I have most of the work to Implement the Huffman Coding done. However, I am stuc
ID: 3695687 • Letter: I
Question
I have most of the work to Implement the Huffman Coding done. However, I am stuck with how to create the Code Table, Encode the into binary. Here is what I have so far: import java.util.*; public class HuffmanEncoding { public static void main(String[] args) { Scanner kbd = new Scanner(System.in); System.out.println("Enter a text: "); String txt = kbd.nextLine(); int[] n = getCharFreq(txt); System.out.printf("%14s%15s%15s%15s ", "ASCII code", "Character", "Frequency", "Code"); //Tree tree = getHuffmanTree(n); for(int i = 0; i < 256; i++) { if(n[i] != 0) { System.out.printf("%14d%15c%15d ", i, (char)i, n[i]); //System.out.println((char)i + " " + n[i]); } } } // This is the frequency public static int[] getCharFreq(String txt) { int[] counts = new int[256]; for(int i = 0; i < txt.length(); i++) { counts[(int)txt.charAt(i)]++; } return counts; } } public class Node { private char element; public int weight; public Node left; public Node right; private String code = ""; public Node() { } public Node(int weight, char element) { this.weight = weight; this.element = element; } } public class Tree { private Node root; // The root of the tree //Create a tree with two subtrees public Tree(Tree t1, Tree t2) { root = new Node(); root.left = t1.root; root.right = t2.root; root.weight = t1.root.weight + t2.root.weight; } //Create a tree containing a leaf node public Tree(int weight, char element) { root = new Node(weight, element); } } I really appreciated any help. Thank you
Explanation / Answer
Huffman coding is a lossless data compression algorithm. The idea is to assign variable-legth codes to input characters, lengths of the assigned codes are based on the frequencies of corresponding characters. The most frequent character gets the smallest code and the least frequent character gets the largest code.
The variable-length codes assigned to input characters are Prefix Codes, means the codes (bit sequences) are assigned in such a way that the code assigned to one character is not prefix of code assigned to any other character. This is how Huffman Coding makes sure that there is no ambiguity when decoding the generated bit stream.
Let us understand prefix codes with a counter example. Let there be four characters a, b, c and d, and their corresponding variable length codes be 00, 01, 0 and 1. This coding leads to ambiguity because code assigned to c is prefix of codes assigned to a and b. If the compressed bit stream is 0001, the de-compressed output may be “cccd” or “ccb” or “acd” or “ab”.
Steps to build Huffman Tree
Input is array of unique characters along with their frequency of occurrences and output is Huffman Tree.
1. Create a leaf node for each unique character and build a min heap of all leaf nodes (Min Heap is used as a priority queue. The value of frequency field is used to compare two nodes in min heap. Initially, the least frequent character is at root)
2. Extract two nodes with the minimum frequency from the min heap.
3. Create a new internal node with frequency equal to the sum of the two nodes frequencies. Make the first extracted node as its left child and the other extracted node as its right child. Add this node to the min heap.
4. Repeat steps#2 and #3 until the heap contains only one node. The remaining node is the root node and the tree is complete.
// C program for Huffman Coding
#include <stdio.h>
#include <stdlib.h>
// This constant can be avoided by explicitly calculating height of Huffman Tree
#define MAX_TREE_HT 100
// A Huffman tree node
struct MinHeapNode
{
char data; // One of the input characters
unsigned freq; // Frequency of the character
struct MinHeapNode *left, *right; // Left and right child of this node
};
// A Min Heap: Collection of min heap (or Hufmman tree) nodes
struct MinHeap
{
unsigned size; // Current size of min heap
unsigned capacity; // capacity of min heap
struct MinHeapNode **array; // Attay of minheap node pointers
};
// A utility function allocate a new min heap node with given character
// and frequency of the character
struct MinHeapNode* newNode(char data, unsigned freq)
{
struct MinHeapNode* temp =
(struct MinHeapNode*) malloc(sizeof(struct MinHeapNode));
temp->left = temp->right = NULL;
temp->data = data;
temp->freq = freq;
return temp;
}
// A utility function to create a min heap of given capacity
struct MinHeap* createMinHeap(unsigned capacity)
{
struct MinHeap* minHeap =
(struct MinHeap*) malloc(sizeof(struct MinHeap));
minHeap->size = 0; // current size is 0
minHeap->capacity = capacity;
minHeap->array =
(struct MinHeapNode**)malloc(minHeap->capacity * sizeof(struct MinHeapNode*));
return minHeap;
}
// A utility function to swap two min heap nodes
void swapMinHeapNode(struct MinHeapNode** a, struct MinHeapNode** b)
{
struct MinHeapNode* t = *a;
*a = *b;
*b = t;
}
// The standard minHeapify function.
void minHeapify(struct MinHeap* minHeap, int idx)
{
int smallest = idx;
int left = 2 * idx + 1;
int right = 2 * idx + 2;
if (left < minHeap->size &&
minHeap->array[left]->freq < minHeap->array[smallest]->freq)
smallest = left;
if (right < minHeap->size &&
minHeap->array[right]->freq < minHeap->array[smallest]->freq)
smallest = right;
if (smallest != idx)
{
swapMinHeapNode(&minHeap->array[smallest], &minHeap->array[idx]);
minHeapify(minHeap, smallest);
}
}
// A utility function to check if size of heap is 1 or not
int isSizeOne(struct MinHeap* minHeap)
{
return (minHeap->size == 1);
}
// A standard function to extract minimum value node from heap
struct MinHeapNode* extractMin(struct MinHeap* minHeap)
{
struct MinHeapNode* temp = minHeap->array[0];
minHeap->array[0] = minHeap->array[minHeap->size - 1];
--minHeap->size;
minHeapify(minHeap, 0);
return temp;
}
// A utility function to insert a new node to Min Heap
void insertMinHeap(struct MinHeap* minHeap, struct MinHeapNode* minHeapNode)
{
++minHeap->size;
int i = minHeap->size - 1;
while (i && minHeapNode->freq < minHeap->array[(i - 1)/2]->freq)
{
minHeap->array[i] = minHeap->array[(i - 1)/2];
i = (i - 1)/2;
}
minHeap->array[i] = minHeapNode;
}
// A standard funvtion to build min heap
void buildMinHeap(struct MinHeap* minHeap)
{
int n = minHeap->size - 1;
int i;
for (i = (n - 1) / 2; i >= 0; --i)
minHeapify(minHeap, i);
}
// A utility function to print an array of size n
void printArr(int arr[], int n)
{
int i;
for (i = 0; i < n; ++i)
printf("%d", arr[i]);
printf(" ");
}
// Utility function to check if this node is leaf
int isLeaf(struct MinHeapNode* root)
{
return !(root->left) && !(root->right) ;
}
// Creates a min heap of capacity equal to size and inserts all character of
// data[] in min heap. Initially size of min heap is equal to capacity
struct MinHeap* createAndBuildMinHeap(char data[], int freq[], int size)
{
struct MinHeap* minHeap = createMinHeap(size);
for (int i = 0; i < size; ++i)
minHeap->array[i] = newNode(data[i], freq[i]);
minHeap->size = size;
buildMinHeap(minHeap);
return minHeap;
}
// The main function that builds Huffman tree
struct MinHeapNode* buildHuffmanTree(char data[], int freq[], int size)
{
struct MinHeapNode *left, *right, *top;
// Step 1: Create a min heap of capacity equal to size. Initially, there are
// modes equal to size.
struct MinHeap* minHeap = createAndBuildMinHeap(data, freq, size);
// Iterate while size of heap doesn't become 1
while (!isSizeOne(minHeap))
{
// Step 2: Extract the two minimum freq items from min heap
left = extractMin(minHeap);
right = extractMin(minHeap);
// Step 3: Create a new internal node with frequency equal to the
// sum of the two nodes frequencies. Make the two extracted node as
// left and right children of this new node. Add this node to the min heap
// '$' is a special value for internal nodes, not used
top = newNode('$', left->freq + right->freq);
top->left = left;
top->right = right;
insertMinHeap(minHeap, top);
}
// Step 4: The remaining node is the root node and the tree is complete.
return extractMin(minHeap);
}
// Prints huffman codes from the root of Huffman Tree. It uses arr[] to
// store codes
void printCodes(struct MinHeapNode* root, int arr[], int top)
{
// Assign 0 to left edge and recur
if (root->left)
{
arr[top] = 0;
printCodes(root->left, arr, top + 1);
}
// Assign 1 to right edge and recur
if (root->right)
{
arr[top] = 1;
printCodes(root->right, arr, top + 1);
}
// If this is a leaf node, then it contains one of the input
// characters, print the character and its code from arr[]
if (isLeaf(root))
{
printf("%c: ", root->data);
printArr(arr, top);
}
}
// The main function that builds a Huffman Tree and print codes by traversing
// the built Huffman Tree
void HuffmanCodes(char data[], int freq[], int size)
{
// Construct Huffman Tree
struct MinHeapNode* root = buildHuffmanTree(data, freq, size);
// Print Huffman codes using the Huffman tree built above
int arr[MAX_TREE_HT], top = 0;
printCodes(root, arr, top);
}
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