Efficient Huffman Coding for Sorted Input

In the previous Huffman code problem, the frequency was not sorted. If the frequency list is given in sorted order, the task of assigning code is being more efficient.

In this problem, we will use two empty queues. Then create a leaf node for each unique character and insert it into the queue in increasing order of frequency.

In this approach, the complexity of the algorithm is O(n).

Input and Output

Input:
Different letters and their frequency in sorted order
Letters: {L, K, X, C, E, B, A, F}
Frequency: {1, 1, 2, 2, 2, 2, 3, 4}
Output:
Codes for the letters
L: 0000
K: 0001
X: 001
C: 010
E: 011
F: 10
B: 110
A: 111

Algorithm

huffmanCodes(dataList, freqList, n)

Input: The data list and the list of frequency, and the number of data in the list n.

Output − Characters assigned to codes.

Begin
   root := huffmanTree(dataList, freqList, n) //create root of Huffman tree create an array to store codes, and top pointer for that array.
   call getCodes(root, array, top) to find codes for each character.
End

getCodes(root :node, array, top)

Input: The root node, array to store codes, top of the array.

Output − Codes for each character

Begin
   if leftChild(root) ≠φ then
      array[top] := 0
      getCodes(leftChild(root), array, top)
   if rightChild(root) ≠φ then
      array[top] = 1
      getCode(rightChild(root), array, top)
   if leftChild(root) = φ AND rightChild(root) = φ then
      display the character ch of root
      for all entries of the array do
         display the code in array[i] for character ch
      done
End

huffmanTree(dataList, freqList, n)

Input − The data list and the list of frequency, and the number of data in the list n.

Output − Creates a Huffman tree

Begin
   for all different character ch do
      add node with ch and frequency of ch into queue q1
   done

   while q1 is not empty OR size of q2 ≠ 1 do
      find two minimum node using q1 and q2 and add them as left and
      right child of a new node.
      add new node in q2
   done

   delete node from q2 and return that node.
End

Example

#include<iostream>
#include<queue>
using namespace std;

struct node {
   char data;
   int freq;
   node *child0, *child1;
};

node *getNode(char d, int f) {
   node *newNode = new node;
   newNode->data = d;
   newNode->freq = f;
   newNode->child0 = NULL;
   newNode->child1 = NULL;
   return newNode;
}

node *findMinNode(queue<node*>&q1, queue<node*>&q2) {
   node *minNode;
   if(q1.empty()) { //if first queue is empty, delete and return node from second queue
      minNode = q2.front();
      q2.pop();
      return minNode;
   }

   if(q2.empty()) { //if second queue is empty, delete and return node from first queue
      minNode = q1.front();
      q1.pop();
      return minNode;
   }

   if((q1.front()->freq) < (q2.front()->freq)) { //find smaller from two queues
      minNode = q1.front();
      q1.pop();
      return minNode;
   }else {
      minNode = q2.front();
      q2.pop();
      return minNode;
   }
}

node *huffmanTree(char data[], int frequency[], int n) {
   node *c0, *c1, *par;
   node *newNode;
   queue<node*> qu1, qu2;

   for(int i = 0; i<n; i++) { //add all node to queue 1
      newNode = getNode(data[i], frequency[i]);
      qu1.push(newNode);
   }

   while(!(qu1.empty() && (qu2.size() == 1))) {
      c0 = findMinNode(qu1, qu2); //find two minimum as two child
      c1 = findMinNode(qu1, qu2);
      node *newNode = getNode('#', c0->freq+c1->freq);

      //intermediate node holds special character
      par = newNode;
      par->child0 = c0;
      par->child1 = c1;
      qu2.push(par); //add sub tree into queue 2
   }

   node *retNode = qu2.front();
   qu2.pop();
   return retNode;
}

void getCodes(node *rootNode, int array[], int n) {  //array to store the code
   if(rootNode->child0 != NULL) {
      array[n] = 0;
      getCodes(rootNode->child0, array, n+1);
   }

   if(rootNode->child1 != NULL) {
      array[n] = 1;
      getCodes(rootNode->child1, array, n+1);
   }

   if(rootNode->child0 == NULL && rootNode->child1 == NULL) {  // when root is leaf node
      cout << rootNode->data << ": ";

      for(int i = 0; i<n; i++)
         cout << array[i];
      cout << endl;
   }
}

void huffmanCodes(char data[], int frequency[], int n) {
   node *rootNode = huffmanTree(data, frequency, n);
   int array[50], top = 0;
   getCodes(rootNode, array, top);
}

int main() {
   char data[] = {'L', 'K', 'X', 'C', 'E', 'B', 'A', 'F'};
   int frequency[] = {1, 1, 2, 2, 2, 2, 3, 4};
   int n = sizeof(data)/sizeof(data[0]);
   huffmanCodes(data, frequency, n);
}

Output

L: 0000
K: 0001
X: 001
C: 010
E: 011
F: 10
B: 110
A: 111