第四次作业
参考书《数据压缩导论（第4版）》 P121 7、8
7、使用LZ77算法对一个序列进行编码。给定C(a)=1,C(/b)=2,C(r)=3,C(t)=5。对一下三元组序列进行编码：
<0,0,3> <0,0,1> <0,0,4> <2,8,2> <3,1,2> <0,0,3> <6,4,4> <9,5,4>
假定窗口的大小为20，现行缓冲区的大小为10。对解码所得到的序列进行编码，确保得到相同的三元组序列。
答：（1）根据题意可知：C(a)=1,C(b)=2,C(r)=3,C(t)=4,所以解码的结果如下：
| 序列 | 输出 |
| <0,0,3> | r |
| <0,0,1> | ra |
| <0,0,4> | rat |
| <2,8,2> | ratatatatatb |
| <3,1,2> | ratatatatatbab |
| <0,0,3> | ratatatatatbabr |
| <6,4,4> | ratatatatatbabratbat |
| <9,5,4> | ratatatatatbabratbatbabrat |
（2）由于窗口的大小为20，先行缓冲区的大小为10，所以编码如下：输入ratatatatatbabratbatbabrat
| 输入 | 输出 |
| ||ratatatatatbabratbatbabrat | <0,0,3> |
| |r|atatatatatbabratbatbabrat | <0,0,1> |
| |ra|tatatatatbabratbatbabrat | <0,0,4> |
| |rat|atatatatbabratbatbabrat | <2,8,2> |
| ra|tatatatatb|abratbatbabrat | <3,1,2> |
| rata|tatatatbab|ratbatbabrat | <0,0,3> |
| ratat|atatatbabr|atbatbabrat | <6,4,4> |
| ratatatata|tbabratbat|babrat | <9,5,4> |
综上可知：编码输出的三元组与解码输入的三元组完全一样。
8、给定一下初始词典和接收序列，构建一个LZW词典，并对所发送的序列进行编码。
接收序列：4,5,3,1,2,8,2,7,9,7,4
答：(1）输入4,5,3,1,2,8,2,7,9,7,4
| 索引 | 条目 |
| 1 | S |
| 2 | - |
| 3 | I |
| 4 | T |
| 5 | H |
解码的序列为：T
(2）输入4,5,3,1,2,8,2,7,9,7,4
| 索引 | 条目 |
| 1 | S |
| 2 | - |
| 3 | I |
| 4 | T |
| 5 | H |
解码的序列为：TH
(3）输入4,5,3,1,2,8,2,7,9,7,4
| 索引 | 条目 |
| 1 | S |
| 2 | - |
| 3 | I |
| 4 | T |
| 5 | H |
| 6 | TH |
解码的序列为：THI
(4）输入4,5,3,1,2,8,2,7,9,7,4
| 索引 | 条目 |
| 1 | S |
| 2 | - |
| 3 | I |
| 4 | T |
| 5 | H |
| 6 | TH |
| 7 | HI |
解码的序列为：THIS
(5）输入4,5,3,1,2,8,2,7,9,7,4
| 索引 | 条目 |
| 1 | S |
| 2 | - |
| 3 | I |
| 4 | T |
| 5 | H |
| 6 | TH |
| 7 | HI |
| 8 | IS |
解码的序列为：THIS-
(6）输入4,5,3,1,2,8,2,7,9,7,4
| 索引 | 条目 |
| 1 | S |
| 2 | - |
| 3 | I |
| 4 | T |
| 5 | H |
| 6 | TH |
| 7 | HI |
| 8 | IS |
| 9 | S- |
解码的序列为：THIS IS
(7）输入4,5,3,1,2,8,2,7,9,7,4
| 索引 | 条目 |
| 1 | S |
| 2 | - |
| 3 | I |
| 4 | T |
| 5 | H |
| 6 | TH |
| 7 | HI |
| 8 | IS |
| 9 | S- |
| 10 | -I |
解码的序列为：THIS IS-
（8）输入4,5,3,1,2,8,2,7,9,7,4
| 索引 | 条目 |
| 1 | S |
| 2 | - |
| 3 | I |
| 4 | T |
| 5 | H |
| 6 | TH |
| 7 | HI |
| 8 | IS |
| 9 | S- |
| 10 | -I |
| 11 | IS- |
解码的序列为：THIS IS HI
(9）输入4,5,3,1,2,8,2,7,9,7,4
| 索引 | 条目 |
| 1 | S |
| 2 | - |
| 3 | I |
| 4 | T |
| 5 | H |
| 6 | TH |
| 7 | HI |
| 8 | IS |
| 9 | S- |
| 10 | -I |
| 11 | IS- |
| 12 | -H |
解码的序列为：THIS IS HIS-
（10）输入4,5,3,1,2,8,2,7,9,7,4
| 索引 | 条目 |
| 1 | S |
| 2 | - |
| 3 | I |
| 4 | T |
| 5 | H |
| 6 | TH |
| 7 | HI |
| 8 | IS |
| 9 | S- |
| 10 | -I |
| 11 | IS- |
| 12 | -H |
| 13 | HIS |
解码的序列为：THIS IS HIS HI
(11）输入4,5,3,1,2,8,2,7,9,7,4
| 索引 | 条目 |
| 1 | S |
| 2 | - |
| 3 | I |
| 4 | T |
| 5 | H |
| 6 | TH |
| 7 | HI |
| 8 | IS |
| 9 | S- |
| 10 | -I |
| 11 | IS- |
| 12 | -H |
| 13 | HIS |
| 14 | S-H |
解码的序列为：THIS IS HIS HIT
最后序列为：THIS IS HIS HIT
