Huffman Decoding
We have discussed Huffman Encoding in a previous post. In this post, decoding is discussed.
Examples:
Input Data: AAAAAABCCCCCCDDEEEEE
Frequencies: A: 6, B: 1, C: 6, D: 2, E: 5Encoded Data: 0000000000001100101010101011111111010101010
Huffman Tree: ‘#’ is the special character usedfor 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 111Encoded Huffman data: 01110100011111000101101011101000111
Decoded Huffman Data: geeksforgeeks
Follow the below steps to solve the problem:
Note: To decode the encoded data we require the Huffman tree. We iterate through the binary encoded data. To find character corresponding to current bits, we use the following simple steps:
- We start from the root and do the following until a leaf is found.
- If the current bit is 0, we move to the left node of the tree.
- If the bit is 1, we move to right node of the tree.
- If during the traversal, we encounter a leaf node, we print the character of that particular leaf node and then again continue the iteration of the encoded data starting from step 1.
The below code takes a string as input, encodes it, and saves it in a variable encoded string. Then it decodes it and prints the original string.
Below is the implementation of the above approach:
CPP
// C++ program to encode and decode a string using// Huffman Coding.#include <bits/stdc++.h>#define MAX_TREE_HT 256using namespace std;// to map each character its huffman valuemap<char, string> codes;// To store the frequency of character of the input datamap<char, int> freq;// A Huffman tree nodestruct 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 queuestruct compare { bool operator()(MinHeapNode* l, MinHeapNode* r) { return (l->freq > r->freq); }};// utility function to print characters along with// there huffman valuevoid printCodes(struct MinHeapNode* root, string str){ if (!root) return; if (root->data != '$') cout << root->data << ": " << str << "\n"; printCodes(root->left, str + "0"); printCodes(root->right, str + "1");}// utility function to store characters along with// there huffman value in a hash table, here we// have C++ STL mapvoid storeCodes(struct MinHeapNode* root, string str){ if (root == NULL) return; if (root->data != '$') 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 valuepriority_queue<MinHeapNode*, vector<MinHeapNode*>, compare> minHeap;// function to build the Huffman tree and store it// in minHeapvoid 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('$', 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 stringvoid 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 stringstring 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 codeint 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; // Function call decodedString = decode_file(minHeap.top(), encodedString); cout << "\nDecoded Huffman Data:\n" << decodedString << endl; return 0;} |
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
Comparing Input file size and Output file size:
Comparing the input file size and the Huffman encoded output file. We can calculate the size of the output data in a simple way. Let’s say our input is a string “geeksforgeeks” and is stored in a file input.txt.
Input File Size:
Input: “geeksforgeeks”
Total number of character i.e. input length: 13
Size: 13 character occurrences * 8 bits = 104 bits or 13 bytes.
Output File Size:
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 bitsTotal Sum: 35 bits approx 5 bytes
Hence, we could see that after encoding the data we saved a large amount of data. The above method can also help us to determine the value of N i.e. the length of the encoded data.
This article is contributed by Harshit Sidhwa. If you like GeeksforGeeks and would like to contribute, you can also write an article using write.geeksforgeeks.org or mail your article to review-team@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.
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