c2java 第4篇 二叉堆和Huffman编码在视频编码中的运用

完全二叉树也可以用数组表示的。

/*Compressor.java -- 压缩一个数组内的数组，使用huffman方法*/class BinaryHeap<T extends Comparable<T>>{/*堆的二叉树数组表示：根节点i=0,节点i的左儿子是2*i+1,右儿子是2*i+2,父亲节点是(i-1)/2。节点的值都比儿子值小，称为最小堆。*/T[] arr;int cap;int last; /*[0,last)为当前的堆*/public BinaryHeap(T[] _arr){cap = _arr.length;arr = _arr;//(T[])new Object[cap];last = 0;}void dump(){int i;for(i = 0; i < last; ++i){System.out.print(" " + arr[i]);}System.out.println();}public void push(T val){/*从叶到某个内部目标节点，下移一位*/int j, i = last;//todo: check capacitywhile(i > 0){j = (i-1)/2;if(val.compareTo(arr[j]) >= 0) break;arr[i] = arr[j];i = j;}arr[i] = val;++last;}public T pop(){/*从根到某个节点，上移一位*/T tmp, ret;int j, i = 0;if(last < 1){return null;}ret = arr[0]; arr[0] = arr[last-1]; arr[last-1] = ret; /*R1 加上这句是为了原地逆序*/ j = 2*i+1;while(j < last-1){/*除开最后一个节点，如果有右儿子比左儿子小*/if( j+1 < last-1 && arr[j].compareTo(arr[j+1]) > 0)j = j+1;if(arr[i].compareTo(arr[j]) <= 0){break;}tmp = arr[i]; arr[i] = arr[j]; arr[j] = tmp; /*若优化此处,则必须保留R1*/i = j;j = 2*i+1;}--last;return ret;}}public class Compressor{static class Node implements Comparable<Node>{int val;int cnt;Node left, right;public Node(int _val, int _cnt, Node _l, Node _r){val = _val; cnt = _cnt; left = _l; right = _r;}public int compareTo(Node b){return (int)this.cnt - b.cnt;}public String toString(){return ""+this.val+":"+this.cnt;}} static void dumpCode(Node root, String code){if(null == root.left && null == root.right){System.out.println(root.val + ":" + code);return;}if(null != root.left){dumpCode(root.left, code+"0");}if(null != root.right){dumpCode(root.right, code+"1"); }}public static void huffmanEncoding(byte[] data){int[] cnt = new int[256];int i, diff = 0;Node x, y, z = null;Node[] arr = new Node[256];BinaryHeap<Node> bh = null;for(i = 0; i< data.length; ++i){cnt[data[i]]++;}for(i = 0; i < cnt.length; ++i){if(0 == cnt[i])continue;arr[diff] = new Node(i, cnt[i], null, null);++diff; }bh = new BinaryHeap<Node>(arr);for(i = 0; i < diff; ++i){bh.push(arr[i]);}bh.dump();for(i = 0; i < diff-1; ++i){x = bh.pop(); y = bh.pop();//System.out.println("x,y= "+x.val+":"+x.cnt + ", "+y.val +":" + y.cnt);z = new Node(255, x.cnt+y.cnt, x, y);bh.push(z);//bh.dump();}dumpCode(z,"");}public static void main(String[] arg){byte[] data = {48,49,50,50,50, 51,51, 52,52,52};huffmanEncoding(data);}public static void main_(String[] arg){Integer[] arr = {5,10,50,11,20,52,55,25,22};int x, i, len = arr.length;BinaryHeap<Integer> bh = new BinaryHeap<Integer>(arr);for(i = 0; i < len; ++i){bh.push(arr[i]);bh.dump();}while(len-- > 0){x = bh.pop();System.out.print(x+", "); //bh.dump();}System.out.println();for(i = 0; i < bh.cap; ++i){System.out.print(bh.arr[i]+", ");}}}/*$ javac -encoding UTF-8 Compressor.java && java Compressor 48:1 49:1 50:3 51:2 52:351:0048:01049:01150:1052:11*/

 

/*
上面的编码过程有个缺点，就是要读两遍原始数据。
第一遍是为了统计频率建表。对于实时流，在实际编码例子中mpeg12/h264，这个表是规范根据普遍情形统计规定死的。运用huffman编码其实是最后一步，在之前针对变换后的系数块，还做了其他压缩工作：mpeg[1]有(run,level)，run 是非零值level前零的个数；h264有CAVLC(TotalCoeff, TrailingOnes)[2]，在毕厚杰的书里面，把8x8 Bytes压缩到了25bits。
编解码时虽说我们只查表就行了，实际上不这么简单，因为不止一张表要查，并且bit位宽可达16。对于[2], 采用三层分级表，我也没完全理解。

[1]http://www.bretl.com/mpeghtml/huffRL.HTM
[2]ffmpeg/h264_cavlc.c: decode_residual()/get_vlc2()

*/