Quadtrees
Implement methods for a quadtree representation of bitmap images.
Our representation of quadtrees will not have a separate Node class. Instead, a QuadtreeBitmap itself can be thought of as a node. A QuadtreeBitmap is either a leaf, in which case it represents a square region of pixels all of the same colour; or an internal node, in which case it has four child QuadtreeBitmaps, one per quadrant of the bitmap image.
You may implement your submission in either Java or Python. The only file which you need to edit is QuadtreeBitmap.java or quadtree_bitmap.py, which contains a class QuadtreeBitmap, which contains the methods you need to implement:
? blackenNorthWestQuadrant() : blacken the entire north-west quadrant.
? countPixels(Colour) : count pixels of a given colour in the bitmap represented by the quadtree.
? invertColours() : invert the colours in the bitmap represented by the quadtree, i.e. turn every black pixel white and every white pixel black.
? setPixel(int x, int y, Colour) : change the colour of a single pixel in the bitmap represented by the quadtree, to the specified colour.
代写java Quadtrees树作业、代做代写java程序作业
? computeOverlay(QuadtreeBitmap bmp1, QuadtreeBitmap bmp2) : construct and return the overlay of the two input images of the same size. In the overlay a pixel is black if either of the input images has a black pixel in the same location. That is, a pixel in the output image is white only when the corresponding pixel in both input images is white, otherwise the output pixel is black. Rather than do the operation pixel by pixel, one can compute the overlay more efficiently by leveraging the quadtree's ability to represent multiple pixels with a single node.
Note: for full marks, the resulting quadtree needs to be in "reduced" form, i.e. any subtree that is entirely one colour needs to be reduced to a single leaf.
Empty method definitions have been provided in the QuadtreeBitmap class for each of the methods you need to implement. They start from line 115 of the Java scaffold, and from line 90 of the Python scaffold.
We have provided a scaffold which includes many helpful things, such as:
? A method which constructs a QuadtreeBitmap from a string representation. See below for details on the string representation format expected.
? A method which converts a QuadtreeBitmap into a string representation.
? Various constructors which you might find helpful, e.g.
o A constructor which creates a leaf QuadtreeBitmap for a given location and size.
o A constructor which creates a QuadtreeBitmap for a given location and size, with quadrants given by a list of QuadtreeBitmaps provided as an argument.
? Convenience methods, e.g.
o A method which enumerates quadrants in the following order: northeast, northwest, southeast, southwest.
o A method which determines which quadrant an input (x, y) coordinate pair lies within. (If any.)
o A convenience method which you may enable, which reads a string representation of a bitmap from standard input and constructs the corresponding QuadtreeBitmap.
o Methods which generate string representations of a QuadtreeBitmap, both as a string representation of the bitmap it encodes, and with boxing interspersed to depict its tree structure.
A main method, which will not be tested, has also been provided and may be used by you for experimentation/testing: it's at line 178 of the Java scaffold and at the top of the Python scaffold. If you run the scaffold code in its initial state, you will be asked to enter a string representing a bitmap. Try entering the example from the sheet:
Text
........
.....***
...***..
..**....
..*.....
.**...**
**...***
*....***
We advise against changing the other methods provided in the scaffold. You are allowed to write additional methods, classes, etc., and add additional source files to your assignment workspace as you see fit, though take note of the University's plagiarism policy.
Colour.java
LANGUAGE
QuadtreeBitmap.java
build.sh
core.py
quadtree_bitmap.py
run.sh
Colour.java:
public enum Colour {
WHITE('.'),
BLACK('*');
// character for printing as text
char texture;
Colour(char texture) {
this.texture = texture;
}
/**
* Returns a character representation of this colour, to be used for rendering as a string.
*
* @return a character representation of this colour
*/
public char getTexture() {
return this.texture;
}
/**
* Returns a string representation of this colour.
*
* @return a string representation of this colour
*/
public String toString() {
return Character.toString(texture);
}
/**
* Returns true if the unicode code point given by the input corresponds to the texture of
* a valid colour.
*
* @param c a unicode code point
* @return true if c corresponds to a valid colour, false otherwise
*/
public static boolean isTexture(int c) {
if (!Character.isBmpCodePoint(c)) {
return false;
}
char ch = (char)c;
for (Colour colour : Colour.values()) {
if (colour.texture == ch) {
return true;
}
}
return false;
}
}
QuadtreeBitmap.java:
import java.util.Arrays;
import java.util.Collections;
import java.util.List;
import java.util.ArrayList;
import java.util.stream.Collectors;
import java.util.Scanner;
import java.io.InputStream;
public class QuadtreeBitmap {
// location
private final int x;
private final int y;
// height and width
private final int size;
// if leaf
private boolean leaf;
// either Colour.BLACK or Colour.WHITE
private Colour colour;
// otherwise
private QuadtreeBitmap northWest;
private QuadtreeBitmap northEast;
private QuadtreeBitmap southWest;
private QuadtreeBitmap southEast;
/**
* Constructs a new quadtree bitmap with height and width equal to the specified size, and
* every pixel initialized to the given colour. The specified size must be a power of 2,
* and must be greater than zero.
*
* @param size the height and width of this quadtree bitmap
* @param colour the colour with which to initialize every pixel in this quadtree bitmap
*/
public QuadtreeBitmap(int size, Colour colour) {
this(0, 0, size, colour);
}
/**
* Constructs a new quadtree bitmap with height and width equal to the specified size, and
* every pixel initialized to white. The specified size must be a power of 2, and must be
* greater than zero.
*
* @param size the height and width of this quadtree bitmap
*/
public QuadtreeBitmap(int size) {
this(0, 0, size, Colour.WHITE);
}
// specifying location only supported internally
private QuadtreeBitmap(int x, int y, int size, Colour colour) {
// only supporting power-of-2 dimensions
if (!powerOfTwo(size)) {
throw new IllegalArgumentException("Size not power of 2.");
}
this.x = x;
this.y = y;
this.size = size;
this.leaf = true;
this.colour = colour;
this.northWest = null;
this.northEast = null;
this.southWest = null;
this.southEast = null;
}
// combining quads to form tree only supported internally, assumes well-positioned
private QuadtreeBitmap(int x, int y, int size, List<QuadtreeBitmap> quads) {
this(x, y, size, Colour.WHITE);
northWest = quads.get(0);
northEast = quads.get(1);
southWest = quads.get(2);
southEast = quads.get(3);
this.leaf = false;
}
// for any basic task which needs to be repeated all four quadrants
private List<QuadtreeBitmap> quadrants() {
return Arrays.asList(northWest, northEast, southWest, southEast);
}
// retrieves the quadrant within which the specified location lies
private QuadtreeBitmap quadrantOf(int x, int y) {
for (QuadtreeBitmap quad : quadrants()) {
if (quad.containsPoint(x, y)) {
return quad;
}
}
return null;
}
/**
* Returns true of this QuadtreeBitmap contains the location specified by the input
* coordinates.
*
* @param x how far right of the origin the query location is
* @param y how far below the origin the query location is
* @return true if the given coordinates lie within this QuadtreeBitmap, false otherwise
*/
public boolean containsPoint(int x, int y) {
return this.x <= x
&& this.y <= y
&& x < this.x + this.size
&& y < this.y + this.size;
}
/**
* Returns the height and width of this quadtree bitmap.
*
* @return the size of this quadtree bitmap.
*/
public int getSize() {
return size;
}
/////////////////////////////////////////////////////////////////////////
// Assignment methods start here
/////////////////////////////////////////////////////////////////////////
/**
* Sets the colour of every pixel in the north-west quadrant of this quadtree bitmap to
* black.
*/
public void blackenNorthWestQuadrant() {
// TODO: implement this
}
/**
* Counts the number of pixels of the given colour in the bitmap represented by this
* quadtree.
*
* @param colour the colour to count the number of pixels of
* @return the number of pixels of the given colour
*/
public int countPixels(Colour colour) {
// TODO: implement this
return 0;
}
/**
* Inverts the colours in the bitmap represented by this quadtree, i.e. turns every black
* pixel white and every white pixel black.
*/
public void invertColours() {
// TODO: implement this
}
/**
* Sets the colour of a single pixel at the specified location to the given colour.
*
* @param x the distance right of the origin of the given location
* @param y the distance below the origin of the given location
* @param colour the colour to set the pixel at the given location to
*/
public void setPixel(int x, int y, Colour colour) {
// TODO: implement this
}
/**
* Constructs and returns the overlay of the two given quadtree bitmaps. The overlay of
* two bitmaps is the bitmap which has a black pixel at every location at which either
* input bitmap has a black pixel, and a white pixel at every location at which both
* input bitmaps have a black pixel. Can be thought of as the bitwise or of two bitmaps.
*
* Only supports bitmaps that are the same size.
*
* @param bmp1 the first of two quadtree bitmaps to compute the overlay of
* @param bmp2 the second of two quadtree bitmaps to compute the overlay of
* @return the newly constructed overlay of the two given quadtree bitmaps
*/
public static QuadtreeBitmap computeOverlay(QuadtreeBitmap bmp1, QuadtreeBitmap bmp2) {
// TODO: implement this
return null;
}
///////////////////////////////////////////////////
// End of assignment methods
///////////////////////////////////////////////////
public static void main(String[] args) {
/* This is here for you to optionally use for your own testing / running.
* This method will NOT be tested. Feel free to experment here.
*/
System.out.println("Enter a string representation for a bitmap, "
+ "followed by EOF or \"end\".");
QuadtreeBitmap inputBmp = readBmpFromStream(System.in);
// System.out.println(inputBmp);
System.out.println(inputBmp.toTreeString());
}
// convenience method for constructing quadtrees from string representations of
// bitmaps from stdin
public static QuadtreeBitmap readBmpFromStream(InputStream stream) {
Scanner scanner = new Scanner(stream);
List<String> lines = new ArrayList<String>();
while (scanner.hasNext()) {
String line = scanner.nextLine();
if (line.equals("end")) {
break;
} else {
lines.add(line);
}
}
return fromString(String.join(System.lineSeparator(), lines));
}
////////////////////////////////////////////////////////////////////////
// You do not need to concern yourself with the code beyond this point
////////////////////////////////////////////////////////////////////////
private static boolean powerOfTwo(int n) {
try {
int x = 1;
while (x < n) {
// throws ArithmeticException on overflow
x = Math.multiplyExact(x, 2);
}
if (x == n) {
return true;
} else {
return false;
}
} catch (ArithmeticException ex) {
return false;
}
}
/**
* Constructs a quadtree from the bitmap represented by the input string. Fails with an
* {@code IllegalArgumentException} if the input string does not properly encode a valid
* bitmap.
*
* @param bmpString input string to be converted into a quadtree bitmap
* @return a quadtree bitmap representation of the input string
*/
public static QuadtreeBitmap fromString(String bmpString) {
validateBmpString(bmpString);
return fromRowStrings(0, 0, Arrays.asList(bmpString.split("\\R")));
}
// recursive helper method for fromString
private static QuadtreeBitmap fromRowStrings(int x, int y, List<String> rows) {
int size = rows.size();
if (!rows.stream().anyMatch(str -> str.contains(Colour.BLACK.toString()))) {
// all white
return new QuadtreeBitmap(x, y, size, Colour.WHITE);
} else if (!rows.stream().anyMatch(str -> str.contains(Colour.WHITE.toString()))) {
// all black
return new QuadtreeBitmap(x, y, size, Colour.BLACK);
} else {
int xMid = x + size/2;
int yMid = y + size/2;
// split rows into quadrants
List<String> nwRows = quadRowStrings(0, 0, rows);
List<String> neRows = quadRowStrings(size/2, 0, rows);
List<String> swRows = quadRowStrings(0, size/2, rows);
List<String> seRows = quadRowStrings(size/2, size/2, rows);
// build each subtree
QuadtreeBitmap northWest = fromRowStrings(x, y, nwRows);
QuadtreeBitmap northEast = fromRowStrings(xMid, y, neRows);
QuadtreeBitmap southWest = fromRowStrings(x, yMid, swRows);
QuadtreeBitmap southEast = fromRowStrings(xMid, yMid, seRows);
// combine
List<QuadtreeBitmap> quads = Arrays.asList(northWest, northEast, southWest, southEast);
return new QuadtreeBitmap(x, y, size, quads);
}
}
// extracts row strings for quadrant from row strings for bitmap
private static List<String> quadRowStrings(int xRel, int yRel, List<String> rows) {
int size = rows.size();
// sublist selects rows, substring selects columns
return rows.subList(yRel, yRel + size/2).stream()
.map(row -> row.substring(xRel, xRel + size/2))
.collect(Collectors.toList());
}
// does nothing if input valid, communicates invalidity via exceptions
private static void validateBmpString(String bmpString) {
String[] rows = bmpString.split("\\R");
if (rows.length == 0) {
throw new IllegalArgumentException("Empty bitmap string.");
} else if (!powerOfTwo(rows.length)) {
throw new IllegalArgumentException("Number of rows not a power of 2.");
} else if (!powerOfTwo(rows[0].length())) {
throw new IllegalArgumentException("Row width not a power of 2.");
} else {
// using first row to determine row width
int width = rows[0].length();
for (int i = 1; i < rows.length; i++) {
if (rows[i].length() != width) {
throw new IllegalArgumentException(
"Row " + i + " not same width as other rows.");
}
}
for (String row : rows) {
if (!row.codePoints().allMatch(Colour::isTexture)) {
int ic = row.codePoints()
.filter(c -> !Colour.isTexture(c))
.findFirst().getAsInt();
throw new IllegalArgumentException("Illegal character detected: "
+ "'" + String.valueOf(Character.toChars(ic)) + "'");
}
}
if (rows.length != width) {
throw new IllegalArgumentException("Number of rows not equal to row width.");
}
}
}
/**
* Returns a string representation of the tree structure of this quadtree bitmap.
* The string representation is similar to the representation returned by {@link #toString},
* but with boxing interspersed to indicate the boundaries of the regions represented by
* leaf nodes in the quadtree.
*
* @return a string representation of this quadtree
*/
public String toTreeString() {
char[][] canvas = new char[2*size + 1][2*size + 1];
printTreeToCanvas(canvas, 2*x, 2*y);
StringBuilder sb = new StringBuilder();
for (int i = 0; i < canvas.length; i++) {
char[] row = canvas[i];
for (char ch : row) {
sb.append(ch);
}
if (i + 1 < canvas.length) {
sb.append(System.lineSeparator());
}
}
return sb.toString();
}
private final char CORNER = '+', V_WALL = '|', H_WALL = '-', FILLER = ' ';
private void printTreeToCanvas(char[][] canvas, int xOffset, int yOffset) {
if (leaf) {
// top left is 2x - xOffset, 2y - yOffset
int topY = 2*y - yOffset;
int bottomY = 2*y + 2*size - yOffset;
int leftX = 2*x - xOffset;
int rightX = 2*x + 2*size - xOffset;
// corners
canvas[topY][leftX] = CORNER;
canvas[topY][rightX] = CORNER;
canvas[bottomY][leftX] = CORNER;
canvas[bottomY][rightX] = CORNER;
// top
for (int i = leftX + 1; i < rightX; i++) {
if (canvas[topY][i] != CORNER) {
canvas[topY][i] = H_WALL;
}
}
// bottom
for (int i = leftX + 1; i < rightX; i++) {
if (canvas[bottomY][i] != CORNER) {
canvas[bottomY][i] = H_WALL;
}
}
// left
for (int i = topY + 1; i < bottomY; i++) {
if (canvas[i][leftX] != CORNER) {
canvas[i][leftX] = V_WALL;
}
}
// right
for (int i = topY + 1; i < bottomY; i++) {
if (canvas[i][rightX] != CORNER) {
canvas[i][rightX] = V_WALL;
}
}
// fill every odd coordinate in interior
for (int i = topY + 1; i < bottomY; i+= 2) {
for (int j = leftX + 1; j < rightX; j+= 2) {
canvas[i][j] = colour.getTexture();
}
}
} else {
for (QuadtreeBitmap quad : quadrants()) {
quad.printTreeToCanvas(canvas, xOffset, yOffset);
}
}
}
/**
* Returns a string representation of this bitmap. The string representation consists
* of a newline-separated sequence of rows, where each row consists of a sequence of
* characters which each encode the colour of a pixel.
*
* For a string representation which depicts the quadtree structure of this bitmap,
* see {@link #toTreeString}.
*
* @return a string representation of this bitmap
*/
@Override
public String toString() {
char[][] canvas = new char[size][size];
printToCanvas(canvas, x, y);
StringBuilder sb = new StringBuilder();
for (int i = 0; i < size; i++) {
char[] row = canvas[i];
for (char ch : row) {
sb.append(ch);
}
if (i + 1 < size) {
sb.append(System.lineSeparator());
}
}
return sb.toString();
}
private void printToCanvas(char[][] canvas, int xOffset, int yOffset) {
if (leaf) {
for (int i = y - yOffset; i < y + size - yOffset; i++) {
Arrays.fill(canvas[i], x - xOffset, x + size - xOffset, colour.getTexture());
}
} else {
for (QuadtreeBitmap quad : quadrants()) {
quad.printToCanvas(canvas, xOffset, yOffset);
}
}
}
}
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