第四次作业
参考书《数据压缩导论（第4版）》 Page 121 7，8
7.使用LZ77算法对一个序列进行编码。给定C（a）=1，C（ ）=2，C（r）=3，C（t）=4.对以下三元组序列进行解码：
<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，先行缓冲区的大小为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。
解：
窗口大小为20，前向缓冲区大小为10，搜索窗口大小10。
C(a) = 1, C( ) = 2, C(r) = 3, C(t) = 4
解码过程为：
| 输入 | 输出 |
| <0, 0, 3> | r |
| <0, 0, 1> | ra |
| <0, 0, 4> | rat |
| <2, 8, 2> | ratatatatat |
| <3, 1, 2> | ratatatatat a |
| <0, 0, 3> | ratatatatat a r |
| <6, 4, 4> | ratatatatat a rat at |
| <9, 5, 4> | ratatatatat a rat at a rat |
编码过程为：
输入 输出：
||ratatatatat a rat at a rat <0, 0, 3>
|r|atatatatat a rat at a rat <0, 0, 1>
|ra|tatatatat a rat at a rat <0, 0, 4>
|rat|atatatat a rat at a rat <2, 8, 2>
ra|tatatatat |a rat at a rat <3, 1, 2>
rata|tatatat a |rat at a rat <0, 0, 3>
ratat|atatat a r|at at a rat <6, 4, 4>
ratatatata|t a rat at| a rat <9, 5, 4>
综上所述，编码输出的三元组与解码输入的三元组完全一样。
8.给定以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解码。
接收序列：4,5,3,1,2,8,2,7,9,7,4
初始词典：
| 索引 | 项 |
| 1 | S |
| 2 | P |
| 3 | I |
| 4 | T |
| 5 | H |
解：依题意，解码过程如下：
1）输入4,5,3,1,2,8,2,7,9,7,4
| 索引 | 条目 |
| 1 | S |
| 2 | _(空格) |
| 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 | _ (空格) |
| 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 | _(空格) |
| 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 | _ (空格) |
| 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 | _ (空格) |
| 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 | _ (空格) |
| 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 | _ (空格) |
| 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 | _ (空格) |
| 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 | _ (空格) |
| 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 | _ (空格) |
| 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 | _ (空格) |
| 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
综上所述：解码的序列为THIS IS HIS HIT。