基于静态huffman编码的压缩

名词解释:哈夫曼编码(HuffmanCoding)是一种编码方式，哈夫曼编码是可变字长编码(VLC)的一种。该方法依据字符出现概率来构造异字头的平均长度最短的码字，有时称之为最佳编码，一般就叫作Huffman编码。 实现过程: 1.计算每个字符在字符串中出现的频率作为构建h

名词解释:哈夫曼编码(Huffman Coding)是一种编码方式，哈夫曼编码是可变字长编码(VLC)的一种。该方法依据字符出现概率来构造异字头的平均长度最短的码字，有时称之为最佳编码，一般就叫作Huffman编码。

实现过程:

1.计算每个字符在字符串中出现的频率作为构建huffman树的权重

2.构建huffman树

3.建立每个字符对应的编码表

4.重建字符串编码,既压缩字符串

5.解压时根据先前的huffman树和字符位长度还原字符串

    <?php   
    /**
    基于静态huffman编码的压缩[PHP语言实现]
    author:        lajabs
    email:        aGl0dHlvQGdtYWlsLmNvbQ==

    本文以PHP作为描述语言较详细讲解huffman树原理及应用
    因保证程序可读性,故不做优化.

    */



    class huffman
    {
            /**
             * 压缩入口
             * $str:待压缩的字符串
             */
            public function encode($str)
            {
                    $len=strlen($str);
                    //计算每个字符权重值(出现的频度)<这边可以做成概率表>
                    for($i=0;$i<$len;$i++)        $array[ord($str{$i})]++;

                    $HuffmanArray=array();
                    asort($array);
                    /**
                     * 构造huffman树,时间复杂度O(nlogn)
                     * 选择两个使用频率较小<字符在字符串中出现的次数>的结点合并生成出一个树
                     */
                    while ($item1 = each($array))
                    {
                            $item2 = each($array);
                            //构建huffman树
                            $this->creat_tree($item1,$item2,$array,$HuffmanArray);
                            //反复排序<优化这步可在构造树时用插入排序算法完成>
                            asort($array);
                    }


                    $HuffmanArray=array_shift($HuffmanArray);
                    //构建编码表<这步可优化为构建树时一同生成>
                    $tab=null;
                    $code_tab=$this->creat_tab($HuffmanArray,$tab);
                    //压缩&转换整个字符串为二进制表达式
                    $binary=null;
                    for($i=0;$i<$len;$i++)        $binary.=$tab[ord($str{$i})];        
                    //转化为压缩后的字符串
                    $code=$this->encode_bin($binary);
                    //静态huffman编码算法压缩后需保留huffman树
                    return array('tree'=>$HuffmanArray,'len'=>strlen($binary),'code'=>$code);
            }

            /**
             * 解压缩入口
             * $huffman:解压所使用的huffman树
             * $str:被压缩的字符
             * $blen:压缩前的位长度
             */
            public function decode($huffman,$str,$blen)
            {
                    $len=strlen($str);
                    $binary=null;
                    //将编码解为二进制表达式
                    for($i=0;$i<$len;$i++)        
                    $binary.=str_pad(base_convert(ord($str{$i}),10,2),8,'0',STR_PAD_LEFT);
                    //去除补码
                    $binary=substr($binary,0,$blen);
                    //从hufman树中配比相应的编码
                    return $this->decode_tree($binary,$huffman,$huffman);
            }

            /**
             * 将压缩后的二进制表达式再转为字符串
             * $binary:二进制表达式字串
             */
            private function encode_bin($binary)
            {
                    $len=strlen($binary);
                    //二进制转字符需要整8位,不足8位补0
                    $blen=$len+8-$len%8;
                    $binary=str_pad($binary,$blen,'0');
                    $encode=null;
                    //每8位转为一个字符
                    for($i=7;$i<$blen;$i+=8)
                    {
                            $frag=substr($binary,$i-7,8);
                            $encode.=chr(base_convert($frag,2,10));
                    }
                    return $encode;
            }

            /**
             * 构造huffman树,使用贪婪算法选择最小的两个元素作为树的子节点
             * $item1:权重最小的元素1
             * $item2:权重次小的元素2
             * $array:所有字符出现次数表<权重表>
             * $HuffmanArray:保存生成的huffman树结构
             */
            private function creat_tree($item1,$item2,&$array,&$HuffmanArray)
            {
                    list($k,$v)=$item1;
                    list($k2,$v2)=$item2;
                    //假设当前树的左右节点为空节点
                    $c1=$k;
                    $c2=$k2;
                    //判断两个元素若为树则直接作为节点并入主树
                    if(isset($HuffmanArray[$k2]))
                    {
                            $c2=$HuffmanArray[$k2];        
                            unset($HuffmanArray[$k2]);
                    }
                    if(isset($HuffmanArray[$k]))
                    {
                            $c1=$HuffmanArray[$k];
                            unset($HuffmanArray[$k]);
                    }
                    //设置树结点权值
                    $array[$k2]=$v+$v2;                                                        
                    //合并节点后删除元素
                    unset($array[$k]);
                    //合并到huffman树中
                    $HuffmanArray[$k2]=array(0=>$c1,1=>$c2);        
            }


            /**
             * 广度优先遍历树,得到所有原字符对应的二进制表达式<01010...>
             * $tree:已经构建好的huffman树
             * $tab:编码表,保存所有字符对应的编码
             * $a0:左遍历树的路径<11010...>
             * $a1:右遍历树的路径
             */
            private function creat_tab($tree,&$tab,$a0=null,$a1=null)
            {
                    if($tree==null) return;
                    //遍历左右子树
                    foreach($tree as $node=>$ctree)
                    {
                            if(is_array($ctree))
                            {
                                    //判断未到达叶子节点时再向下遍历
                                    $this->creat_tab($ctree,$tab,$a0.$node,$a1.$node);
                            }
                            else
                            {
                                    //遍历到叶子节点<原字符ascii码>时的所有路径,既二进制表达式,下同
                                    $tab[$ctree]=${'a'.$node}.$node;
                            }
                    }
            }

            /**
             * 使用进制表达式深度优先遍历树,0为左子树,1为右子树,而到根节点,即为二进制表达式所指向的原字符
             * $binary:二进制表达式字串
             * $huffman:huffman树
             * $tree:当前所遍历的子树
             * $i:指向二进制表达式字串的<指针>
             * $code:解码后的字符串
             */
            private function decode_tree($binary,$huffman,$tree,$i=0,$code=null)
            {
                    $lr=$binary{$i};
                    //遍历完成
                    if($lr==null) return $code;
                    //判断是否到根节点,根节点既为二进制表达式对应的原字符ascii码
                    if(is_array($tree[$lr]))
                    {
                            //继续向下遍历子树
                            return $this->decode_tree($binary,$huffman,$tree[$lr],$i+1,$code);
                    }
                    else
                    {
                            //将二进制表达式解码为原字符
                            $code.=chr($tree[$lr]);
                            return $this->decode_tree($binary,$huffman,$huffman,$i+1,$code);
                    }
            }
    }
    ?>

    $str='
    In computer science and information theory, Huffman coding is an entropy encoding algorithm used for lossless data compression. The term refers to the use of a variable-length code table for encoding a source symbol (such as a character in a file) where the variable-length code table has been derived in a particular way based on the estimated probability of occurrence for each possible value of the source symbol. It was developed by David A. Huffman while he was a Ph.D. student at MIT, and published in the 1952 paper "A Method for the Construction of Minimum-Redundancy Codes".
    ';

    $huffman=new huffman();
    $obj=$huffman->encode($str);
    echo '压缩前的编码长度:',strlen($str),"\n";
    echo '压缩后的编码:',"\n";
    var_dump($obj['code']);
    echo '解压后的字符:',$huffman->decode($obj['tree'],$obj['code'],$obj['len']);

压缩前的编码长度:587压缩后的编码:string(330) "sp閉h颚?6鵞+王d挓吷s霒zk洚磗脎|t?*?;娳9蹴??>楏4O3 5 F凣rRuＪ解压后的字符:In computer science and information theory, Huffman coding is an entropy encoding algorithm used for lossless data compression. The term refers to the use of a variable-length code table for encoding a source symbol (such as a character in a file) where the variable-length code table has been derived in a particular way based on the estimated probability of occurrence for each possible value of the source symbol. It was developed by David A. Huffman while he was a Ph.D. student at MIT, and published in the 1952 paper "A Method for the Construction of Minimum-Redundancy Codes".