霍夫曼解码
我们在之前的文章中讨论过霍夫曼编码。本文讨论后解码。
示例:
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
为了解码编码数据，我们需要霍夫曼树。我们遍历二进制编码的数据。要查找对应于当前位的字符，我们使用以下简单步骤。
- 我们从根开始，一直到找到一片叶子。
- 如果当前位为 0，我们移动到树的左节点。
- 如果该位为 1，我们移动到树的右节点。
- 如果在遍历过程中，我们遇到一个叶节点，我们打印该特定叶节点的字符，然后从步骤 1 开始再次继续编码数据的迭代。
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变量 encodedString 中。然后它解码并打印原始字符串。
下面的代码执行给定输入数据的完全霍夫曼编码和解码。
// C++ program to encode and decode a string using
// Huffman Coding.
#include <bits/stdc++.h>
#define MAX_TREE_HT 256
using namespace std;
// to map each character its huffman value
map<char, string> codes;
// to store the frequency of character of the input data
map<char, int> 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 != '{content}apos;)
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 != '{content}apos;)
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<MinHeapNode*, vector<MinHeapNode*>, compare> minHeap;
// function to build the Huffman tree and store it
// in minHeap
void HuffmanCodes(int size)
{
struct MinHeapNode *left, *right, *top;
for (map<char, int>::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('{content}apos;, 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; i<str.size(); i++)
freq[str[i]]++;
}
// function iterates through the encoded string s
// if s[i]=='1' then move to node->right
// 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;i<s.size();i++)
{
if (s[i] == '0')
curr = curr->left;
else
curr = curr->right;
// reached leaf node
if (curr->left==NULL and curr->right==NULL)
{
ans += curr->data;
curr = root;
}
}
// cout<<ans<<endl;
return ans+'\0';
}
// Driver program to test above functions
int main()
{
string str = "geeksforgeeks";
string encodedString, decodedString;
calcFreq(str, str.length());
HuffmanCodes(str.length());
cout << "Character With there Frequencies:\n";
for (auto v=codes.begin(); v!=codes.end(); v++)
cout << v->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计算输出数据的大小。假设我们的输入是一个字符串“geeksforgeeks”，存储在一个文件 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，在对数据进行编码后，我们保存了大量数据。 上述方法也可以帮助我们确定 N 的值，即编码数据的长度。
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