哈夫曼編碼，是一種可變字長(zhǎng)編碼(VLC)的高效算法。該算法是Huffman于1952年提出一種編碼方法，該方法完全依據(jù)字符出現(xiàn)概率來(lái)構(gòu)造異字頭的平均長(zhǎng)度最短的碼字，有時(shí)稱(chēng)之為最佳編碼。

相比定長(zhǎng)編碼來(lái)說(shuō)，這種編碼實(shí)現(xiàn)的壓縮率（衡量壓縮算法效率的重要指標(biāo)）非常高，也就是說(shuō)，哈夫曼編碼比定長(zhǎng)編碼占用更少的存儲(chǔ)空間。

假設(shè)我們要對(duì)某個(gè)字母表創(chuàng)建一套二進(jìn)制前綴碼，那么我們一般都會(huì)講字母表中的字符與二進(jìn)制的葉子聯(lián)系起來(lái)，樹(shù)中所有的左向邊都為0，右向邊都為1.可以通過(guò)記錄根到字符葉子的簡(jiǎn)單路徑上的標(biāo)記來(lái)獲得一個(gè)字符的代碼字。這樣任何一棵這樣的樹(shù)都可以生成一套前綴碼。但是我們都知道即使在英文單詞中，每個(gè)字母出現(xiàn)的概率都是不同的，如果僅僅是放到二叉樹(shù)中，對(duì)于一些高頻字符很可能需要更長(zhǎng)的代碼串來(lái)表示，這是非常不友好的。

一個(gè)方法就是通過(guò)根據(jù)字符出現(xiàn)的概率，盡可能將短位串分配給高頻字符，長(zhǎng)位串分配給低頻字符。這里就用到了貪婪思想。

思路：

1. 初始化n個(gè)單節(jié)點(diǎn)的數(shù)，表上字母表中的字符，并將其概率記錄，用來(lái)表示權(quán)重。

2. 找出兩顆權(quán)重最小的樹(shù)（對(duì)于權(quán)重都相同的樹(shù)，任選其一），將它們作為新樹(shù)中的左右子樹(shù)，并將權(quán)值之和記錄到新的樹(shù)根中。迭代這一步操作，直到剩下一棵單獨(dú)的樹(shù)。

以下面的例子來(lái)描述哈夫曼樹(shù)的構(gòu)造過(guò)程：

字符	A	B	C	D	_
出現(xiàn)概率	0.35	0.1	0.2	0.2	0.15

由上面的過(guò)程我們得到了下面的代碼字：

字符	A	B	C	D	_
出現(xiàn)概率	0.35	0.1	0.2	0.2	0.15
代碼字	11	100	00	01	101

Input:

5

A B C D _

35 10 20 20 15

Output:

A : 11

B : 100

C : 00

D : 01

_ : 101

完整代碼如下：

import java.util.Scanner; public class Main {//建立數(shù)的節(jié)點(diǎn)類(lèi)static class Node{int weight;//頻數(shù)int parent;int leftChild;int rightChild;public Node(int weight, int parent, int leftChild, int rightChild){this.weight = weight;this.parent = parent;this.leftChild = leftChild;this.rightChild = rightChild;}void setWeight(int weight){this.weight = weight;}void setParent(int parent){this.parent = parent;}void setLeftChild(int leftChild){this.leftChild = leftChild;}void setRightChild(int rightChild){this.rightChild = rightChild;}int getWeight(){return weight;}int getParent(){return parent;}int getLeftChild(){return leftChild;}int getRightChild(){return rightChild;}}//新建哈夫曼編碼static class NodeCode {String character;String code;NodeCode(String character, String code) {this.character = character;this.code = code;}NodeCode(String code) {this.code = code;}void setCharacter(String character) {this.character = character;}void setCode(String code) {this.code = code;}String getCharacter() {return character;}String getCode() {return code;}}//初始化一個(gè)哈弗曼樹(shù)public static void initHuffmanTree(Node[] huffmanTree, int m){for(int i = 0; i < m; i++){huffmanTree[i] = new Node(0, -1, -1, -1);}}//初始化編碼public static void initHuffmanCode(NodeCode[] huffmanCode, int n){for(int i = 0; i < n; i++){huffmanCode[i] = new NodeCode("","");}}//獲取huffmanCode的符號(hào)public static void getHuffmanCode(NodeCode[] huffmanCode, int n){Scanner input = new Scanner(System.in);for(int i = 0; i < n; i++){String temp = input.next();huffmanCode[i] = new NodeCode(temp,"");}}//獲取頻率public static void getHuffmanWeight(Node[] huffmanTree , int n){Scanner input = new Scanner(System.in);for(int i = 0; i < n;i ++){int temp = input.nextInt();huffmanTree[i] = new Node(temp, -1, -1, -1);}}//選取兩個(gè)較小的結(jié)點(diǎn)public static int[] selectMin(Node[] huffmanTree ,int n) {int min[] = new int[2];class TempNode {int newWeight;//存儲(chǔ)權(quán)int place;//存儲(chǔ)該結(jié)點(diǎn)所在的位置TempNode(int newWeight, int place){this.newWeight = newWeight;this.place = place;}void setNewWeight(int newWeight){this.newWeight = newWeight;}void setPlace(int place){this.place = place;}int getNewWeight(){return newWeight;}int getPlace(){return place;}}TempNode[] tempTree = new TempNode[n];//將huffmanTree中沒(méi)有雙親的結(jié)點(diǎn)存儲(chǔ)到tempTree中int i=0,j=0;for(i = 0; i < n; i++) {if(huffmanTree[i].getParent() == -1 && huffmanTree[i].getWeight()!=0) {tempTree[j] = new TempNode(huffmanTree[i].getWeight(),i);j++;}}int m1,m2;m1 = m2 = 0;for(i = 0; i < j; i++) {if(tempTree[i].getNewWeight() < tempTree[m1].getNewWeight())//此處不讓取到相等，是因?yàn)榻Y(jié)點(diǎn)中有相同權(quán)值的時(shí)候，m1取最前的m1 = i;}for(i = 0; i < j; i++) {if(m1 == m2)m2++;//當(dāng)m1在第一個(gè)位置的時(shí)候，m2向后移一位if(tempTree[i].getNewWeight() <= tempTree[m2].getNewWeight() && i != m1)//此處取到相等，是讓在結(jié)點(diǎn)中有相同的權(quán)值的時(shí)候，//m2取最后的那個(gè)。m2 = i;}min[0] = tempTree[m1].getPlace();min[1] = tempTree[m2].getPlace();return min;}//創(chuàng)建哈弗曼樹(shù)public static void createHaffmanTree(Node[] huffmanTree,int n){if(n <= 1)System.out.println("Parameter Error!");int m = 2 * n - 1;//initHuffmanTree(huffmanTree,m);for(int i = n; i < m; i++) {int[] min = selectMin(huffmanTree, i);int min1 = min[0];int min2 = min[1];huffmanTree[min1].setParent(i);huffmanTree[min2].setParent(i);huffmanTree[i].setLeftChild(min1);huffmanTree[i].setRightChild(min2);huffmanTree[i].setWeight(huffmanTree[min1].getWeight() + huffmanTree[min2].getWeight());}}//創(chuàng)建哈夫曼編碼public static void createHaffmanCode(Node[] huffmanTree,NodeCode[] huffmanCode,int n){Scanner input = new Scanner(System.in);char[] code = new char[10];int start;int c;int parent;int temp;code[n-1] = '0';for(int i = 0; i < n; i++){StringBuffer stringBuffer = new StringBuffer();start = n-1;c = i;while((parent=huffmanTree[c].getParent()) >= 0){start--;code[start] = ((huffmanTree[parent].getLeftChild() == c) ? '0' : '1');c = parent;}for(;start < n-1; start++){stringBuffer.append(code[start]);}huffmanCode[i].setCode(stringBuffer.toString());}}//輸出public static void ouputHaffmanCode(NodeCode[] huffmanCode,int n){for(int i = 0; i < n; i++){System.out.println(huffmanCode[i].getCharacter() + " : " + huffmanCode[i].getCode());}}//主函數(shù)public static void main(String[] args){Scanner input = new Scanner(System.in);int n;int m;n = input.nextInt();m = 2*n-1;Node[] huffmanTree = new Node[m];NodeCode[] huffmanCode = new NodeCode[n];//初始化initHuffmanTree(huffmanTree, m);initHuffmanCode(huffmanCode, n);//獲取符號(hào)getHuffmanCode(huffmanCode, n);//獲取概率getHuffmanWeight(huffmanTree, n);//創(chuàng)建哈夫曼樹(shù)createHaffmanTree(huffmanTree, n);//創(chuàng)建哈夫曼編碼createHaffmanCode(huffmanTree, huffmanCode, n);//輸出ouputHaffmanCode(huffmanCode, n);} }注意：輸出哈夫曼樹(shù)和輸出哈夫曼編碼時(shí)不同的操作。

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