简介
昨天刚拿到的需求，要求用二叉树设计一个huffman算法，主要用于压缩数据，就简单的用javascript实现了一个，在实现的过程中，画树进行的很顺利，但在测试编解码的时候出现了一些问题，也是自己对huffman算法的理解错误，好在及时改正。
算法实现
对huffman算法实现原理如果不了解的话最好自己去研究一下在看，否则可能有些地方看不懂，在这不做具体说明。
废话到此为止了，直接上代码，如果认为对自己有用的，请点个赞，谢谢
/**
* 定义一个节点
*
* @param weight 权值
* @param char 字符
* */
function node(weight, char) {
this.left = 0;//左孩子
this.right = 0;//右孩子
this.parent = 0;//父节点
this.weight = weight || 0;//字符的权值
this.char = char || '';
}
let nodes = [];
let selectStart = 0;
//
function prepareNodes() {
const arr = [1, 2, 3, 4, 5];
const arrChar = ['a', 'b', 'c', 'd', 'e'];
arr.forEach(function (value, index) {
nodes.push(new node(value, arrChar[index]));
})
return nodes;
}
function buildHTree(nodes) {
selectStart = 0;
// const nodes = prepareNodes();
let left,//左孩子索引
right;//右孩子
let n = nodes.length;//外部节点数量
let m = 2 * n - 1;//内部节点+外部节点总数量
let HT = [];//存储节点的对象
// console.log('n = ',n,'m = ',m,'nodes = ',nodes);
for (let i = 0; i < m; i++) {//给所有节点一个默认权值
HT.push(new node(0, ''));
}
//把叶子节点的值赋值给HT[0,n-1];
for (let i = 0; i < n; i++) {
HT[i].char = nodes[i].char;
HT[i].weight = nodes[i].weight;
}
// console.log('HT = ',HT);
//计算内部节点的值
for (let i = n; i < m; i++) {
left = selectMinWeightNode(HT, i, 0);//获取HT中权值最小的node下标
right = selectMinWeightNode(HT, i, 1);
// console.log('left = ',left,'right = ',right);
HT[i].left = left || 0;
HT[i].right = right || 0;
HT[i].weight = HT[left].weight + HT[right].weight; //计算当前节点权值
HT[left].parent = i;
HT[right].parent = i;
selectStart += 2;
}
return HT;
}
/**
* 返回权值排名为rank的节点在HT中的下标（权值从小到大排列）
*
* @param HT 所有节点对象
* @param rang 处理的节点范围
* @rank left/right*/
function selectMinWeightNode(HT, rang, rank) {
let copyNodes = [];
for (let i = 0; i < rang; i++) {
copyNodes.push(HT[i])
}
//sort 小->大
copyNodes.sort((a, b) => a.weight - b.weight);
//从未参与合成的节点中选出最小的值
const targetNode = copyNodes[rank + selectStart];
// console.log(targetNode);
for (let i = 0; i < HT.length; i++) {
if (targetNode === HT[i]) {
return i;
}
}
return null;
}
function huffmanCode(char, bit) {
this.char = char;
this.bit = bit;
}
/**
* huffman编码
*
* @param HT huffman树
* @param nodes 待编码数据*/
function encode(HT, nodes) {
let HC = [];
let HCStr = '';
let bit = '';
for (let i = 0; i < nodes.length; i++) {//遍历叶子节点
for (let j = 0; j < HT.length; j++) {
bit = '';
let char = nodes[i];
if (HT[j].char === char) {
let nodeIndex = j;
while (HT[nodeIndex].parent !== 0) {
let parentIndex = HT[nodeIndex].parent;
if (HT[parentIndex].left === nodeIndex) {
bit = '0' + bit;
} else {
bit = '1' + bit;
}
nodeIndex = parentIndex;
}
const code = new huffmanCode(HT[j].char, bit);
HC.push(code);
HCStr = HCStr+code.bit;
break;
}
}
}
console.log(HC);
return HCStr;
}
/**
* huffman解码
*
* @param HT huffman树
* @param ecode*/
function decode(HT, ecode) {
let str = '';
const bit = ecode;
let nodeIndex = HT.length - 1;
//遍历bit 从根节点开始遍历
for (const c of bit) {
if (c === '1') {//证明有右节点
nodeIndex = HT[nodeIndex].right;
} else {
nodeIndex = HT[nodeIndex].left;
}
if (HT[nodeIndex].left === 0 && HT[nodeIndex].right === 0) {
str += HT[nodeIndex].char;
nodeIndex = HT.length - 1;
}
}
return str;
}
function main() {
const nodes = prepareNodes();//数据准备
const HT = buildHTree(nodes);//建树
const a = encode(HT,'abcdeaabcdddddbe');//编码
// const a = decode(HT, '01001100101101001001100101010011');//解码
console.log(a);
}
main();
测试结果
01001100101101001001100101010101001111
[ huffmanCode { char: 'a', bit: '010' },
huffmanCode { char: 'b', bit: '011' },
huffmanCode { char: 'c', bit: '00' },
huffmanCode { char: 'd', bit: '10' },
huffmanCode { char: 'e', bit: '11' },
huffmanCode { char: 'a', bit: '010' },
huffmanCode { char: 'a', bit: '010' },
huffmanCode { char: 'b', bit: '011' },
huffmanCode { char: 'c', bit: '00' },
huffmanCode { char: 'd', bit: '10' },
huffmanCode { char: 'd', bit: '10' },
huffmanCode { char: 'd', bit: '10' },
huffmanCode { char: 'd', bit: '10' },
huffmanCode { char: 'd', bit: '10' },
huffmanCode { char: 'b', bit: '011' },
huffmanCode { char: 'e', bit: '11' } ]
➜ service-mqtt-backup git:(master) ✗ node huffman.js
010 011 00 10 11 010 010 011 00 10 10 10 10 10 011 11
➜ service-mqtt-backup git:(master) ✗