Notes

// 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 {

// One of the input characters
char data;

// Frequency of the character
unsigned freq;

// Left and right child of this node
struct MinHeapNode *left, *right;
};

// A Min Heap: Collection of
// min heap (or Hufmman tree) nodes
struct MinHeap {

// Current size of min heap
unsigned size;

// capacity of min heap
unsigned capacity;

// Attay of minheap node pointers
struct MinHeapNode** array;
};

// 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));

// current size is 0
minHeap->size = 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("n");
}

// 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);
}

// Driver program to test above functions
int main()
{

char arr[] = { 'a', 'b', 'c', 'd', 'e', 'f' };
int freq[] = { 5, 9, 12, 13, 16, 45 };

int size = sizeof(arr) / sizeof(arr[0]);

HuffmanCodes(arr, freq, size);

return 0;
}