我们在上一篇文章中讨论了霍夫曼编码。在这篇文章中，讨论了解码。
例子：
Input Data : AAAAAABCCCCCCDDEEEEE
Frequencies : A: 6, B: 1, C: 6, D: 2, E: 5
Encoded Data :
0000000000001100101010101011111111010101010
Huffman Tree: '#' is the special character used
for internal nodes as character field
is not needed for internal nodes.
#(20)
/ \
#(12) #(8)
/ \ / \
A(6) C(6) E(5) #(3)
/ \
B(1) D(2)
Code of 'A' is '00', code of 'C' is '01', ..
Decoded Data : AAAAAABCCCCCCDDEEEEE
Input Data : GeeksforGeeks
Character With there Frequencies
e 10, f 1100, g 011, k 00, o 010, r 1101, s 111
Encoded Huffman data :
01110100011111000101101011101000111
Decoded Huffman Data
geeksforgeeks
为了解码编码的数据，我们需要霍夫曼树。我们遍历二进制编码的数据。为了找到与当前位相对应的字符，我们使用以下简单步骤。
- 我们从根开始，然后进行跟踪直到找到叶子。
- 如果当前位为0，则移至树的左侧节点。
- 如果该位为1，则移至树的右节点。
- 如果在遍历期间遇到一个叶子节点，我们将打印该特定叶子节点的字符，然后再次从步骤1开始继续进行编码数据的迭代。
下面的代码将一个字符串作为输入，对其进行编码并保存在一个变量encodeString中。然后将其解码并打印原始字符串。
以下代码对给定的输入数据执行完整的霍夫曼编码和解码。
// C++ program to encode and decode a string using
// Huffman Coding.
#include
#define MAX_TREE_HT 256
using namespace std;
// to map each character its huffman value
map codes;
// to store the frequency of character of the input data
map freq;
// A Huffman tree node
struct MinHeapNode
{
char data; // One of the input characters
int freq; // Frequency of the character
MinHeapNode *left, *right; // Left and right child
MinHeapNode(char data, int freq)
{
left = right = NULL;
this->data = data;
this->freq = freq;
}
};
// utility function for the priority queue
struct compare
{
bool operator()(MinHeapNode* l, MinHeapNode* r)
{
return (l->freq > r->freq);
}
};
// utility function to print characters along with
// there huffman value
void printCodes(struct MinHeapNode* root, string str)
{
if (!root)
return;
if (root->data != '$')
cout << root->data << ": " << str << "\n";
printCodes(root->left, str + "0");
printCodes(root->right, str + "1");
}
// utility function to store characters along with
// there huffman value in a hash table, here we
// have C++ STL map
void storeCodes(struct MinHeapNode* root, string str)
{
if (root==NULL)
return;
if (root->data != '$')
codes[root->data]=str;
storeCodes(root->left, str + "0");
storeCodes(root->right, str + "1");
}
// STL priority queue to store heap tree, with respect
// to their heap root node value
priority_queue, compare> minHeap;
// function to build the Huffman tree and store it
// in minHeap
void HuffmanCodes(int size)
{
struct MinHeapNode *left, *right, *top;
for (map::iterator v=freq.begin(); v!=freq.end(); v++)
minHeap.push(new MinHeapNode(v->first, v->second));
while (minHeap.size() != 1)
{
left = minHeap.top();
minHeap.pop();
right = minHeap.top();
minHeap.pop();
top = new MinHeapNode('$', left->freq + right->freq);
top->left = left;
top->right = right;
minHeap.push(top);
}
storeCodes(minHeap.top(), "");
}
// utility function to store map each character with its
// frequency in input string
void calcFreq(string str, int n)
{
for (int i=0; iright
// if s[i]=='0' then move to node->left
// if leaf node append the node->data to our output string
string decode_file(struct MinHeapNode* root, string s)
{
string ans = "";
struct MinHeapNode* curr = root;
for (int i=0;ileft;
else
curr = curr->right;
// reached leaf node
if (curr->left==NULL and curr->right==NULL)
{
ans += curr->data;
curr = root;
}
}
// cout<first <<' ' << v->second << endl;
for (auto i: str)
encodedString+=codes[i];
cout << "\nEncoded Huffman data:\n" << encodedString << endl;
decodedString = decode_file(minHeap.top(), encodedString);
cout << "\nDecoded Huffman Data:\n" << decodedString << endl;
return 0;
}
输出：
Character With there Frequencies
e 10
f 1100
g 011
k 00
o 010
r 1101
s 111
Encoded Huffman data
01110100011111000101101011101000111
Decoded Huffman Data
geeksforgeeks
比较输入文件大小和输出文件大小：
比较输入文件的大小和霍夫曼编码的输出文件。我们可以用一种简单的方法来计算输出数据的大小。可以说我们的输入是字符串“ geeksforgeeks”，并存储在文件input.txt中。
输入文件大小：
Input: "geeksforgeeks"
Total number of character i.e. input length: 13
Size: 13 character occurrences * 8 bits = 104 bits or 13 bytes.
输出文件大小：
Input: "geeksforgeeks"
------------------------------------------------
Character | Frequency | Binary Huffman Value |
------------------------------------------------
e | 4 | 10 |
f | 1 | 1100 |
g | 2 | 011 |
k | 2 | 00 |
o | 1 | 010 |
r | 1 | 1101 |
s | 2 | 111 |
------------------------------------------------
So to calculate output size:
e: 4 occurrences * 2 bits = 8 bits
f: 1 occurrence * 4 bits = 4 bits
g: 2 occurrences * 3 bits = 6 bits
k: 2 occurrences * 2 bits = 4 bits
o: 1 occurrence * 3 bits = 3 bits
r: 1 occurrence * 4 bits = 4 bits
s: 2 occurrences * 3 bits = 6 bits
Total Sum: 35 bits approx 5 bytes
因此，我们可以看到，在对数据进行编码之后，我们已经保存了大量数据。
上述方法还可以帮助我们确定N的值，即编码数据的长度。