animation parameter
int s1, s2;
// indics of the current pair to be swapped
Jarek Rossignac
http://www.gvu.gatech.edu/~jarek
MAGIC Lab
Georgia Tech, IIC, GVU, 2006
3
Setup
void setup() {
// executed only once as initialization
size(500, 500);
// opens graphic window of 600x600 pixels. \
cw=int(35);
// computes cell sizes leaving a margin, Cast to integer
ch=int(0.9*height/H);
// (height and width of window are keywords)
fontUsed = loadFont("Times-Roman-25.vlw"); // this font must be loaded
(MENU-BAR > TOOLS > CREATE FONTS)
textFont(fontUsed, 20);
// selects font and assigns size
for (int i=0; i<H; i++) {T[i]=int(random(2*H)); }; // init with random numbers
for (int i=0; i<H; i++) {AT[i]=T[i]; };
// copy to animation table
println(); println(" *** unsorted list ***");
for (int i=0; i<H; i++) { println("T["+i+"]="+T[i]);};
bubbleSort();
// call to my naive sorting routine
};
// end of setup
Jarek Rossignac
http://www.gvu.gatech.edu/~jarek
MAGIC Lab
Georgia Tech, IIC, GVU, 2006
4
bubbleSort
void bubbleSort() {
// my simple sorting, replace by
yours
for (int j=H-1; j>0; j--) {
for (int i=0; i<j; i++) {
if (T[i]>T[i+1]) {doSwap(i,i+1);};
}; }; };
void doSwap(int s1, int s2) {
int temp=T[s1]; T[s1]=T[s2]; T[s2]=temp;
the swap
swaps[swapMax][0]=s1; // records the swap
swaps[swapMax][1]=s2;
swapMax++; };
Jarek Rossignac
http://www.gvu.gatech.edu/~jarek
MAGIC Lab
// performs
Georgia Tech, IIC, GVU, 2006
5
Draw
// will be executed continuously to refresh the window many frames per second
void draw() {
background(200); // erases screen and set up a light grey background
strokeWeight(2); // lines will be drawn thicker
translate(width*0.05,height*0.05);
// move the origin to leave a margin
if (mousePressed) // moves animation by one step when mouse pressed
{advanceAnimation(); };
ShowTable();
// Displays the partially sorted table with animation state
if (done) {noLoop();}; // stops when done
};
// end of draw
Jarek Rossignac
http://www.gvu.gatech.edu/~jarek
MAGIC Lab
Georgia Tech, IIC, GVU, 2006
6
advanceAnimation
void advanceAnimation () {
s1=swaps[swap][0]; s2=swaps[swap][1];
// entries to be swapped are retrieved from list of swaps
if (w<mw) {w++;}
// advance the wait counter
if(w==mw) {
// when done waiting
t=float(c)/float(mc);
// compute animation time in [0,1]
c++;
// advance animation counter
if (c==mc) {
// when animation done for this swap
w=0; c=0; t=0;
// reset time and counters
int temp=AT[s1]; AT[s1]=AT[s2]; AT[s2]=temp; // do the actual swap
swap++;
// next swap
if (swap==swapMax) {done=true; swap=swapMax;} // all swaps done
};
};
};
Jarek Rossignac
http://www.gvu.gatech.edu/~jarek
MAGIC Lab
Georgia Tech, IIC, GVU, 2006
7
ShowTable
void ShowTable() {
// displays able animated
int ax, ay;
// displacements for the cels being swapped
color cellColor = myGreen;
// default color for cells
float r=(s2-s1)*ch;
// radius for circular animation
int sa=int(r*sin(t*TWO_PI/2.0)/2.0); // horizontal displacement
for (int h=0; h<H; h++) {
// go through the cells
cellColor=myGreen;
// default color for non-swapping cells is green
ax=0; ay=0;
// no displacement for non-swapping cells
if (h==s1) {ay=int(t*r); ax=sa; cellColor=myRed; }; // if upper swap cell
if (h==s2) {ay=-int(t*r); ax=-sa; cellColor=myBlue; }; // if lower swap cell
drawCell(width/2-cw+ax,h*ch+ay,cw,ch,cellColor,AT[h]);
}; };
void drawCell(int wp, int hp, int cwp, int chp, color cp, int vp) {
fill(cp); rect(wp,hp,cwp,chp); // draws and fills a rectangular region
fill(0); text(nf(vp,2),wp+cwp/10,hp+chp*0.8); }; // writes vp on the screen
Jarek Rossignac
http://www.gvu.gatech.edu/~jarek
MAGIC Lab
Georgia Tech, IIC, GVU, 2006
8
Implement 3 variants of bubblesort
• Bubble sort is described page 125
• Add three alternatives to bubbleSort
– A modified bubble sort algorithm that stops when no interchange is
required (exercise 37 page 130)
– Modified insertion sort
• If the next nth element is smaller than the one it follows,
• then bubble it up
• until it is in the correct place in the sorted list of the first n elements
– A modified selection sort (presented at the bottom of page 130)
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Jarek Rossignac
Start with n=1
Assume that the first n–1 elements are sorted.
Find the smallest of the remaining elements
Swap it with the nth element
Increment n
http://www.gvu.gatech.edu/~jarek
MAGIC Lab
Georgia Tech, IIC, GVU, 2006
9
Enhance the user interface
Increase the size of the array.
Let the user press a key for the following actions:
“r”: to select a new random set of numbers
“n”: to select a nearly sorted set of numbers
“b”: to run my naïve bubblesort
“e”: to run your modified bubblesort that stops early
“i”: to run your modified insertion sort
“s”: to run your modified selection sort
When the mouse is in the window and pressed, run the animation
of the algorithm that was run last (make sure that you write in
the graphics window the total number of swaps).
Jarek Rossignac
http://www.gvu.gatech.edu/~jarek
MAGIC Lab
Georgia Tech, IIC, GVU, 2006
10
Report results
• Debug your program and make images for each combination
• Execute all 4 algorithms on several sets of random numbers and
on several sets of nearly sorted numbers
• Watch the 4 algorithms and provide a qualitative
characterization of the differences in their behavior for random
and nearly sorted numbers
• Report statistics of the average number of swaps for each
algorithm (separating random and nearly sorted sets).
• Post on your PPP:
– images (before and after) with number of swaps for each algorithm on a
random and on a nearly sorted set.
– your qualitative characterization
– statistics with conclusions
– links to applet and source code
Jarek Rossignac
http://www.gvu.gatech.edu/~jarek
MAGIC Lab
Georgia Tech, IIC, GVU, 2006
11