函數功能說明
// C program for Huffman Coding
#include <stdio.h>
#include <stdlib.h>
// This constant can be avoided by explicitly
// calculating height of Huffman Tree
//https://www.geeksforgeeks.org/huffman-coding-greedy-algo-3/
#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 Huffman tree) nodes
struct MinHeap {
// Current size of min heap
unsigned size;
// capacity of min heap
unsigned capacity;
// Array 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 function 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);
}
// Function to decode the Huffman encoded string
// ... (rest of the code)
// Function to decode the Huffman encoded string
void decodeHuffman(struct MinHeapNode* root, char* encodedString) {
struct MinHeapNode* current = root;
printf("Decoded Message: ");
for (int i = 0; encodedString[i] != '\\0'; i++) {
if (encodedString[i] == '0') {
current = current->left;
} else if (encodedString[i] == '1') {
current = current->right;
}
// Check if it's a leaf node
if (isLeaf(current)) {
printf("%c", current->data);
current = root; // Reset to the root for the next character
}
}
printf("\\n");
}
// ... (rest of the code)
// Driver code
int main()
{
char arr[] = { 'b', 'd', 'a', 'c', 'e' };
int freq[] = { 9, 12, 19, 21, 41 };
int size = sizeof(arr) / sizeof(arr[0]); struct MinHeapNode* root = buildHuffmanTree(arr, freq, size);
HuffmanCodes(arr, freq, size);
// Encoded string (dummy value for illustration)
char encodedString[] = "1110110111111101101111100";
decodeHuffman(root, encodedString);
return 0;
}
Binary Search Tree with default names give (Week 11 Question)