| 774 |      1 | 1
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|  |      2 | 00:00:06,410 --> 00:00:09,390
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|  |      3 | The final video for this week.
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|  |      4 | 
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|  |      5 | 2
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|  |      6 | 00:00:09,390 --> 00:00:12,465
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|  |      7 | And let me say something
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|  |      8 | about the coursework.
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|  |      9 | 
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|  |     10 | 3
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|  |     11 | 00:00:12,465 --> 00:00:15,300
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|  |     12 | First. You can solve
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|  |     13 | 
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|  |     14 | 4
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|  |     15 | 00:00:15,300 --> 00:00:17,745
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|  |     16 | the coursework in any programming
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|  |     17 | language you're like,
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|  |     18 | 
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|  |     19 | 5
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|  |     20 | 00:00:17,745 --> 00:00:22,440
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|  |     21 | I already said that. You
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|  |     22 | have to submit a PDF file.
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|  |     23 | 
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|  |     24 | 6
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|  |     25 | 00:00:22,440 --> 00:00:23,850
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|  |     26 | There will be some questions,
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|  |     27 | 
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|  |     28 | 7
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|  |     29 | 00:00:23,850 --> 00:00:26,250
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|  |     30 | so you have to write down the
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|  |     31 | solution to this questions.
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|  |     32 | 
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|  |     33 | 8
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|  |     34 | 00:00:26,250 --> 00:00:30,315
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|  |     35 | Please use a PDF and you have
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|  |     36 | to submit your source code.
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|  |     37 | 
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|  |     38 | 9
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|  |     39 | 00:00:30,315 --> 00:00:35,580
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|  |     40 | And yes, if you do use a
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|  |     41 | language which isn't Scala,
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|  |     42 | 
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|  |     43 | 10
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|  |     44 | 00:00:35,580 --> 00:00:39,450
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|  |     45 | it might help to tell me
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|  |     46 | how I can run your code.
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|  |     47 | 
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|  |     48 | 11
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|  |     49 | 00:00:39,450 --> 00:00:42,550
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|  |     50 | If I can't run your code,
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|  |     51 | I will ask you anyway.
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|  |     52 | 
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|  |     53 | 12
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|  |     54 | 00:00:42,550 --> 00:00:50,044
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|  |     55 | Also, please submit both the
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|  |     56 | PDF and the code in a file,
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|  |     57 | 
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|  |     58 | 13
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|  |     59 | 00:00:50,044 --> 00:00:52,730
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|  |     60 | in a zip file, which generates
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|  |     61 | 
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|  |     62 | 14
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|  |     63 | 00:00:52,730 --> 00:00:55,835
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|  |     64 | a subdirectory with your
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|  |     65 | name and your family name.
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|  |     66 | 
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|  |     67 | 15
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|  |     68 | 00:00:55,835 --> 00:00:58,970
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|  |     69 | That we'll just save a
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|  |     70 | lot of time for me to try
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|  |     71 | 
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|  |     72 | 16
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|  |     73 | 00:00:58,970 --> 00:01:02,030
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|  |     74 | to figure out who
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|  |     75 | has submitted what.
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|  |     76 | 
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|  |     77 | 17
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|  |     78 | 00:01:02,030 --> 00:01:04,445
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|  |     79 | Please do that.
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|  |     80 | 
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|  |     81 | 18
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|  |     82 | 00:01:04,445 --> 00:01:07,789
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|  |     83 | So what is the task
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|  |     84 | into coursework?
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|  |     85 | 
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|  |     86 | 19
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|  |     87 | 00:01:07,789 --> 00:01:09,885
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|  |     88 | I essentially showed you how
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|  |     89 | 
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|  |     90 | 20
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|  |     91 | 00:01:09,885 --> 00:01:11,995
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|  |     92 | the Brzozowski matcher
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|  |     93 | 
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|  |     94 | 21
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|  |     95 | 00:01:11,995 --> 00:01:14,645
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|  |     96 | works for the basic
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|  |     97 | regular expressions.
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|  |     98 | 
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|  |     99 | 22
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|  |    100 | 00:01:14,645 --> 00:01:16,295
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|  |    101 | I also showed you actually how it
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|  |    102 | 
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|  |    103 | 23
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|  |    104 | 00:01:16,295 --> 00:01:18,110
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|  |    105 | works for the n-times.
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|  |    106 | 
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|  |    107 | 24
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|  |    108 | 00:01:18,110 --> 00:01:20,300
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|  |    109 | And the task in coursework
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|  |    110 | 
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|  |    111 | 25
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|  |    112 | 00:01:20,300 --> 00:01:22,970
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|  |    113 | is that you extend the
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|  |    114 | Brzozowski matcher to
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|  |    115 | 
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|  |    116 | 26
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|  |    117 | 00:01:22,970 --> 00:01:25,820
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|  |    118 | the other regular expressions
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|  |    119 | 
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|  |    120 | 27
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|  |    121 | 00:01:25,820 --> 00:01:27,800
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|  |    122 | from the extended
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|  |    123 | regular expressions.
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|  |    124 | 
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|  |    125 | 28
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|  |    126 | 00:01:27,800 --> 00:01:30,245
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|  |    127 | So you're supposed
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|  |    128 | to extended with
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|  |    129 | 
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|  |    130 | 29
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|  |    131 | 00:01:30,245 --> 00:01:34,490
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|  |    132 | r-plus, optional r, for n-times.
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|  |    133 | 
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|  |    134 | 30
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|  |    135 | 00:01:34,490 --> 00:01:38,420
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|  |    136 | You've already seen that.
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|  |    137 | For 0 or more times,
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|  |    138 | 
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|  |    139 | 31
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|  |    140 | 00:01:38,420 --> 00:01:41,120
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|  |    141 | but not more than m
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|  |    142 | times regular expression.
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|  |    143 | 
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|  |    144 | 32
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|  |    145 | 00:01:41,120 --> 00:01:45,890
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|  |    146 | For at least n-times regular
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|  |    147 | expression and for between
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|  |    148 | 
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|  |    149 | 33
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|  |    150 | 00:01:45,890 --> 00:01:47,480
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|  |    151 | n times and m times
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|  |    152 | 
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|  |    153 | 34
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|  |    154 | 00:01:47,480 --> 00:01:50,810
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|  |    155 | regular expression and also this
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|  |    156 | NOT regular expression.
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|  |    157 | 
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|  |    158 | 35
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|  |    159 | 00:01:50,810 --> 00:01:52,790
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|  |    160 | So your task is to
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|  |    161 | 
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|  |    162 | 36
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|  |    163 | 00:01:52,790 --> 00:01:55,310
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|  |    164 | essentially find the definition
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|  |    165 | 
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|  |    166 | 37
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|  |    167 | 00:01:55,310 --> 00:01:57,155
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|  |    168 | for nullable in these cases.
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|  |    169 | 
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|  |    170 | 38
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|  |    171 | 00:01:57,155 --> 00:02:00,215
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|  |    172 | Find a definition for derivative,
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|  |    173 | 
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|  |    174 | 39
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|  |    175 | 00:02:00,215 --> 00:02:02,480
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|  |    176 | implement them,
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|  |    177 | write them down in
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|  |    178 | 
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|  |    179 | 40
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|  |    180 | 00:02:02,480 --> 00:02:06,065
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|  |    181 | a PDF and then do some
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|  |    182 | experiments with them.
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|  |    183 | 
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|  |    184 | 41
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|  |    185 | 00:02:06,065 --> 00:02:08,875
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|  |    186 | Well, how can you do that?
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|  |    187 | 
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|  |    188 | 42
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|  |    189 | 00:02:08,875 --> 00:02:10,370
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|  |    190 | Well I've given you
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|  |    191 | 
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|  |    192 | 43
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|  |    193 | 00:02:10,370 --> 00:02:13,565
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|  |    194 | the meaning of these additional
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|  |    195 | regular expressions.
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|  |    196 | 
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|  |    197 | 44
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|  |    198 | 00:02:13,565 --> 00:02:16,730
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|  |    199 | So here's, for example, the
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|  |    200 | meaning of this r-plus.
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|  |    201 | 
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|  |    202 | 45
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|  |    203 | 00:02:16,730 --> 00:02:18,290
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|  |    204 | So that would be, I have
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|  |    205 | 
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|  |    206 | 46
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|  |    207 | 00:02:18,290 --> 00:02:22,115
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|  |    208 | at least one copy up to infinity.
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|  |    209 | 
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|  |    210 | 47
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|  |    211 | 00:02:22,115 --> 00:02:25,070
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|  |    212 | And the optional-r would be it's
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|  |    213 | 
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|  |    214 | 48
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|  |    215 | 00:02:25,070 --> 00:02:28,370
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|  |    216 | the language of r plus
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|  |    217 | the empty string.
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|  |    218 | 
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|  |    219 | 49
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|  |    220 | 00:02:28,370 --> 00:02:30,440
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|  |    221 | If I have it exactly n times,
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|  |    222 | 
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|  |    223 | 50
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|  |    224 | 00:02:30,440 --> 00:02:31,985
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|  |    225 | then it would be
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|  |    226 | just the language
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|  |    227 | 
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|  |    228 | 51
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|  |    229 | 00:02:31,985 --> 00:02:34,010
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|  |    230 | of r exactly n-times.
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|  |    231 | 
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|  |    232 | 52
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|  |    233 | 00:02:34,010 --> 00:02:38,105
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|  |    234 | And here you have union
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|  |    235 | from 0 to m and so on.
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|  |    236 | 
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|  |    237 | 53
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|  |    238 | 00:02:38,105 --> 00:02:42,560
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|  |    239 | This might be a slightly
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|  |    240 | interesting regular expression.
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|  |    241 | 
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|  |    242 | 54
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|  |    243 | 00:02:42,560 --> 00:02:46,580
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|  |    244 | So that's supposed to be the
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|  |    245 | character set that is very
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|  |    246 | 
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|  |    247 | 55
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|  |    248 | 00:02:46,580 --> 00:02:48,410
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|  |    249 | similar to character ranges like
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|  |    250 | 
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|  |    251 | 56
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|  |    252 | 00:02:48,410 --> 00:02:51,005
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|  |    253 | in the existing regular
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|  |    254 | expression matchers.
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|  |    255 | 
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|  |    256 | 57
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|  |    257 | 00:02:51,005 --> 00:02:52,820
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|  |    258 | So this just says
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|  |    259 | 
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|  |    260 | 58
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|  |    261 | 00:02:52,820 --> 00:02:55,565
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|  |    262 | ...this regular
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|  |    263 | expression can match
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|  |    264 | 
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|  |    265 | 59
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|  |    266 | 00:02:55,565 --> 00:03:00,860
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|  |    267 | either the character c1 or
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|  |    268 | the character c2 up to cn.
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|  |    269 | 
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|  |    270 | 60
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|  |    271 | 00:03:00,860 --> 00:03:03,620
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|  |    272 | Why do I include
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|  |    273 | that regular expression?
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|  |    274 | 
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|  |    275 | 61
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|  |    276 | 00:03:03,620 --> 00:03:09,050
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|  |    277 | I could also just say
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|  |    278 | c1 plus c2 plus c3...
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|  |    279 | 
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|  |    280 | 62
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|  |    281 | 00:03:09,050 --> 00:03:12,889
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|  |    282 | a big alternative.
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|  |    283 | Well that's possible.
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|  |    284 | 
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|  |    285 | 63
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|  |    286 | 00:03:12,889 --> 00:03:16,595
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|  |    287 | But remember the Achilles'
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|  |    288 | heel of this algorithm is,
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|  |    289 | 
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|  |    290 | 64
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|  |    291 | 00:03:16,595 --> 00:03:18,425
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|  |    292 | if the regular expression is large,
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|  |    293 | 
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|  |    294 | 65
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|  |    295 | 00:03:18,425 --> 00:03:20,825
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|  |    296 | then the computation
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|  |    297 | take always a long time.
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|  |    298 | 
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|  |    299 | 66
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|  |    300 | 00:03:20,825 --> 00:03:23,840
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|  |    301 | So I'm trying to compress
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|  |    302 | that as much as I can.
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|  |    303 | 
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|  |    304 | 67
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|  |    305 | 00:03:23,840 --> 00:03:25,370
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|  |    306 | So instead of giving a big
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|  |    307 | 
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|  |    308 | 68
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|  |    309 | 00:03:25,370 --> 00:03:29,134
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|  |    310 | alternative, I am trying to
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|  |    311 | give one regular expression,
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|  |    312 | 
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|  |    313 | 69
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|  |    314 | 00:03:29,134 --> 00:03:31,340
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|  |    315 | which can not just match
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|  |    316 | a single character,
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|  |    317 | 
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|  |    318 | 70
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|  |    319 | 00:03:31,340 --> 00:03:34,230
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|  |    320 | but a set of characters.
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|  |    321 | 
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|  |    322 | 71
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|  |    323 | 00:03:34,630 --> 00:03:36,980
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|  |    324 | How can you be sure that
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|  |    325 | 
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|  |    326 | 72
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|  |    327 | 00:03:36,980 --> 00:03:39,215
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|  |    328 | definition you come
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|  |    329 | up with are correct?
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|  |    330 | 
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|  |    331 | 73
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|  |    332 | 00:03:39,215 --> 00:03:41,450
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|  |    333 | Well, I showed you which are
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|  |    334 | 
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|  |    335 | 74
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|  |    336 | 00:03:41,450 --> 00:03:45,170
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|  |    337 | the properties these two
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|  |    338 | functions need to satisfy.
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|  |    339 | 
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|  |    340 | 75
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|  |    341 | 00:03:45,170 --> 00:03:47,060
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|  |    342 | I've given you here what
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|  |    343 | 
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|  |    344 | 76
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|  |    345 | 00:03:47,060 --> 00:03:49,325
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|  |    346 | the meaning of these
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|  |    347 | expressions are.
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|  |    348 | 
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|  |    349 | 77
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|  |    350 | 00:03:49,325 --> 00:03:52,700
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|  |    351 | So you will always know what's
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|  |    352 | on the right-hand side.
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|  |    353 | 
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|  |    354 | 78
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|  |    355 | 00:03:52,700 --> 00:03:54,515
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|  |    356 | This is completely determined.
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|  |    357 | 
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|  |    358 | 79
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|  |    359 | 00:03:54,515 --> 00:03:56,720
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|  |    360 | You essentially
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|  |    361 | have to fill something
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|  |    362 | 
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|  |    363 | 80
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|  |    364 | 00:03:56,720 --> 00:03:58,910
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|  |    365 | equivalent on the left-hand side.
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|  |    366 | 
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|  |    367 | 81
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|  |    368 | 00:03:58,910 --> 00:04:02,105
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|  |    369 | That's the main task
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|  |    370 | of the coursework.
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|  |    371 | 
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|  |    372 | 82
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|  |    373 | 00:04:02,105 --> 00:04:08,090
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|  |    374 | And you can start from the
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|  |    375 | files I provided on KEATS.
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|  |    376 | 
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|  |    377 | 83
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|  |    378 | 00:04:08,090 --> 00:04:12,125
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|  |    379 | So you would just have to
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|  |    380 | add these additional cases.
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|  |    381 | 
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|  |    382 | 84
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|  |    383 | 00:04:12,125 --> 00:04:15,020
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|  |    384 | When you add these
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|  |    385 | additional cases
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|  |    386 | 
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|  |    387 | 85
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|  |    388 | 00:04:15,020 --> 00:04:17,330
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|  |    389 | and you're using the Scala language,
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|  |    390 | 
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|  |    391 | 86
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|  |    392 | 00:04:17,330 --> 00:04:18,980
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|  |    393 | you can do me a favour.
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|  |    394 | 
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|  |    395 | 87
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|  |    396 | 00:04:18,980 --> 00:04:22,550
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|  |    397 | You can call these
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|  |    398 | constructors for
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|  |    399 | 
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|  |    400 | 88
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|  |    401 | 00:04:22,550 --> 00:04:25,400
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|  |    402 | these different regular
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|  |    403 | expressions as RANGE,
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|  |    404 | 
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|  |    405 | 89
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|  |    406 | 00:04:25,400 --> 00:04:28,985
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|  |    407 | PLUS, OPTIONAL and NTIMES,
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|  |    408 | UPTO, FROM and BETWEEN.
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|  |    409 | 
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|  |    410 | 90
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|  |    411 | 00:04:28,985 --> 00:04:31,370
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|  |    412 | Remember I have this
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|  |    413 | convention to always
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|  |    414 | 
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|  |    415 | 91
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|  |    416 | 00:04:31,370 --> 00:04:34,025
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|  |    417 | use capital letters
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|  |    418 | for regular expressions.
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|  |    419 | 
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|  |    420 | 92
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|  |    421 | 00:04:34,025 --> 00:04:36,680
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|  |    422 | It would be nice if you could use
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|  |    423 | 
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|  |    424 | 93
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|  |    425 | 00:04:36,680 --> 00:04:39,260
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|  |    426 | these names because
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|  |    427 | then it will be
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|  |    428 | 
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|  |    429 | 94
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|  |    430 | 00:04:39,260 --> 00:04:42,335
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|  |    431 | very easy for me
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|  |    432 | to test your code.
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|  |    433 | 
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|  |    434 | 95
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|  |    435 | 00:04:42,335 --> 00:04:44,690
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|  |    436 | If you're using a different
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|  |    437 | programming language
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|  |    438 | 
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|  |    439 | 96
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|  |    440 | 00:04:44,690 --> 00:04:46,370
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|  |    441 | like let's say Rust,
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|  |    442 | 
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|  |    443 | 97
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|  |    444 | 00:04:46,370 --> 00:04:48,860
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|  |    445 | I expect some people will use that, where I
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|  |    446 | 
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|  |    447 | 98
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|  |    448 | 00:04:48,860 --> 00:04:51,380
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|  |    449 | have no idea what are the
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|  |    450 | conventions in your language,
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|  |    451 | 
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|  |    452 | 99
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|  |    453 | 00:04:51,380 --> 00:04:53,420
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|  |    454 | how you have to call
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|  |    455 | these constructors,
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|  |    456 | 
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|  |    457 | 100
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|  |    458 | 00:04:53,420 --> 00:04:56,420
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|  |    459 | we will see whatever you
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|  |    460 | submit. I'll have a look.
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|  |    461 | 
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|  |    462 | 101
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|  |    463 | 00:04:56,420 --> 00:04:59,360
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|  |    464 | There's one more
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|  |    465 | constraint I have to
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|  |    466 | 
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|  |    467 | 102
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|  |    468 | 00:04:59,360 --> 00:05:02,194
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|  |    469 | impose to make this
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|  |    470 | coursework interesting.
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|  |    471 | 
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|  |    472 | 103
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|  |    473 | 00:05:02,194 --> 00:05:04,730
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|  |    474 | I do not want you 
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|  |    475 | that you just take
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|  |    476 | 
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|  |    477 | 104
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|  |    478 | 00:05:04,730 --> 00:05:07,370
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|  |    479 | these extended regular
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|  |    480 | expressions and that you
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|  |    481 | 
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|  |    482 | 105
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|  |    483 | 00:05:07,370 --> 00:05:10,550
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|  |    484 | expand them using
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|  |    485 | their definition.
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|  |    486 | 
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|  |    487 | 106
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|  |    488 | 00:05:10,550 --> 00:05:12,320
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|  |    489 | Because that would make the regular
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|  |    490 | 
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|  |    491 | 107
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|  |    492 | 00:05:12,320 --> 00:05:13,955
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|  |    493 | expression matcher very slow.
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|  |    494 | 
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|  |    495 | 108
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|  |    496 | 00:05:13,955 --> 00:05:16,160
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|  |    497 | So for example, if
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|  |    498 | you want to define
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|  |    499 | 
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|  |    500 | 109
 | 
|  |    501 | 00:05:16,160 --> 00:05:18,785
 | 
|  |    502 | what's the derivative for r-plus,
 | 
|  |    503 | 
 | 
|  |    504 | 110
 | 
|  |    505 | 00:05:18,785 --> 00:05:21,560
 | 
|  |    506 | then what does not
 | 
|  |    507 | count as a solution:
 | 
|  |    508 | 
 | 
|  |    509 | 111
 | 
|  |    510 | 00:05:21,560 --> 00:05:24,770
 | 
|  |    511 | if you just expand that
 | 
|  |    512 | to the definition that r
 | 
|  |    513 | 
 | 
|  |    514 | 112
 | 
|  |    515 | 00:05:24,770 --> 00:05:28,935
 | 
|  |    516 | plus is equivalent to
 | 
|  |    517 | r followed by r-star.
 | 
|  |    518 | 
 | 
|  |    519 | 113
 | 
|  |    520 | 00:05:28,935 --> 00:05:32,845
 | 
|  |    521 | So in code, what I
 | 
|  |    522 | would like to not see,
 | 
|  |    523 | 
 | 
|  |    524 | 114
 | 
|  |    525 | 00:05:32,845 --> 00:05:35,680
 | 
|  |    526 | I would not give any
 | 
|  |    527 | marks for that is,
 | 
|  |    528 | 
 | 
|  |    529 | 115
 | 
|  |    530 | 00:05:35,680 --> 00:05:37,780
 | 
|  |    531 | if you add the plus as follows,
 | 
|  |    532 | 
 | 
|  |    533 | 116
 | 
|  |    534 | 00:05:37,780 --> 00:05:39,910
 | 
|  |    535 | so that is still perfectly fine.
 | 
|  |    536 | 
 | 
|  |    537 | 117
 | 
|  |    538 | 00:05:39,910 --> 00:05:42,160
 | 
|  |    539 | There's nothing you
 | 
|  |    540 | can do differently.
 | 
|  |    541 | 
 | 
|  |    542 | 118
 | 
|  |    543 | 00:05:42,160 --> 00:05:44,065
 | 
|  |    544 | That would be the constructor.
 | 
|  |    545 | 
 | 
|  |    546 | 119
 | 
|  |    547 | 00:05:44,065 --> 00:05:46,480
 | 
|  |    548 | But when you define nullable,
 | 
|  |    549 | 
 | 
|  |    550 | 120
 | 
|  |    551 | 00:05:46,480 --> 00:05:49,180
 | 
|  |    552 | I do not want to see
 | 
|  |    553 | that you defined
 | 
|  |    554 | 
 | 
|  |    555 | 121
 | 
|  |    556 | 00:05:49,180 --> 00:05:51,790
 | 
|  |    557 | this plus r as nullable
 | 
|  |    558 | 
 | 
|  |    559 | 122
 | 
|  |    560 | 00:05:51,790 --> 00:05:54,385
 | 
|  |    561 | of the sequence of r and star-r,
 | 
|  |    562 | 
 | 
|  |    563 | 123
 | 
|  |    564 | 00:05:54,385 --> 00:05:58,075
 | 
|  |    565 | just unfolding
 | 
|  |    566 | the definition.
 | 
|  |    567 | 
 | 
|  |    568 | 124
 | 
|  |    569 | 00:05:58,075 --> 00:06:00,415
 | 
|  |    570 | As you can see, when you come
 | 
|  |    571 | 
 | 
|  |    572 | 125
 | 
|  |    573 | 00:06:00,415 --> 00:06:02,815
 | 
|  |    574 | up with a much better
 | 
|  |    575 | solution for that.
 | 
|  |    576 | 
 | 
|  |    577 | 126
 | 
|  |    578 | 00:06:02,815 --> 00:06:05,110
 | 
|  |    579 | This is a very inefficient way
 | 
|  |    580 | 
 | 
|  |    581 | 127
 | 
|  |    582 | 00:06:05,110 --> 00:06:07,090
 | 
|  |    583 | for how to calculate nullable.
 | 
|  |    584 | 
 | 
|  |    585 | 128
 | 
|  |    586 | 00:06:07,090 --> 00:06:10,825
 | 
|  |    587 | And so the same for derivative
 | 
|  |    588 | would not be allowed.
 | 
|  |    589 | 
 | 
|  |    590 | 129
 | 
|  |    591 | 00:06:10,825 --> 00:06:13,895
 | 
|  |    592 | If you, I have the plus r here,
 | 
|  |    593 | 
 | 
|  |    594 | 130
 | 
|  |    595 | 00:06:13,895 --> 00:06:16,685
 | 
|  |    596 | you can't just unfold
 | 
|  |    597 | the definition,
 | 
|  |    598 | 
 | 
|  |    599 | 131
 | 
|  |    600 | 00:06:16,685 --> 00:06:19,790
 | 
|  |    601 | with r-plus
 | 
|  |    602 | being defined as r
 | 
|  |    603 | 
 | 
|  |    604 | 132
 | 
|  |    605 | 00:06:19,790 --> 00:06:21,350
 | 
|  |    606 | followed by r star and
 | 
|  |    607 | 
 | 
|  |    608 | 133
 | 
|  |    609 | 00:06:21,350 --> 00:06:23,375
 | 
|  |    610 | then just build the
 | 
|  |    611 | derivative of that.
 | 
|  |    612 | 
 | 
|  |    613 | 134
 | 
|  |    614 | 00:06:23,375 --> 00:06:25,280
 | 
|  |    615 | You have to find something more
 | 
|  |    616 | 
 | 
|  |    617 | 135
 | 
|  |    618 | 00:06:25,280 --> 00:06:28,730
 | 
|  |    619 | primitive that involves
 | 
|  |    620 | only the derivative of r,
 | 
|  |    621 | 
 | 
|  |    622 | 136
 | 
|  |    623 | 00:06:28,730 --> 00:06:31,790
 | 
|  |    624 | essentially, nothing
 | 
|  |    625 | more involved. The same
 | 
|  |    626 | 
 | 
|  |    627 | 137
 | 
|  |    628 | 00:06:31,790 --> 00:06:33,815
 | 
|  |    629 | if you have n-times, for example,
 | 
|  |    630 | 
 | 
|  |    631 | 138
 | 
|  |    632 | 00:06:33,815 --> 00:06:39,935
 | 
|  |    633 | you can't just unfold this
 | 
|  |    634 | n-times in this sequence
 | 
|  |    635 | 
 | 
|  |    636 | 139
 | 
|  |    637 | 00:06:39,935 --> 00:06:43,310
 | 
|  |    638 | of .... n-copies
 | 
|  |    639 | 
 | 
|  |    640 | 140
 | 
|  |    641 | 00:06:43,310 --> 00:06:47,285
 | 
|  |    642 | of this r. You have to get
 | 
|  |    643 | something more primitive.
 | 
|  |    644 | 
 | 
|  |    645 | 141
 | 
|  |    646 | 00:06:47,285 --> 00:06:49,760
 | 
|  |    647 | Otherwise, as you've
 | 
|  |    648 | seen earlier,
 | 
|  |    649 | 
 | 
|  |    650 | 142
 | 
|  |    651 | 00:06:49,760 --> 00:06:53,135
 | 
|  |    652 | your regular expression matcher
 | 
|  |    653 | would be totally slow.
 | 
|  |    654 | 
 | 
|  |    655 | 143
 | 
|  |    656 | 00:06:53,135 --> 00:06:55,475
 | 
|  |    657 | When you submit your solution,
 | 
|  |    658 | 
 | 
|  |    659 | 144
 | 
|  |    660 | 00:06:55,475 --> 00:06:58,445
 | 
|  |    661 | please submit this
 | 
|  |    662 | solution in the PDF.
 | 
|  |    663 | 
 | 
|  |    664 | 145
 | 
|  |    665 | 00:06:58,445 --> 00:07:01,580
 | 
|  |    666 | So give the cases of your definition
 | 
|  |    667 | 
 | 
|  |    668 | 146
 | 
|  |    669 | 00:07:01,580 --> 00:07:06,004
 | 
|  |    670 | in a form like that for
 | 
|  |    671 | nullable and derivative.
 | 
|  |    672 | 
 | 
|  |    673 | 147
 | 
|  |    674 | 00:07:06,004 --> 00:07:08,405
 | 
|  |    675 | And also implement it in code.
 | 
|  |    676 | 
 | 
|  |    677 | 148
 | 
|  |    678 | 00:07:08,405 --> 00:07:10,910
 | 
|  |    679 | That is just helping me to
 | 
|  |    680 | 
 | 
|  |    681 | 149
 | 
|  |    682 | 00:07:10,910 --> 00:07:13,400
 | 
|  |    683 | find out whether you have
 | 
|  |    684 | the correct solution or not.
 | 
|  |    685 | 
 | 
|  |    686 | 150
 | 
|  |    687 | 00:07:13,400 --> 00:07:15,710
 | 
|  |    688 | So you needed a kind of
 | 
|  |    689 | mathematical notation of
 | 
|  |    690 | 
 | 
|  |    691 | 151
 | 
|  |    692 | 00:07:15,710 --> 00:07:18,695
 | 
|  |    693 | your solution, and
 | 
|  |    694 | an actual code.
 | 
|  |    695 | 
 | 
|  |    696 | 152
 | 
|  |    697 | 00:07:18,695 --> 00:07:22,414
 | 
|  |    698 | And then once you
 | 
|  |    699 | have your definition,
 | 
|  |    700 | 
 | 
|  |    701 | 153
 | 
|  |    702 | 00:07:22,414 --> 00:07:25,699
 | 
|  |    703 | also make sure you try
 | 
|  |    704 | it out on some examples.
 | 
|  |    705 | 
 | 
|  |    706 | 154
 | 
|  |    707 | 00:07:25,699 --> 00:07:28,970
 | 
|  |    708 | These will be the examples
 | 
|  |    709 | I will definitely try out,
 | 
|  |    710 | 
 | 
|  |    711 | 155
 | 
|  |    712 | 00:07:28,970 --> 00:07:30,560
 | 
|  |    713 | but probably also more
 | 
|  |    714 | 
 | 
|  |    715 | 156
 | 
|  |    716 | 00:07:30,560 --> 00:07:33,215
 | 
|  |    717 | depending on what
 | 
|  |    718 | definitions you give me.
 | 
|  |    719 | 
 | 
|  |    720 | 157
 | 
|  |    721 | 00:07:33,215 --> 00:07:38,300
 | 
|  |    722 | There's one more question I
 | 
|  |    723 | ask you to do. You've seen
 | 
|  |    724 | 
 | 
|  |    725 | 158
 | 
|  |    726 | 00:07:38,300 --> 00:07:40,130
 | 
|  |    727 | there's some regular
 | 
|  |    728 | expressions that
 | 
|  |    729 | 
 | 
|  |    730 | 159
 | 
|  |    731 | 00:07:40,130 --> 00:07:42,215
 | 
|  |    732 | are involved for characters,
 | 
|  |    733 | 
 | 
|  |    734 | 160
 | 
|  |    735 | 00:07:42,215 --> 00:07:46,925
 | 
|  |    736 | for character ranges or
 | 
|  |    737 | character sets essentially.
 | 
|  |    738 | 
 | 
|  |    739 | 161
 | 
|  |    740 | 00:07:46,925 --> 00:07:48,665
 | 
|  |    741 | And sometimes I also want to have
 | 
|  |    742 | 
 | 
|  |    743 | 162
 | 
|  |    744 | 00:07:48,665 --> 00:07:51,665
 | 
|  |    745 | just a reg expression which
 | 
|  |    746 | can match any character!!
 | 
|  |    747 | 
 | 
|  |    748 | 163
 | 
|  |    749 | 00:07:51,665 --> 00:07:56,195
 | 
|  |    750 | And I could have for all of
 | 
|  |    751 | them separate definitions.
 | 
|  |    752 | 
 | 
|  |    753 | 164
 | 
|  |    754 | 00:07:56,195 --> 00:07:57,710
 | 
|  |    755 | And that would mean I also need
 | 
|  |    756 | 
 | 
|  |    757 | 165
 | 
|  |    758 | 00:07:57,710 --> 00:07:59,645
 | 
|  |    759 | separate definitions for nullable,
 | 
|  |    760 | 
 | 
|  |    761 | 166
 | 
|  |    762 | 00:07:59,645 --> 00:08:02,405
 | 
|  |    763 | separate definitions
 | 
|  |    764 | for derivative.
 | 
|  |    765 | 
 | 
|  |    766 | 167
 | 
|  |    767 | 00:08:02,405 --> 00:08:05,825
 | 
|  |    768 | But actually they can be
 | 
|  |    769 | generalized to just one constructor.
 | 
|  |    770 | 
 | 
|  |    771 | 168
 | 
|  |    772 | 00:08:05,825 --> 00:08:08,210
 | 
|  |    773 | And that is if we introduce
 | 
|  |    774 | 
 | 
|  |    775 | 169
 | 
|  |    776 | 00:08:08,210 --> 00:08:11,630
 | 
|  |    777 | a constructor for regular expressions,
 | 
|  |    778 | 
 | 
|  |    779 | 170
 | 
|  |    780 | 00:08:11,630 --> 00:08:13,760
 | 
|  |    781 | which not just takes
 | 
|  |    782 | a single character
 | 
|  |    783 | 
 | 
|  |    784 | 171
 | 
|  |    785 | 00:08:13,760 --> 00:08:15,469
 | 
|  |    786 | or set of characters.
 | 
|  |    787 | 
 | 
|  |    788 | 172
 | 
|  |    789 | 00:08:15,469 --> 00:08:18,245
 | 
|  |    790 | But, which I call here CFUN.
 | 
|  |    791 | 
 | 
|  |    792 | 173
 | 
|  |    793 | 00:08:18,245 --> 00:08:23,165
 | 
|  |    794 | And it takes a function from
 | 
|  |    795 | characters to booleans.
 | 
|  |    796 | 
 | 
|  |    797 | 174
 | 
|  |    798 | 00:08:23,165 --> 00:08:24,470
 | 
|  |    799 | So if I want to match
 | 
|  |    800 | 
 | 
|  |    801 | 175
 | 
|  |    802 | 00:08:24,470 --> 00:08:26,900
 | 
|  |    803 | just a single character
 | 
|  |    804 | then this function f
 | 
|  |    805 | 
 | 
|  |    806 | 176
 | 
|  |    807 | 00:08:26,900 --> 00:08:29,060
 | 
|  |    808 | would only say true
 | 
|  |    809 | 
 | 
|  |    810 | 177
 | 
|  |    811 | 00:08:29,060 --> 00:08:32,225
 | 
|  |    812 | if it gets as argument
 | 
|  |    813 | the single character.
 | 
|  |    814 | 
 | 
|  |    815 | 178
 | 
|  |    816 | 00:08:32,225 --> 00:08:34,850
 | 
|  |    817 | If I have a character set,
 | 
|  |    818 | 
 | 
|  |    819 | 179
 | 
|  |    820 | 00:08:34,850 --> 00:08:36,515
 | 
|  |    821 | then I would say, well,
 | 
|  |    822 | 
 | 
|  |    823 | 180
 | 
|  |    824 | 00:08:36,515 --> 00:08:38,300
 | 
|  |    825 | I need a function
 | 
|  |    826 | which says true
 | 
|  |    827 | 
 | 
|  |    828 | 181
 | 
|  |    829 | 00:08:38,300 --> 00:08:40,970
 | 
|  |    830 | for all the characters
 | 
|  |    831 | in this set.
 | 
|  |    832 | 
 | 
|  |    833 | 182
 | 
|  |    834 | 00:08:40,970 --> 00:08:43,460
 | 
|  |    835 | And otherwise it's false.
 | 
|  |    836 | 
 | 
|  |    837 | 183
 | 
|  |    838 | 00:08:43,460 --> 00:08:46,205
 | 
|  |    839 | And if I want to
 | 
|  |    840 | match any character!!,
 | 
|  |    841 | 
 | 
|  |    842 | 184
 | 
|  |    843 | 00:08:46,205 --> 00:08:48,500
 | 
|  |    844 | then they should get a function
 | 
|  |    845 | 
 | 
|  |    846 | 185
 | 
|  |    847 | 00:08:48,500 --> 00:08:53,450
 | 
|  |    848 | which says true for
 | 
|  |    849 | all characters.
 | 
|  |    850 | 
 | 
|  |    851 | 186
 | 
|  |    852 | 00:08:53,450 --> 00:08:56,630
 | 
|  |    853 | Okay? If I have
 | 
|  |    854 | such a constructor
 | 
|  |    855 | 
 | 
|  |    856 | 187
 | 
|  |    857 | 00:08:56,630 --> 00:09:00,140
 | 
|  |    858 | that actually I can save
 | 
|  |    859 | myself a bit of work.
 | 
|  |    860 | 
 | 
|  |    861 | 188
 | 
|  |    862 | 00:09:00,140 --> 00:09:03,200
 | 
|  |    863 | And I can just have one case
 | 
|  |    864 | 
 | 
|  |    865 | 189
 | 
|  |    866 | 00:09:03,200 --> 00:09:06,920
 | 
|  |    867 | for nullable and one
 | 
|  |    868 | case for CFUNS.
 | 
|  |    869 | 
 | 
|  |    870 | 190
 | 
|  |    871 | 00:09:06,920 --> 00:09:09,800
 | 
|  |    872 | So that would then subsume
 | 
|  |    873 | the character ranges and
 | 
|  |    874 | 
 | 
|  |    875 | 191
 | 
|  |    876 | 00:09:09,800 --> 00:09:13,385
 | 
|  |    877 | the character and also
 | 
|  |    878 | this ALL regular expression.
 | 
|  |    879 | 
 | 
|  |    880 | 192
 | 
|  |    881 | 00:09:13,385 --> 00:09:15,380
 | 
|  |    882 | Ok, this was not explicitly
 | 
|  |    883 | included at the beginning,
 | 
|  |    884 | 
 | 
|  |    885 | 193
 | 
|  |    886 | 00:09:15,380 --> 00:09:17,510
 | 
|  |    887 | but that's what I can now define.
 | 
|  |    888 | 
 | 
|  |    889 | 194
 | 
|  |    890 | 00:09:17,510 --> 00:09:21,740
 | 
|  |    891 | And then I can define
 | 
|  |    892 | this for characters,
 | 
|  |    893 | 
 | 
|  |    894 | 195
 | 
|  |    895 | 00:09:21,740 --> 00:09:23,885
 | 
|  |    896 | just as special cases
 | 
|  |    897 | for these functions.
 | 
|  |    898 | 
 | 
|  |    899 | 196
 | 
|  |    900 | 00:09:23,885 --> 00:09:25,610
 | 
|  |    901 | And I told you already
 | 
|  |    902 | what this function
 | 
|  |    903 | 
 | 
|  |    904 | 197
 | 
|  |    905 | 00:09:25,610 --> 00:09:28,025
 | 
|  |    906 | should look like in
 | 
|  |    907 | these three cases.
 | 
|  |    908 | 
 | 
|  |    909 | 198
 | 
|  |    910 | 00:09:28,025 --> 00:09:30,350
 | 
|  |    911 | So I let ...
 | 
|  |    912 | 
 | 
|  |    913 | 199
 | 
|  |    914 | 00:09:30,350 --> 00:09:33,515
 | 
|  |    915 | you decide how you're
 | 
|  |    916 | going to implement that.
 | 
|  |    917 | 
 | 
|  |    918 | 200
 | 
|  |    919 | 00:09:33,515 --> 00:09:35,450
 | 
|  |    920 | If you first define
 | 
|  |    921 | 
 | 
|  |    922 | 201
 | 
|  |    923 | 00:09:35,450 --> 00:09:38,495
 | 
|  |    924 | your implementation is
 | 
|  |    925 | all these explicit cases.
 | 
|  |    926 | 
 | 
|  |    927 | 202
 | 
|  |    928 | 00:09:38,495 --> 00:09:41,900
 | 
|  |    929 | Because in these cases it's
 | 
|  |    930 | actually more intuitive,
 | 
|  |    931 | 
 | 
|  |    932 | 203
 | 
|  |    933 | 00:09:41,900 --> 00:09:45,980
 | 
|  |    934 | what nullable and
 | 
|  |    935 | derivative should be.
 | 
|  |    936 | 
 | 
|  |    937 | 204
 | 
|  |    938 | 00:09:45,980 --> 00:09:48,035
 | 
|  |    939 | And then in a second step,
 | 
|  |    940 | 
 | 
|  |    941 | 205
 | 
|  |    942 | 00:09:48,035 --> 00:09:51,140
 | 
|  |    943 | you implement these
 | 
|  |    944 | more general cases.
 | 
|  |    945 | 
 | 
|  |    946 | 206
 | 
|  |    947 | 00:09:51,140 --> 00:09:53,360
 | 
|  |    948 | And just keep the original ones
 | 
|  |    949 | 
 | 
|  |    950 | 207
 | 
|  |    951 | 00:09:53,360 --> 00:09:54,500
 | 
|  |    952 | in your implementation if you
 | 
|  |    953 | 
 | 
|  |    954 | 208
 | 
|  |    955 | 00:09:54,500 --> 00:09:57,710
 | 
|  |    956 | want, or if you feel
 | 
|  |    957 | adventurous enough,
 | 
|  |    958 | 
 | 
|  |    959 | 209
 | 
|  |    960 | 00:09:57,710 --> 00:09:59,225
 | 
|  |    961 | and want to be lazy,
 | 
|  |    962 | 
 | 
|  |    963 | 210
 | 
|  |    964 | 00:09:59,225 --> 00:10:01,115
 | 
|  |    965 | that you just implement that.
 | 
|  |    966 | 
 | 
|  |    967 | 211
 | 
|  |    968 | 00:10:01,115 --> 00:10:02,660
 | 
|  |    969 | And then you have already done
 | 
|  |    970 | 
 | 
|  |    971 | 212
 | 
|  |    972 | 00:10:02,660 --> 00:10:06,530
 | 
|  |    973 | at least two constructors
 | 
|  |    974 | by just implementing one.
 | 
|  |    975 | 
 | 
|  |    976 | 213
 | 
|  |    977 | 00:10:06,530 --> 00:10:08,915
 | 
|  |    978 | But as said that 
 | 
|  |    979 | requires a bit skill
 | 
|  |    980 | 
 | 
|  |    981 | 214
 | 
|  |    982 | 00:10:08,915 --> 00:10:11,450
 | 
|  |    983 | of generalizing how
 | 
|  |    984 | that should be.
 | 
|  |    985 | 
 | 
|  |    986 | 215
 | 
|  |    987 | 00:10:11,450 --> 00:10:14,180
 | 
|  |    988 | And the other questions
 | 
|  |    989 | are just then
 | 
|  |    990 | 
 | 
|  |    991 | 216
 | 
|  |    992 | 00:10:14,180 --> 00:10:16,745
 | 
|  |    993 | trying out your
 | 
|  |    994 | expression matcher on
 | 
|  |    995 | 
 | 
|  |    996 | 217
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|  |    997 | 00:10:16,745 --> 00:10:19,580
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|  |    998 | some examples, more
 | 
|  |    999 | power examples,
 | 
|  |   1000 | 
 | 
|  |   1001 | 218
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|  |   1002 | 00:10:19,580 --> 00:10:22,400
 | 
|  |   1003 | and they should be
 | 
|  |   1004 | very easy to solve.
 | 
|  |   1005 | 
 | 
|  |   1006 | 219
 | 
|  |   1007 | 00:10:22,400 --> 00:10:24,605
 | 
|  |   1008 | So I hope it's not
 | 
|  |   1009 | too much asked for
 | 
|  |   1010 | 
 | 
|  |   1011 | 220
 | 
|  |   1012 | 00:10:24,605 --> 00:10:26,615
 | 
|  |   1013 | and I hope you have fun.
 | 
|  |   1014 | 
 | 
|  |   1015 | 221
 | 
|  |   1016 | 00:10:26,615 --> 00:10:29,675
 | 
|  |   1017 | It is not too much ask
 | 
|  |   1018 | because you can,
 | 
|  |   1019 | 
 | 
|  |   1020 | 222
 | 
|  |   1021 | 00:10:29,675 --> 00:10:32,420
 | 
|  |   1022 | I hope it's not too much
 | 
|  |   1023 | because you can start from
 | 
|  |   1024 | 
 | 
|  |   1025 | 223
 | 
|  |   1026 | 00:10:32,420 --> 00:10:35,615
 | 
|  |   1027 | my definitions or
 | 
|  |   1028 | my implementation.
 | 
|  |   1029 | 
 | 
|  |   1030 | 224
 | 
|  |   1031 | 00:10:35,615 --> 00:10:39,425
 | 
|  |   1032 | It's really essentially
 | 
|  |   1033 | mostly is brain work,
 | 
|  |   1034 | 
 | 
|  |   1035 | 225
 | 
|  |   1036 | 00:10:39,425 --> 00:10:42,170
 | 
|  |   1037 | how these nullable and
 | 
|  |   1038 | derivative should work.
 | 
|  |   1039 | 
 | 
|  |   1040 | 226
 | 
|  |   1041 | 00:10:42,170 --> 00:10:44,510
 | 
|  |   1042 | If you're in a
 | 
|  |   1043 | language like Scala,
 | 
|  |   1044 | 
 | 
|  |   1045 | 227
 | 
|  |   1046 | 00:10:44,510 --> 00:10:48,875
 | 
|  |   1047 | the implementation should
 | 
|  |   1048 | then be easy-peasy.
 | 
|  |   1049 | 
 | 
|  |   1050 | 228
 | 
|  |   1051 | 00:10:48,875 --> 00:10:51,365
 | 
|  |   1052 | If you are in a different language
 | 
|  |   1053 | 
 | 
|  |   1054 | 229
 | 
|  |   1055 | 00:10:51,365 --> 00:10:52,610
 | 
|  |   1056 | I assume you also
 | 
|  |   1057 | 
 | 
|  |   1058 | 230
 | 
|  |   1059 | 00:10:52,610 --> 00:10:54,890
 | 
|  |   1060 | dedicated to that
 | 
|  |   1061 | language to start with,
 | 
|  |   1062 | 
 | 
|  |   1063 | 231
 | 
|  |   1064 | 00:10:54,890 --> 00:10:58,475
 | 
|  |   1065 | so it should be also very
 | 
|  |   1066 | easy for you to translate
 | 
|  |   1067 | 
 | 
|  |   1068 | 232
 | 
|  |   1069 | 00:10:58,475 --> 00:11:01,100
 | 
|  |   1070 | my Scala code into whatever
 | 
|  |   1071 | language you want to
 | 
|  |   1072 | 
 | 
|  |   1073 | 233
 | 
|  |   1074 | 00:11:01,100 --> 00:11:04,280
 | 
|  |   1075 | do, first and then
 | 
|  |   1076 | start from there.
 | 
|  |   1077 | 
 | 
|  |   1078 | 234
 | 
|  |   1079 | 00:11:04,280 --> 00:11:06,230
 | 
|  |   1080 | If there are any questions,
 | 
|  |   1081 | 
 | 
|  |   1082 | 235
 | 
|  |   1083 | 00:11:06,230 --> 00:11:08,360
 | 
|  |   1084 | please ask me or the TAs.
 | 
|  |   1085 | 
 | 
|  |   1086 | 236
 | 
|  |   1087 | 00:11:08,360 --> 00:11:10,040
 | 
|  |   1088 | We are trying to be as helpful
 | 
|  |   1089 | 
 | 
|  |   1090 | 237
 | 
|  |   1091 | 00:11:10,040 --> 00:11:12,900
 | 
|  |   1092 | as possible with the coursework.
 | 
|  |   1093 | 
 | 
|  |   1094 | 238
 | 
|  |   1095 | 00:11:13,240 --> 00:11:17,885
 | 
|  |   1096 | Bear in mind, this is the
 | 
|  |   1097 | first step in our compiler.
 | 
|  |   1098 | 
 | 
|  |   1099 | 239
 | 
|  |   1100 | 00:11:17,885 --> 00:11:21,005
 | 
|  |   1101 | The coursework 2 will then
 | 
|  |   1102 | build on top of that.
 | 
|  |   1103 | 
 | 
|  |   1104 | 240
 | 
|  |   1105 | 00:11:21,005 --> 00:11:25,770
 | 
|  |   1106 | So it's better to get this
 | 
|  |   1107 | correct first. Thanks.
 |