You will construct a Huffman tree based on the given frequencies of 26 English a
ID: 3711425 • Letter: Y
Question
You will construct a Huffman tree based on the given frequencies of 26 English
alphabets in upper case plus the space character. An internal tree node class in
HuffmanTree with necessary information is required.
• You will not randomly switch left and right children when merger two trees. Instead, you will
build a right-heavy tree according to the following strategies to select the right child.
(1) The tree that is taller will be the right child, i.e., the height is greater;
(2) If the two tree of the same height, then the tree with more nodes will be the right child;
(3) If (1) and (2) fail to discriminate, then the sum of the ASCII values of the alphabets in
the tree is greater will be the right child.
Use the same criteria if frequency is not sufficient to decide which two trees should be merged.
(1) HuffmanTree(char[] a, int[] f)
This is a constructor that builds a Huffman tree based on a and f, where a is an array of
characters to be encoded and f is an array of frequencies corresponding to the characters
in a. For example, if a[3] = ’D’ and f[3] = 43, that means the frequency of ’D’ is 43.
(2) public void printCodeWords()
This method prints out all codewords in the Huffman tree from left leaves to right leaves
in the tree. Use the following format:
Huffman Codes:
E[69]:000 (127)
H[72]:0010 (61)
S[82]:0011 (63)
.....
Z[90]:1111111111 (1)
The 0-1 string indicates that 000 is the Huffman code
for E, [69] indicates the ASCII value of character E, and
(127) is the frequency; same to characters H, S and Z.
(3) public String encode(String text)
This method will return a 0-1 String using the Huffman codes. For example, encode("EHS")
should return "00000100011".
(4) public String decode(String codeString)
The reverse of the function above. For example, decode("00000100011") returns "EHS".
--------------------------------------------------------------------------------------------------------------------------
Here is the driver and huffman tree node provided
/**
* You should not modify this program. You should develop your own
* HuffmanTree.java and put it in the package, myUtil.
*
* @author cli2
*
*/
import myUtil.HuffmanTree;
public class Asg7 {
// this example is extended from Corman's book
static public void CormanFrequency() {
int[] f = {82,15,29,43,127,22,20,61,70,5,8,40,24,67,75,19,4,60,63,91,28,10,23,2,21,1,123};
char[] a = {'A','B','C','D','E','F','G','H','I','J','K','L','M','N','O','P','Q','R','S','T','U','V','W','X','Y','Z',' '};
HuffmanTree ht = new HuffmanTree(a, f); // Construct a Huffman Tree based on a and f
ht.printCodeWords();
System.out.printf("%nCode: %s%n", ht.encodeToStr("HUFFMAN ENCODING IS VERY USEFUL"));
System.out.printf("%nText: %s%n", ht.decodeFromStr("00100111011110011110011111011001000010000100001111101011010100110001101100101001001101010111110000110110111010011111010101010110"));
System.out.printf("%nText: %s%n", ht.decodeFromStr("0111101101101111011101110101011011001101100101110001011011101010010011010111100011101000"));
System.out.printf("%nText: %s%n", ht.decodeFromStr("11100010100100110101001001101011100010000010101101100001111100101100001100111001110110100011111000010001110"));
}
public static void main(String[] args) {
CormanFrequency();
}
}
private class HTreeNode {
private int f;
private char a;
private HTreeNode left, right;
private HTreeNode(char a, int f) {
this.a = a;
Someone previously submitted the following code which does not work:
public class HuffmanTree {
private int size = 0;
private HuffNode root = new HuffNode();
private PriorityQueue<HuffNode> huffQueue = new PriorityQueue();
public ArrayList<String> pathTable = new ArrayList();
public ArrayList<Character> valueTable = new ArrayList();
public HuffmanTree(char[] code, int[] freq) {
// get the counts
this.size = freq.length;
// throw exception if arrays are different sizes
if (freq.length != code.length) {
throw new UnsupportedOperationException("Error: Character and code length mismatch.");
}
// build huffQueue from frequencies given
for (int i = 0; i < this.size; i++) {
huffQueue.offer(new HuffNode(code[i], freq[i], null, null, null));
}
// build huffman tree from queue
createTree();
// build code table from huffman tree
createTable(this.root, "");
}
/**
* creates code table for a huffman tree
*
* @param HuffNode
* -- root for tree, string -- for building paths
*/
private void createTable(HuffNode curr, String str) {
// if iterator is null, return
if (curr == null)
return;
// else if leaf, display path and value
if (curr.leftTree == null && curr.rightTree == null) {
char tempChar;
if (curr.value == 32)
tempChar = ' ';
if (curr.value == 10)
tempChar = 'n';
else
tempChar = (char) curr.value;
// add value and path to code tables
this.valueTable.add(tempChar);
this.pathTable.add(str);
}
// add 0 if before moving to left child
str += "0";
// recursively call in pre-order
createTable(curr.leftTree, str);
// adjust path and add 1 before moving to right child
str = str.substring(0, str.length() - 1);
str += "1";
createTable(curr.rightTree, str);
}
/**
* creates Huffman Tree from frequencies and values
*
* @param null
*/
private void createTree() {
// while elements remain in huffQueue, add to tree
while (huffQueue.size() > 1) {
// pop off two minimum elements in huffQueue
HuffNode tempL = huffQueue.poll();
HuffNode tempR = huffQueue.poll();
// create root for two minimum elements and build tree
HuffNode parent = new HuffNode(0, tempL.weight + tempR.weight, tempL, tempR, null);
tempL.parent = parent;
tempR.parent = parent;
// add new tree back in huffQueue
huffQueue.offer(parent);
this.size++;
}
// set HuffTree root to remaining element in huffQueue
this.root = huffQueue.peek();
}
public void printCodeWords() {
System.out.println("Display Tree:");
HuffNode curr = this.root;
this.getTree(curr);
System.out.println("");
}
/**
* returns decoded string for a given set of bits
*
* @param String
* -- bits to be decoded
* @return String -- decoded version of bits
*/
public String decodeFromStr(String bits) {
// create empty string to hold decoded message
String decodedStr = "";
// iterate through bits
for (int i = 0; i < bits.length(); i++) {
if (!getChar(bits.substring(0, i + 1)).equals("")) {
decodedStr += getChar(bits.substring(0, i + 1));
bits = bits.substring(i + 1);
i = 0;
}
}
return decodedStr;
}
/**
* returns encoded bits for a given string
*
* @param String
* -- to be encoded
* @return String -- encoded version of original string
*/
public String encodeToStr(String input) {
// create empty string to hold code
String str = "";
// iterate through given string
for (int x = 0; x < input.length(); x++) {
// iterate through code tables
for (int i = 0; i < valueTable.size(); i++) {
// if char in string matches code in table, add path to string
if (valueTable.get(i) == input.charAt(x))
str += pathTable.get(i);
}
}
return str;
}
/**
* returns character for a given set of bits
*
* @param String
* -- bits to be checked
* @return String -- character associated with bits if any
*/
private String getChar(String bits) {
// create string to hold potential character
String character = "";
// traverse code table to seek match
for (int i = 0; i < pathTable.size(); i++) {
// add to string if match is found
if (pathTable.get(i).equals(bits))
character = valueTable.get(i).toString();
}
return character;
}
/**
* display given huffman tree using pre-order traversal
*
* @param HuffNode
* -- root of tree to be displayed
*/
// global variable used for representing 'levels' of tree
String tacks = "";
public void getTree(HuffNode curr) {
// if iterator is null, return
if (curr == null)
return;
// else if leaf, display level, weight, and value
if (curr.leftTree == null && curr.rightTree == null) {
// case statements to handle displaying space and newline
switch (curr.value) {
case 32:
System.out.println(tacks + curr.weight + ": sp");
break;
case 10:
System.out.println(tacks + curr.weight + ": nl");
break;
default:
System.out.println(tacks + curr.weight + ": " + (char) curr.value);
break;
}
}
}
private class HuffNode implements Comparable<HuffNode> {
public int value;
public int weight;
public HuffNode leftTree;
public HuffNode rightTree;
public HuffNode parent;
// constructors
public HuffNode() {
parent = null;
}
public HuffNode(int v, int w, HuffNode lTree, HuffNode rTree, HuffNode par) {
value = v;
weight = w;
leftTree = lTree;
rightTree = rTree;
parent = par;
}
@Override
public int compareTo(HuffNode o) {
// TODO Auto-generated method stub
return 0;
}
}
this.f = f; left = right = null;
}
private HTreeNode(HTreeNode left, HTreeNode right) {
a = (char)0;
f = left.f+right.f;
this.left = left;
this.right = right;
}
}
Output should be in following format
Huffman Codes:
E[69]:000 (127)
H[72]:0010 (61)
S[82]:0011 (63)
Explanation / Answer
Java code :
package myUtil;
import java.util.ArrayList;
import java.util.PriorityQueue;
class HuffNode implements Comparable<HuffNode> {
// fields
public int value;
public int weight;
public HuffNode leftTree;
public HuffNode rightTree;
public HuffNode parent;
// constructors
public HuffNode() {
parent = null;
}
public HuffNode(int v, int w, HuffNode lTree, HuffNode rTree, HuffNode par) {
value = v;
weight = w;
leftTree = lTree;
rightTree = rTree;
parent = par;
}
// setters/getters
@Override
public int compareTo(HuffNode rhs) {
return weight - rhs.weight;
}
@Override
public String toString() {
String str = "";
str += this.value;
return str;
}
}
// object representing a huffman tree
public class HuffmanTree {
// fields
private int size = 0;
private HuffNode root = new HuffNode();
private PriorityQueue<HuffNode> huffQueue = new PriorityQueue();
public ArrayList<String> pathTable = new ArrayList();
public ArrayList<Character> valueTable = new ArrayList();
// constructor
public HuffmanTree(char[] code, int[] freq) {
// get the counts
this.size = freq.length;
// throw exception if arrays are different sizes
if (freq.length != code.length) {
throw new UnsupportedOperationException("Error: Character and code length mismatch.");
}
// build huffQueue from frequencies given
for (int i = 0; i < this.size; i++) {
huffQueue.offer(new HuffNode(code[i], freq[i], null, null, null));
}
// build huffman tree from queue
createTree();
// build code table from huffman tree
createTable(this.root, "");
}
// setters/getters
/**
* creates Huffman Tree from frequencies and values
*
* @param null
*/
private void createTree() {
// while elements remain in huffQueue, add to tree
while (huffQueue.size() > 1) {
// pop off two minimum elements in huffQueue
HuffNode tempL = huffQueue.poll();
HuffNode tempR = huffQueue.poll();
// create root for two minimum elements and build tree
HuffNode parent = new HuffNode(0, tempL.weight + tempR.weight, tempL, tempR, null);
tempL.parent = parent;
tempR.parent = parent;
// add new tree back in huffQueue
huffQueue.offer(parent);
this.size++;
}
// set HuffTree root to remaining element in huffQueue
this.root = huffQueue.peek();
}
/**
* creates code table for a huffman tree
*
* @param HuffNode
* -- root for tree, string -- for building paths
*/
private void createTable(HuffNode curr, String str) {
// if iterator is null, return
if (curr == null)
return;
// else if leaf, display path and value
if (curr.leftTree == null&& curr.rightTree == null) {
char tempChar;
if (curr.value == 32)
tempChar = ' ';
if (curr.value == 10)
tempChar = 'n';
else
tempChar = (char) curr.value;
// add value and path to code tables
this.valueTable.add(tempChar);
this.pathTable.add(str);
}
// add 0 if before moving to left child
str += "0";
// recursively call in pre-order
createTable(curr.leftTree, str);
// adjust path and add 1 before moving to right child
str = str.substring(0, str.length() - 1);
str += "1";
createTable(curr.rightTree, str);
}
/**
* display given huffman tree using pre-order traversal
*
* @param HuffNode
* -- root of tree to be displayed
*/
// global variable used for representing 'levels' of tree
String tacks = "";
public void getTree(HuffNode curr) {
// if iterator is null, return
if (curr == null)
return;
// else if leaf, display level, weight, and value
if (curr.leftTree == null&& curr.rightTree == null) {
// case statements to handle displaying space and newline
switch (curr.value) {
case 32:
System.out.println(tacks + curr.weight + ": sp");
break;
case 10:
System.out.println(tacks + curr.weight + ": nl");
break;
default:
System.out.println(tacks + curr.weight + ": " + (char) curr.value);
break;
}
}
// else display level and weight
else
System.out.println(tacks + curr.weight);
// increment level marker
tacks += "- ";
// recursively call in pre-order
getTree(curr.leftTree);
getTree(curr.rightTree);
// decrement level marker
tacks = tacks.substring(0, tacks.length() - 2);
}
/**
* returns size of a given huffman tree
*
* @param HuffTree
* - to obtain size of
* @return int -- size of tree
*/
public int getSize() {
return this.size;
}
/**
* returns encoded bits for a given string
*
* @param String
* -- to be encoded
* @return String -- encoded version of original string
*/
public String encodeToStr(String input) {
// create empty string to hold code
String str = "";
// iterate through given string
for (int x = 0; x < input.length(); x++) {
// iterate through code tables
for (int i = 0; i < valueTable.size(); i++) {
// if char in string matches code in table, add path to string
if (valueTable.get(i) == input.charAt(x))
str += pathTable.get(i);
}
}
return str;
}
/**
* returns decoded string for a given set of bits
*
* @param String
* -- bits to be decoded
* @return String -- decoded version of bits
*/
public String decodeFromStr(String bits) {
// create empty string to hold decoded message
String decodedStr = "";
// iterate through bits
for (int i = 0; i < bits.length(); i++) {
if (!getChar(bits.substring(0, i + 1)).equals("")) {
decodedStr += getChar(bits.substring(0, i + 1));
bits = bits.substring(i + 1);
i = 0;
}
}
return decodedStr;
}
/**
* returns character for a given set of bits
*
* @param String
* -- bits to be checked
* @return String -- character associated with bits if any
*/
private String getChar(String bits) {
// create string to hold potential character
String character = "";
// traverse code table to seek match
for (int i = 0; i < pathTable.size(); i++) {
// add to string if match is found
if (pathTable.get(i).equals(bits))
character = valueTable.get(i).toString();
}
return character;
}
public void printCodeWords() {
System.out.println("Display Tree:");
HuffNode curr = this.root;
this.getTree(curr);
System.out.println("");
}
}
=====O/P=====
Display Tree:
1133
- 491
- - 240
- - - 117
- - - - 57
- - - - - 28: U
- - - - - 29: C
- - - - 60: R
- - - 123: sp
- - 251
- - - 124
- - - - 61: H
- - - - 63: S
- - - 127: E
- 642
- - 289
- - - 137
- - - - 67: N
- - - - 70: I
- - - 152
- - - - 75: O
- - - - 77
- - - - - 37
- - - - - - 18
- - - - - - - 8: K
- - - - - - - 10: V
- - - - - - 19: P
- - - - - 40: L
- - 353
- - - 166
- - - - 82: A
- - - - 84
- - - - - 41
- - - - - - 20: G
- - - - - - 21: Y
- - - - - 43: D
- - - 187
- - - - 91: T
- - - - 96
- - - - - 45
- - - - - - 22: F
- - - - - - 23: W
- - - - - 51
- - - - - - 24: M
- - - - - - 27
- - - - - - - 12
- - - - - - - - 5: J
- - - - - - - - 7
- - - - - - - - - 3
- - - - - - - - - - 1: Z
- - - - - - - - - - 2: X
- - - - - - - - - 4: Q
- - - - - - - 15: B
Code: 010000000111100111100111110110010000010111000000011010110111001100011010000110010101001101100101100011101010010000001010111111000000010111
Text: DAFMANH CWES ND HIOLA PGMOO
Text: EDEEDLSEE VENPY OFEO
Text: T HIOI OT UODCFKE ATGETRR
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