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1 1 |
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2 00:00:06,020 --> 00:00:09,945 |
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3 They come back after |
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4 this disappointment |
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5 |
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6 2 |
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7 00:00:09,945 --> 00:00:14,115 |
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8 and case of over promising |
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9 and under achieving. |
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10 |
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11 3 |
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12 00:00:14,115 --> 00:00:17,295 |
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13 Let's have a look whether |
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14 we can recover from that. |
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15 |
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16 4 |
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17 00:00:17,295 --> 00:00:20,535 |
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18 So here's one problem. |
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19 |
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20 5 |
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21 00:00:20,535 --> 00:00:23,790 |
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22 Then we looked at this end |
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23 times vk expression and |
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24 |
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25 6 |
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26 00:00:23,790 --> 00:00:27,330 |
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27 be able to represent |
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28 that directly. |
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29 |
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30 7 |
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31 00:00:27,330 --> 00:00:31,275 |
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32 We had two represented as a |
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33 sequence record expression. |
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34 |
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35 8 |
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36 00:00:31,275 --> 00:00:32,850 |
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37 So we expanded it. |
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38 |
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39 9 |
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40 00:00:32,850 --> 00:00:36,510 |
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41 So times one would be just a, |
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42 |
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43 10 |
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44 00:00:36,510 --> 00:00:40,595 |
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45 t, times two would |
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46 be a, and so on. |
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47 |
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48 11 |
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49 00:00:40,595 --> 00:00:43,535 |
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50 And so you can see if |
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51 you go already to 13, |
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52 |
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53 12 |
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54 00:00:43,535 --> 00:00:47,960 |
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55 N equals 13, the record |
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56 expression becomes quite large. |
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57 |
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58 13 |
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59 00:00:47,960 --> 00:00:52,865 |
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60 And now the functions |
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61 nullable and also derivative. |
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62 |
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63 14 |
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64 00:00:52,865 --> 00:00:56,360 |
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65 They need to traverse |
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66 this reg expression. |
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67 |
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68 15 |
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69 00:00:56,360 --> 00:00:59,060 |
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70 Remember this tree in sometimes |
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71 |
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72 16 |
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73 00:00:59,060 --> 00:01:01,820 |
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74 they have to traverse |
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75 that even several times. |
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76 |
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77 17 |
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78 00:01:01,820 --> 00:01:04,535 |
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79 So that will slow |
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80 down the algorithm. |
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81 |
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82 18 |
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83 00:01:04,535 --> 00:01:08,150 |
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84 And in particular, because |
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85 our first reg expression was |
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86 |
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87 19 |
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88 00:01:08,150 --> 00:01:11,840 |
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89 actually not just a bot |
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90 a plus one. So b hat. |
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91 |
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92 20 |
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93 00:01:11,840 --> 00:01:14,330 |
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94 In the case of 13, |
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95 we had a plus one, |
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96 |
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97 21 |
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98 00:01:14,330 --> 00:01:17,330 |
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99 a plus one a plus born 13 times. |
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100 |
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101 22 |
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102 00:01:17,330 --> 00:01:20,150 |
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103 And this reg |
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104 expression just grows, |
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105 |
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106 23 |
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107 00:01:20,150 --> 00:01:25,475 |
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108 stay in number n. Just to |
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109 show you this also encode, |
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110 |
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111 24 |
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112 00:01:25,475 --> 00:01:28,115 |
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113 I'm Stern, This File rewarm |
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114 |
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115 25 |
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116 00:01:28,115 --> 00:01:30,920 |
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117 and D and I have a size function. |
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118 |
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119 26 |
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120 00:01:30,920 --> 00:01:33,140 |
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121 The size function takes |
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122 a regular expression as |
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123 |
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124 27 |
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125 00:01:33,140 --> 00:01:36,215 |
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126 argument and produces in teacher. |
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127 |
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128 28 |
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129 00:01:36,215 --> 00:01:39,980 |
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130 And essentially it takes |
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131 this rec expression scene as |
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132 |
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133 29 |
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134 00:01:39,980 --> 00:01:44,045 |
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135 a tree and count how many |
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136 nodes are in this tree. |
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137 |
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138 30 |
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139 00:01:44,045 --> 00:01:49,490 |
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140 And so if I take this even |
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141 one reg expression, this one, |
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142 |
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143 31 |
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144 00:01:49,490 --> 00:01:52,160 |
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145 and increase now this n. So you |
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146 |
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147 32 |
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148 00:01:52,160 --> 00:01:54,680 |
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149 can already see |
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150 for any cross one, |
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151 |
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152 33 |
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153 00:01:54,680 --> 00:01:56,540 |
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154 the size of this |
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155 record expression is |
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156 |
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157 34 |
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158 00:01:56,540 --> 00:01:59,615 |
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159 five and you see it |
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160 slowly increases. |
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161 |
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162 35 |
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163 00:01:59,615 --> 00:02:02,150 |
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164 And this 20 n equals 20. |
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165 |
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166 36 |
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167 00:02:02,150 --> 00:02:07,100 |
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168 The size of this record |
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169 expression is SMOW already a 119. |
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170 |
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171 37 |
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172 00:02:07,100 --> 00:02:10,145 |
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173 So now the interesting |
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174 line as this one. |
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175 |
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176 38 |
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177 00:02:10,145 --> 00:02:13,295 |
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178 Remember it when we |
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179 built the derivative, |
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180 |
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181 39 |
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182 00:02:13,295 --> 00:02:17,150 |
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183 very often parts of a reg |
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184 expression gets copied. |
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185 |
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186 40 |
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187 00:02:17,150 --> 00:02:19,280 |
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188 So if you have like EVA, |
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189 |
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190 41 |
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191 00:02:19,280 --> 00:02:22,325 |
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192 one of 2019 nodes, |
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193 |
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194 42 |
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195 00:02:22,325 --> 00:02:25,475 |
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196 now this will be often copied. |
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197 |
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198 43 |
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199 00:02:25,475 --> 00:02:31,475 |
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200 And we want to see what's the |
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201 resulting tree look like, |
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202 |
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203 44 |
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204 00:02:31,475 --> 00:02:32,780 |
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205 how many nodes it has. |
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206 |
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207 45 |
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208 00:02:32,780 --> 00:02:34,985 |
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209 So I take here either one of 20 |
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210 |
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211 46 |
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212 00:02:34,985 --> 00:02:38,405 |
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213 and the derivative |
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214 according to 20 a's. |
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215 |
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216 47 |
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217 00:02:38,405 --> 00:02:41,820 |
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218 And just have a look |
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219 what the size is. |
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220 |
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221 48 |
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222 00:02:43,210 --> 00:02:45,680 |
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223 Okay, that takes away. |
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224 |
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225 49 |
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226 00:02:45,680 --> 00:02:48,410 |
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227 You see now this rec expression, |
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228 |
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229 50 |
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230 00:02:48,410 --> 00:02:52,280 |
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231 the derivative has already |
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232 8 million plus nodes. |
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233 |
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234 51 |
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235 00:02:52,280 --> 00:02:55,400 |
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236 And now nullable and |
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237 derivative have to |
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238 |
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239 52 |
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240 00:02:55,400 --> 00:02:58,430 |
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241 traverse these trees with |
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242 a million plus nodes. |
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243 |
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244 53 |
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245 00:02:58,430 --> 00:03:01,400 |
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246 So it's no wonder |
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247 that this is slow. |
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248 |
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249 54 |
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250 00:03:01,400 --> 00:03:03,860 |
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251 The first thing we |
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252 can try to mitigate |
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253 |
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254 55 |
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255 00:03:03,860 --> 00:03:06,350 |
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256 this explosion problem is to |
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257 |
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258 56 |
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259 00:03:06,350 --> 00:03:09,050 |
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260 have an explicit and |
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261 times reg expression. |
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262 |
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263 57 |
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264 00:03:09,050 --> 00:03:11,600 |
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265 So instead of expanding |
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266 |
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267 58 |
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268 00:03:11,600 --> 00:03:13,415 |
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269 it to the sequence |
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270 reg expression, |
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271 |
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272 59 |
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273 00:03:13,415 --> 00:03:17,510 |
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274 let's just have a single |
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275 wreck expression and times, |
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276 |
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277 60 |
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278 00:03:17,510 --> 00:03:20,540 |
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279 which takes an expression and |
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280 |
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281 61 |
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282 00:03:20,540 --> 00:03:24,470 |
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283 a number and keeps that |
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284 regular expression Small. |
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285 |
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286 62 |
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287 00:03:24,470 --> 00:03:27,095 |
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288 I'm here in the fire V2, |
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289 |
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290 63 |
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291 00:03:27,095 --> 00:03:29,090 |
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292 which is also on Keats. |
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293 |
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294 64 |
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295 00:03:29,090 --> 00:03:32,570 |
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296 And the only change I made |
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297 is I added explicitly |
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298 |
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299 65 |
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300 00:03:32,570 --> 00:03:33,860 |
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301 a wrecker expression for |
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302 |
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303 66 |
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304 00:03:33,860 --> 00:03:36,770 |
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305 N times the optional |
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306 reg expression. |
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307 |
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308 67 |
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309 00:03:36,770 --> 00:03:39,920 |
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310 Very leaf out at the |
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311 moment because this a |
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312 |
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313 68 |
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314 00:03:39,920 --> 00:03:41,975 |
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315 optional is represented as |
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316 |
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317 69 |
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318 00:03:41,975 --> 00:03:44,645 |
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319 a plus one and doesn't |
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320 explain too much. |
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321 |
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322 70 |
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323 00:03:44,645 --> 00:03:47,375 |
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324 The really the culprit |
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325 is this n times. |
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326 |
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327 71 |
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328 00:03:47,375 --> 00:03:51,095 |
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329 And instead of expanding |
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330 it n times, which has, |
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331 |
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332 72 |
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333 00:03:51,095 --> 00:03:54,275 |
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334 take here a wreck expression |
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335 and a natural number, |
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336 |
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337 73 |
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338 00:03:54,275 --> 00:03:56,960 |
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339 which says how many times |
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340 it should be repeated. |
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341 |
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342 74 |
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343 00:03:56,960 --> 00:03:59,165 |
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344 And in this week we |
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345 can keep it small. |
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346 |
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347 75 |
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348 00:03:59,165 --> 00:04:01,370 |
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349 But by adding that |
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350 reg expression, |
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351 |
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352 76 |
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353 00:04:01,370 --> 00:04:05,150 |
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354 we now have to think about |
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355 cases for nullable and |
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356 |
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357 77 |
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358 00:04:05,150 --> 00:04:07,340 |
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359 derivative so that we have |
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360 |
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361 78 |
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362 00:04:07,340 --> 00:04:10,205 |
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363 to now calculate next |
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364 what they look like. |
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365 |
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366 79 |
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367 00:04:10,205 --> 00:04:14,060 |
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368 We can actually |
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369 calculate what the rule |
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370 |
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371 80 |
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372 00:04:14,060 --> 00:04:17,525 |
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373 for nullable should be from |
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374 how we defined it earlier. |
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375 |
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376 81 |
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377 00:04:17,525 --> 00:04:19,580 |
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378 Remember, if you have |
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379 a regular expression, |
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380 |
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381 82 |
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382 00:04:19,580 --> 00:04:21,980 |
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383 R and B take in |
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384 times of this are, |
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385 |
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386 83 |
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387 00:04:21,980 --> 00:04:25,220 |
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388 then indicates if n equals 0, |
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389 |
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390 84 |
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391 00:04:25,220 --> 00:04:28,130 |
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392 we find that as the |
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393 one reg expression. |
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394 |
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395 85 |
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396 00:04:28,130 --> 00:04:30,380 |
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397 If n equals one, |
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398 |
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399 86 |
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400 00:04:30,380 --> 00:04:32,495 |
|
401 it will be just a |
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402 single copy of on. |
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403 |
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404 87 |
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405 00:04:32,495 --> 00:04:33,725 |
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406 If n equals two, |
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407 |
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408 88 |
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409 00:04:33,725 --> 00:04:35,270 |
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410 it will be two copies. |
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411 |
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412 89 |
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413 00:04:35,270 --> 00:04:39,260 |
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414 Sequence if three, we have |
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415 three copies and so on. |
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416 |
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417 90 |
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418 00:04:39,260 --> 00:04:41,390 |
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419 Now we have to |
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420 somehow characterize |
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421 |
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422 91 |
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423 00:04:41,390 --> 00:04:44,285 |
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424 when these cases all nullable. |
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425 |
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426 92 |
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427 00:04:44,285 --> 00:04:47,810 |
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428 Well, if n equals 0, |
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429 |
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430 93 |
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431 00:04:47,810 --> 00:04:49,850 |
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432 then this will be defined as one, |
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433 |
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434 94 |
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435 00:04:49,850 --> 00:04:52,100 |
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436 so one can match |
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437 the empty string. |
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438 |
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439 95 |
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440 00:04:52,100 --> 00:04:54,785 |
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441 So that should be |
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442 definitely true. |
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443 |
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444 96 |
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445 00:04:54,785 --> 00:04:57,725 |
|
446 Okay, if any cross one, |
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447 |
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448 97 |
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449 00:04:57,725 --> 00:05:00,470 |
|
450 when can this reg expression |
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451 match the empty string? |
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452 |
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453 98 |
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454 00:05:00,470 --> 00:05:02,000 |
|
455 So vent should be nullable. |
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456 |
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457 99 |
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458 00:05:02,000 --> 00:05:07,535 |
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459 Well, if nullable of our holes, |
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460 |
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461 100 |
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462 00:05:07,535 --> 00:05:09,860 |
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463 okay, so if I can match |
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464 the empty string, |
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465 |
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466 101 |
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467 00:05:09,860 --> 00:05:12,110 |
|
468 then we can match |
|
469 the empty string. |
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470 |
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471 102 |
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472 00:05:12,110 --> 00:05:14,870 |
|
473 When can this regular expression |
|
474 match the empty string? |
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475 |
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476 103 |
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477 00:05:14,870 --> 00:05:16,265 |
|
478 So these are now two copies of |
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479 |
|
480 104 |
|
481 00:05:16,265 --> 00:05:20,690 |
|
482 our well-posed copies need |
|
483 to match the empty string. |
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484 |
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485 105 |
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486 00:05:20,690 --> 00:05:22,820 |
|
487 So again, we have to ask |
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488 |
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489 106 |
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490 00:05:22,820 --> 00:05:25,774 |
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491 both of them need to be nullable. |
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492 |
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493 107 |
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494 00:05:25,774 --> 00:05:28,520 |
|
495 Ok? Similarly, in the third case, |
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496 |
|
497 108 |
|
498 00:05:28,520 --> 00:05:30,710 |
|
499 all three copies need to be |
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500 |
|
501 109 |
|
502 00:05:30,710 --> 00:05:33,230 |
|
503 able to match the empty |
|
504 string. Men, is that the case? |
|
505 |
|
506 110 |
|
507 00:05:33,230 --> 00:05:38,360 |
|
508 Well, if nullable of |
|
509 our holes and so on. |
|
510 |
|
511 111 |
|
512 00:05:38,360 --> 00:05:48,754 |
|
513 So we can actually define that |
|
514 if n equals 0, then true. |
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515 |
|
516 112 |
|
517 00:05:48,754 --> 00:05:56,045 |
|
518 Else we have to ask with |
|
519 nullable of our holes. |
|
520 |
|
521 113 |
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522 00:05:56,045 --> 00:05:58,550 |
|
523 So that will be the clause we |
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524 |
|
525 114 |
|
526 00:05:58,550 --> 00:06:01,625 |
|
527 have to implement for |
|
528 n times and nullable. |
|
529 |
|
530 115 |
|
531 00:06:01,625 --> 00:06:04,280 |
|
532 Deriving the definition for |
|
533 |
|
534 116 |
|
535 00:06:04,280 --> 00:06:06,920 |
|
536 the derivative of the n terms |
|
537 |
|
538 117 |
|
539 00:06:06,920 --> 00:06:10,175 |
|
540 reg expression. |
|
541 It's not that easy. |
|
542 |
|
543 118 |
|
544 00:06:10,175 --> 00:06:12,755 |
|
545 So we have to look again |
|
546 how it was defined |
|
547 |
|
548 119 |
|
549 00:06:12,755 --> 00:06:16,010 |
|
550 earlier and we somehow |
|
551 have to spot a pattern. |
|
552 |
|
553 120 |
|
554 00:06:16,010 --> 00:06:18,380 |
|
555 The voice, our |
|
556 algorithm will be again |
|
557 |
|
558 121 |
|
559 00:06:18,380 --> 00:06:20,975 |
|
560 quite slow if you don't |
|
561 spot that pattern. |
|
562 |
|
563 122 |
|
564 00:06:20,975 --> 00:06:22,550 |
|
565 So let's have a look. |
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566 |
|
567 123 |
|
568 00:06:22,550 --> 00:06:26,240 |
|
569 So in the case that |
|
570 n is equal to 0, |
|
571 |
|
572 124 |
|
573 00:06:26,240 --> 00:06:29,885 |
|
574 then r n times most |
|
575 defined as just one. |
|
576 |
|
577 125 |
|
578 00:06:29,885 --> 00:06:32,030 |
|
579 What would be the |
|
580 derivative of one? |
|
581 |
|
582 126 |
|
583 00:06:32,030 --> 00:06:36,140 |
|
584 So the derivative of c of one. |
|
585 |
|
586 127 |
|
587 00:06:36,140 --> 00:06:38,990 |
|
588 Peaches defined as 0. |
|
589 |
|
590 128 |
|
591 00:06:38,990 --> 00:06:41,465 |
|
592 Okay, fair enough. |
|
593 |
|
594 129 |
|
595 00:06:41,465 --> 00:06:44,960 |
|
596 If he have any cross one, |
|
597 |
|
598 130 |
|
599 00:06:44,960 --> 00:06:48,125 |
|
600 then we just have one copy |
|
601 of this regular expression. |
|
602 |
|
603 131 |
|
604 00:06:48,125 --> 00:06:50,120 |
|
605 So there's not much as we can do. |
|
606 |
|
607 132 |
|
608 00:06:50,120 --> 00:06:53,735 |
|
609 We would have to calculate |
|
610 the derivative of air are. |
|
611 |
|
612 133 |
|
613 00:06:53,735 --> 00:06:57,395 |
|
614 Now in the n equals two case. |
|
615 |
|
616 134 |
|
617 00:06:57,395 --> 00:07:00,245 |
|
618 That would mean we |
|
619 have two copies of |
|
620 |
|
621 135 |
|
622 00:07:00,245 --> 00:07:03,425 |
|
623 R. And they would be a sequence. |
|
624 |
|
625 136 |
|
626 00:07:03,425 --> 00:07:07,775 |
|
627 How would be the derivative C of |
|
628 |
|
629 137 |
|
630 00:07:07,775 --> 00:07:10,340 |
|
631 R four by R be |
|
632 |
|
633 138 |
|
634 00:07:10,340 --> 00:07:13,265 |
|
635 defined where we would |
|
636 look up the definition. |
|
637 |
|
638 139 |
|
639 00:07:13,265 --> 00:07:15,470 |
|
640 And it would say that's |
|
641 the complicated case |
|
642 |
|
643 140 |
|
644 00:07:15,470 --> 00:07:16,760 |
|
645 d sequence or |
|
646 |
|
647 141 |
|
648 00:07:16,760 --> 00:07:21,875 |
|
649 if null a bowl of R, |
|
650 |
|
651 142 |
|
652 00:07:21,875 --> 00:07:25,250 |
|
653 Then the most complicated case. |
|
654 |
|
655 143 |
|
656 00:07:25,250 --> 00:07:28,225 |
|
657 Else, That's the easy |
|
658 case that would be |
|
659 |
|
660 144 |
|
661 00:07:28,225 --> 00:07:32,660 |
|
662 derivative of c of R four |
|
663 |
|
664 145 |
|
665 00:07:32,660 --> 00:07:35,540 |
|
666 by R. And then I |
|
667 just have to copy |
|
668 |
|
669 146 |
|
670 00:07:35,540 --> 00:07:40,775 |
|
671 that derivative of C |
|
672 of four by r here. |
|
673 |
|
674 147 |
|
675 00:07:40,775 --> 00:07:43,130 |
|
676 But in this case I have also |
|
677 |
|
678 148 |
|
679 00:07:43,130 --> 00:07:51,145 |
|
680 the alternative derivative |
|
681 of c of r. And from that, |
|
682 |
|
683 149 |
|
684 00:07:51,145 --> 00:07:55,030 |
|
685 it looks like we can |
|
686 do much better than |
|
687 |
|
688 150 |
|
689 00:07:55,030 --> 00:07:58,390 |
|
690 that unless we do |
|
691 |
|
692 151 |
|
693 00:07:58,390 --> 00:08:02,560 |
|
694 a little bit of magic and the |
|
695 magic to do with this case. |
|
696 |
|
697 152 |
|
698 00:08:02,560 --> 00:08:07,420 |
|
699 So let me look at this |
|
700 case a bit more closely. |
|
701 |
|
702 153 |
|
703 00:08:07,420 --> 00:08:09,819 |
|
704 Let me go back to slides |
|
705 |
|
706 154 |
|
707 00:08:09,819 --> 00:08:12,940 |
|
708 because actually the calculation |
|
709 might be a bit hairy. |
|
710 |
|
711 155 |
|
712 00:08:12,940 --> 00:08:16,945 |
|
713 So remember we are in this |
|
714 case where n equals two. |
|
715 |
|
716 156 |
|
717 00:08:16,945 --> 00:08:18,550 |
|
718 And this was defined as |
|
719 |
|
720 157 |
|
721 00:08:18,550 --> 00:08:20,680 |
|
722 this sequence work |
|
723 expression R followed |
|
724 |
|
725 158 |
|
726 00:08:20,680 --> 00:08:23,080 |
|
727 by r. And the question was, |
|
728 |
|
729 159 |
|
730 00:08:23,080 --> 00:08:26,365 |
|
731 can we somehow make sense |
|
732 out of this derivative |
|
733 |
|
734 160 |
|
735 00:08:26,365 --> 00:08:30,370 |
|
736 where we have to build the |
|
737 derivative of a sequence. |
|
738 |
|
739 161 |
|
740 00:08:30,370 --> 00:08:33,020 |
|
741 So features the definition. |
|
742 |
|
743 162 |
|
744 00:08:33,020 --> 00:08:36,050 |
|
745 We would ask if |
|
746 the r is nullable, |
|
747 |
|
748 163 |
|
749 00:08:36,050 --> 00:08:39,095 |
|
750 In this case, we return |
|
751 this alternative. |
|
752 |
|
753 164 |
|
754 00:08:39,095 --> 00:08:40,640 |
|
755 And if it's not nullable, |
|
756 |
|
757 165 |
|
758 00:08:40,640 --> 00:08:44,135 |
|
759 It is just this |
|
760 record expression. |
|
761 |
|
762 166 |
|
763 00:08:44,135 --> 00:08:49,550 |
|
764 Now my claim is that |
|
765 this whole if condition |
|
766 |
|
767 167 |
|
768 00:08:49,550 --> 00:08:55,895 |
|
769 can be replaced by just this |
|
770 simple derivative here. |
|
771 |
|
772 168 |
|
773 00:08:55,895 --> 00:08:58,775 |
|
774 And if that claim is correct, |
|
775 |
|
776 169 |
|
777 00:08:58,775 --> 00:09:01,520 |
|
778 there would be very nice |
|
779 because in contrast to |
|
780 |
|
781 170 |
|
782 00:09:01,520 --> 00:09:04,130 |
|
783 this if condition where |
|
784 |
|
785 171 |
|
786 00:09:04,130 --> 00:09:06,280 |
|
787 we have to calculate |
|
788 like nullable, |
|
789 |
|
790 172 |
|
791 00:09:06,280 --> 00:09:08,330 |
|
792 decide in which branch we are. |
|
793 |
|
794 173 |
|
795 00:09:08,330 --> 00:09:10,580 |
|
796 We don't have to |
|
797 calculate your now, |
|
798 |
|
799 174 |
|
800 00:09:10,580 --> 00:09:13,880 |
|
801 but we can just replace |
|
802 it by this expression. |
|
803 |
|
804 175 |
|
805 00:09:13,880 --> 00:09:16,670 |
|
806 So if we can |
|
807 substantiate that claim, |
|
808 |
|
809 176 |
|
810 00:09:16,670 --> 00:09:19,860 |
|
811 that will be definitely |
|
812 good file algorithm. |
|
813 |
|
814 177 |
|
815 00:09:20,140 --> 00:09:22,775 |
|
816 And to substantiate that, |
|
817 |
|
818 178 |
|
819 00:09:22,775 --> 00:09:26,795 |
|
820 I will focus on this |
|
821 record expression here. |
|
822 |
|
823 179 |
|
824 00:09:26,795 --> 00:09:31,100 |
|
825 And notice that this record |
|
826 expression the only be |
|
827 |
|
828 180 |
|
829 00:09:31,100 --> 00:09:35,780 |
|
830 called or only be generated |
|
831 if r is nullable. |
|
832 |
|
833 181 |
|
834 00:09:35,780 --> 00:09:38,075 |
|
835 So in any other case, |
|
836 |
|
837 182 |
|
838 00:09:38,075 --> 00:09:40,060 |
|
839 I will actually not go into it |
|
840 |
|
841 183 |
|
842 00:09:40,060 --> 00:09:43,850 |
|
843 that if branch and would |
|
844 be in the other one. |
|
845 |
|
846 184 |
|
847 00:09:43,850 --> 00:09:45,260 |
|
848 So if we are in this if branch, |
|
849 |
|
850 185 |
|
851 00:09:45,260 --> 00:09:47,705 |
|
852 we definitely know |
|
853 that R is nullable. |
|
854 |
|
855 186 |
|
856 00:09:47,705 --> 00:09:52,955 |
|
857 Okay? Okay, so here's |
|
858 our regular expression. |
|
859 |
|
860 187 |
|
861 00:09:52,955 --> 00:09:55,940 |
|
862 And we know it's nullable. |
|
863 |
|
864 188 |
|
865 00:09:55,940 --> 00:09:57,920 |
|
866 So we have to somehow find |
|
867 |
|
868 189 |
|
869 00:09:57,920 --> 00:10:00,380 |
|
870 an equivalent expression that |
|
871 |
|
872 190 |
|
873 00:10:00,380 --> 00:10:04,100 |
|
874 is smaller or simpler |
|
875 than that one. |
|
876 |
|
877 191 |
|
878 00:10:04,100 --> 00:10:05,945 |
|
879 Let's see what we can do. |
|
880 |
|
881 192 |
|
882 00:10:05,945 --> 00:10:10,160 |
|
883 So the first thing |
|
884 actually is we multiplying |
|
885 |
|
886 193 |
|
887 00:10:10,160 --> 00:10:16,595 |
|
888 this right hand side of the |
|
889 alternative is times one. |
|
890 |
|
891 194 |
|
892 00:10:16,595 --> 00:10:19,700 |
|
893 We can do that |
|
894 because this does not |
|
895 |
|
896 195 |
|
897 00:10:19,700 --> 00:10:23,090 |
|
898 change which strings this |
|
899 work expression can match. |
|
900 |
|
901 196 |
|
902 00:10:23,090 --> 00:10:25,685 |
|
903 Remember we even had it |
|
904 as a simplification row, |
|
905 |
|
906 197 |
|
907 00:10:25,685 --> 00:10:27,425 |
|
908 just in this case B, |
|
909 |
|
910 198 |
|
911 00:10:27,425 --> 00:10:29,705 |
|
912 don't apply it as a |
|
913 simplification will |
|
914 |
|
915 199 |
|
916 00:10:29,705 --> 00:10:31,310 |
|
917 actually make this |
|
918 work expression |
|
919 |
|
920 200 |
|
921 00:10:31,310 --> 00:10:32,720 |
|
922 a bit more complicated. |
|
923 |
|
924 201 |
|
925 00:10:32,720 --> 00:10:34,910 |
|
926 But times one doesn't make |
|
927 |
|
928 202 |
|
929 00:10:34,910 --> 00:10:37,820 |
|
930 a difference because it |
|
931 means the end of the string, |
|
932 |
|
933 203 |
|
934 00:10:37,820 --> 00:10:40,070 |
|
935 we still want to match |
|
936 the empty string. |
|
937 |
|
938 204 |
|
939 00:10:40,070 --> 00:10:42,155 |
|
940 Okay, so that is possible. |
|
941 |
|
942 205 |
|
943 00:10:42,155 --> 00:10:45,740 |
|
944 I can do that. Once |
|
945 we have done that, |
|
946 |
|
947 206 |
|
948 00:10:45,740 --> 00:10:48,410 |
|
949 you will notice that this |
|
950 factor derivative of |
|
951 |
|
952 207 |
|
953 00:10:48,410 --> 00:10:51,860 |
|
954 stuff are exactly the |
|
955 same as that one. |
|
956 |
|
957 208 |
|
958 00:10:51,860 --> 00:10:54,650 |
|
959 And in between is a plus. |
|
960 |
|
961 209 |
|
962 00:10:54,650 --> 00:10:57,440 |
|
963 So you probably remember the law |
|
964 |
|
965 210 |
|
966 00:10:57,440 --> 00:11:00,170 |
|
967 from school math |
|
968 that I can pull out |
|
969 |
|
970 211 |
|
971 00:11:00,170 --> 00:11:02,735 |
|
972 this factor derivative of c of r. |
|
973 |
|
974 212 |
|
975 00:11:02,735 --> 00:11:06,320 |
|
976 And I'm inside the parentheses |
|
977 is left with that. |
|
978 |
|
979 213 |
|
980 00:11:06,320 --> 00:11:09,245 |
|
981 So now I have r plus one. |
|
982 |
|
983 214 |
|
984 00:11:09,245 --> 00:11:13,055 |
|
985 Usually we cannot |
|
986 simplify r plus one. |
|
987 |
|
988 215 |
|
989 00:11:13,055 --> 00:11:15,530 |
|
990 If it had been R |
|
991 plus 0, then yes, |
|
992 |
|
993 216 |
|
994 00:11:15,530 --> 00:11:18,665 |
|
995 we could have got rid of the CRO. |
|
996 |
|
997 217 |
|
998 00:11:18,665 --> 00:11:21,590 |
|
999 Plus one often |
|
1000 makes a difference, |
|
1001 |
|
1002 218 |
|
1003 00:11:21,590 --> 00:11:22,970 |
|
1004 but not in our case. |
|
1005 |
|
1006 219 |
|
1007 00:11:22,970 --> 00:11:25,940 |
|
1008 Remember, we know that |
|
1009 this R is nullable, |
|
1010 |
|
1011 220 |
|
1012 00:11:25,940 --> 00:11:29,840 |
|
1013 so on its own can already |
|
1014 match the empty string. |
|
1015 |
|
1016 221 |
|
1017 00:11:29,840 --> 00:11:33,305 |
|
1018 So we don't really need this |
|
1019 alternative plus one there, |
|
1020 |
|
1021 222 |
|
1022 00:11:33,305 --> 00:11:35,300 |
|
1023 so we can just get rid of that. |
|
1024 |
|
1025 223 |
|
1026 00:11:35,300 --> 00:11:37,070 |
|
1027 Okay, and so now we have |
|
1028 |
|
1029 224 |
|
1030 00:11:37,070 --> 00:11:40,535 |
|
1031 a much simpler wound |
|
1032 reg expression. |
|
1033 |
|
1034 225 |
|
1035 00:11:40,535 --> 00:11:44,285 |
|
1036 And this actually helps a |
|
1037 lot for our if condition. |
|
1038 |
|
1039 226 |
|
1040 00:11:44,285 --> 00:11:46,925 |
|
1041 Look, this was the |
|
1042 original if condition |
|
1043 |
|
1044 227 |
|
1045 00:11:46,925 --> 00:11:50,270 |
|
1046 and this is direct expression |
|
1047 h. We just simplified. |
|
1048 |
|
1049 228 |
|
1050 00:11:50,270 --> 00:11:53,105 |
|
1051 If we replace it with this one, |
|
1052 |
|
1053 229 |
|
1054 00:11:53,105 --> 00:11:56,090 |
|
1055 then we just end up with this. |
|
1056 |
|
1057 230 |
|
1058 00:11:56,090 --> 00:11:59,510 |
|
1059 And now you will see that |
|
1060 the if condition is actually |
|
1061 |
|
1062 231 |
|
1063 00:11:59,510 --> 00:12:02,750 |
|
1064 pointless because you |
|
1065 check if it's null above, |
|
1066 |
|
1067 232 |
|
1068 00:12:02,750 --> 00:12:05,060 |
|
1069 we return this reg |
|
1070 expression or it's |
|
1071 |
|
1072 233 |
|
1073 00:12:05,060 --> 00:12:08,210 |
|
1074 not nullable and we |
|
1075 return exactly the same. |
|
1076 |
|
1077 234 |
|
1078 00:12:08,210 --> 00:12:10,025 |
|
1079 That doesn't make any difference. |
|
1080 |
|
1081 235 |
|
1082 00:12:10,025 --> 00:12:11,750 |
|
1083 So we can just get rid of |
|
1084 |
|
1085 236 |
|
1086 00:12:11,750 --> 00:12:14,645 |
|
1087 that one and can |
|
1088 replace it by that. |
|
1089 |
|
1090 237 |
|
1091 00:12:14,645 --> 00:12:16,865 |
|
1092 And you see, this is now |
|
1093 |
|
1094 238 |
|
1095 00:12:16,865 --> 00:12:20,720 |
|
1096 a much simpler case than |
|
1097 what we had before. |
|
1098 |
|
1099 239 |
|
1100 00:12:20,720 --> 00:12:24,170 |
|
1101 So let's take stock |
|
1102 what we have so far. |
|
1103 |
|
1104 240 |
|
1105 00:12:24,170 --> 00:12:26,915 |
|
1106 So we know India CEO case, |
|
1107 |
|
1108 241 |
|
1109 00:12:26,915 --> 00:12:30,920 |
|
1110 the derivative needs |
|
1111 to be defined as 0. |
|
1112 |
|
1113 242 |
|
1114 00:12:30,920 --> 00:12:33,095 |
|
1115 So because we define this |
|
1116 |
|
1117 243 |
|
1118 00:12:33,095 --> 00:12:36,785 |
|
1119 and times as one, |
|
1120 the derivative is 0. |
|
1121 |
|
1122 244 |
|
1123 00:12:36,785 --> 00:12:39,889 |
|
1124 For chest r, this will |
|
1125 be the derivative. |
|
1126 |
|
1127 245 |
|
1128 00:12:39,889 --> 00:12:42,170 |
|
1129 And we can't do any |
|
1130 better than that |
|
1131 |
|
1132 246 |
|
1133 00:12:42,170 --> 00:12:45,620 |
|
1134 for our followed by |
|
1135 RB just found out. |
|
1136 |
|
1137 247 |
|
1138 00:12:45,620 --> 00:12:47,270 |
|
1139 Actually it is quite simple. |
|
1140 |
|
1141 248 |
|
1142 00:12:47,270 --> 00:12:51,410 |
|
1143 Reg expression is equivalent |
|
1144 to the derivative. |
|
1145 |
|
1146 249 |
|
1147 00:12:51,410 --> 00:12:53,870 |
|
1148 Now, we have to continue with |
|
1149 |
|
1150 250 |
|
1151 00:12:53,870 --> 00:12:56,090 |
|
1152 that case where n is |
|
1153 equal to three and we |
|
1154 |
|
1155 251 |
|
1156 00:12:56,090 --> 00:12:58,099 |
|
1157 now have three copies |
|
1158 |
|
1159 252 |
|
1160 00:12:58,099 --> 00:13:02,390 |
|
1161 of this or what should |
|
1162 be the derivative? |
|
1163 |
|
1164 253 |
|
1165 00:13:02,390 --> 00:13:05,330 |
|
1166 Well, if you look very carefully |
|
1167 |
|
1168 254 |
|
1169 00:13:05,330 --> 00:13:08,465 |
|
1170 at this emerging pattern, |
|
1171 |
|
1172 255 |
|
1173 00:13:08,465 --> 00:13:12,410 |
|
1174 I have to say then |
|
1175 what would be nice if, |
|
1176 |
|
1177 256 |
|
1178 00:13:12,410 --> 00:13:16,400 |
|
1179 if he could show that in |
|
1180 the n equals three case, |
|
1181 |
|
1182 257 |
|
1183 00:13:16,400 --> 00:13:18,275 |
|
1184 we end up with this. |
|
1185 |
|
1186 258 |
|
1187 00:13:18,275 --> 00:13:21,290 |
|
1188 Because then what we have is. |
|
1189 |
|
1190 259 |
|
1191 00:13:21,290 --> 00:13:25,370 |
|
1192 We can define our |
|
1193 nullable for n times |
|
1194 |
|
1195 260 |
|
1196 00:13:25,370 --> 00:13:31,025 |
|
1197 s. If any cross 0 then |
|
1198 true as nullable. |
|
1199 |
|
1200 261 |
|
1201 00:13:31,025 --> 00:13:33,875 |
|
1202 And for the derivative, |
|
1203 |
|
1204 262 |
|
1205 00:13:33,875 --> 00:13:37,190 |
|
1206 we can save if n is equal to 0, |
|
1207 |
|
1208 263 |
|
1209 00:13:37,190 --> 00:13:40,235 |
|
1210 then we return the |
|
1211 Sierra reg expression. |
|
1212 |
|
1213 264 |
|
1214 00:13:40,235 --> 00:13:43,295 |
|
1215 Otherwise, as you can see |
|
1216 from this pattern here, |
|
1217 |
|
1218 265 |
|
1219 00:13:43,295 --> 00:13:50,735 |
|
1220 it would be derivative of |
|
1221 c r four by r n minus one. |
|
1222 |
|
1223 266 |
|
1224 00:13:50,735 --> 00:13:54,770 |
|
1225 Okay? And the only |
|
1226 |
|
1227 267 |
|
1228 00:13:54,770 --> 00:13:56,330 |
|
1229 thing we have to make choice that |
|
1230 |
|
1231 268 |
|
1232 00:13:56,330 --> 00:13:58,175 |
|
1233 this pattern actually holds. |
|
1234 |
|
1235 269 |
|
1236 00:13:58,175 --> 00:14:00,470 |
|
1237 So that's, I will |
|
1238 show you next in |
|
1239 |
|
1240 270 |
|
1241 00:14:00,470 --> 00:14:03,735 |
|
1242 the case for n equals three. |
|
1243 |
|
1244 271 |
|
1245 00:14:03,735 --> 00:14:07,810 |
|
1246 If we have a wreck expression R |
|
1247 |
|
1248 272 |
|
1249 00:14:07,810 --> 00:14:09,820 |
|
1250 and it's followed |
|
1251 by r and another r, |
|
1252 |
|
1253 273 |
|
1254 00:14:09,820 --> 00:14:11,275 |
|
1255 three copies of it. |
|
1256 |
|
1257 274 |
|
1258 00:14:11,275 --> 00:14:14,245 |
|
1259 We can just unfold |
|
1260 again the definition. |
|
1261 |
|
1262 275 |
|
1263 00:14:14,245 --> 00:14:16,930 |
|
1264 So we would ask if I is nullable, |
|
1265 |
|
1266 276 |
|
1267 00:14:16,930 --> 00:14:19,765 |
|
1268 then we have this if branch. |
|
1269 |
|
1270 277 |
|
1271 00:14:19,765 --> 00:14:23,905 |
|
1272 And if i is not nullable |
|
1273 or we have this as branch. |
|
1274 |
|
1275 278 |
|
1276 00:14:23,905 --> 00:14:27,010 |
|
1277 Okay? What can we do here? |
|
1278 |
|
1279 279 |
|
1280 00:14:27,010 --> 00:14:30,310 |
|
1281 Well, we notice that |
|
1282 this one is just now |
|
1283 |
|
1284 280 |
|
1285 00:14:30,310 --> 00:14:34,510 |
|
1286 the derivative of two |
|
1287 Rs, one after another. |
|
1288 |
|
1289 281 |
|
1290 00:14:34,510 --> 00:14:37,330 |
|
1291 But this we just |
|
1292 calculated a moment ago, |
|
1293 |
|
1294 282 |
|
1295 00:14:37,330 --> 00:14:40,120 |
|
1296 so we can just |
|
1297 replace it by this. |
|
1298 |
|
1299 283 |
|
1300 00:14:40,120 --> 00:14:43,255 |
|
1301 Ok. That's what we |
|
1302 calculated earlier. |
|
1303 |
|
1304 284 |
|
1305 00:14:43,255 --> 00:14:46,665 |
|
1306 But now you will see |
|
1307 again this factor, |
|
1308 |
|
1309 285 |
|
1310 00:14:46,665 --> 00:14:48,695 |
|
1311 and this factor is the same. |
|
1312 |
|
1313 286 |
|
1314 00:14:48,695 --> 00:14:52,700 |
|
1315 So I can pull that |
|
1316 out to be like that. |
|
1317 |
|
1318 287 |
|
1319 00:14:52,700 --> 00:14:57,380 |
|
1320 And I have now followed |
|
1321 by R plus R. Oh, |
|
1322 |
|
1323 288 |
|
1324 00:14:57,380 --> 00:14:59,030 |
|
1325 hey, man, now you probably |
|
1326 |
|
1327 289 |
|
1328 00:14:59,030 --> 00:15:00,680 |
|
1329 remember how we did it earlier. |
|
1330 |
|
1331 290 |
|
1332 00:15:00,680 --> 00:15:03,080 |
|
1333 We can now pull out one copy of |
|
1334 |
|
1335 291 |
|
1336 00:15:03,080 --> 00:15:06,020 |
|
1337 this are to just get |
|
1338 something like this. |
|
1339 |
|
1340 292 |
|
1341 00:15:06,020 --> 00:15:08,765 |
|
1342 We have to add one essentially, |
|
1343 |
|
1344 293 |
|
1345 00:15:08,765 --> 00:15:11,615 |
|
1346 but we now get r plus one. |
|
1347 |
|
1348 294 |
|
1349 00:15:11,615 --> 00:15:15,065 |
|
1350 And this r here is |
|
1351 now just pulled out. |
|
1352 |
|
1353 295 |
|
1354 00:15:15,065 --> 00:15:18,995 |
|
1355 Well, here again kicks |
|
1356 in this reasoning. |
|
1357 |
|
1358 296 |
|
1359 00:15:18,995 --> 00:15:22,700 |
|
1360 We go in this if branch |
|
1361 only if r is nullable, |
|
1362 |
|
1363 297 |
|
1364 00:15:22,700 --> 00:15:26,150 |
|
1365 so on its own can already |
|
1366 match the empty string. |
|
1367 |
|
1368 298 |
|
1369 00:15:26,150 --> 00:15:28,895 |
|
1370 So I don't need |
|
1371 really this plus one. |
|
1372 |
|
1373 299 |
|
1374 00:15:28,895 --> 00:15:30,695 |
|
1375 I can just get rid of it. |
|
1376 |
|
1377 300 |
|
1378 00:15:30,695 --> 00:15:33,140 |
|
1379 And so I now just have |
|
1380 to rearrange the parent, |
|
1381 |
|
1382 301 |
|
1383 00:15:33,140 --> 00:15:35,450 |
|
1384 the thesis which we |
|
1385 said we can also do. |
|
1386 |
|
1387 302 |
|
1388 00:15:35,450 --> 00:15:37,595 |
|
1389 So we have something like that. |
|
1390 |
|
1391 303 |
|
1392 00:15:37,595 --> 00:15:39,740 |
|
1393 And here again, the |
|
1394 same reasoning, |
|
1395 |
|
1396 304 |
|
1397 00:15:39,740 --> 00:15:41,975 |
|
1398 we have a if condition |
|
1399 |
|
1400 305 |
|
1401 00:15:41,975 --> 00:15:43,310 |
|
1402 where it doesn't |
|
1403 really matter what |
|
1404 |
|
1405 306 |
|
1406 00:15:43,310 --> 00:15:44,405 |
|
1407 we're going to return, |
|
1408 |
|
1409 307 |
|
1410 00:15:44,405 --> 00:15:46,205 |
|
1411 it's in both branches the same. |
|
1412 |
|
1413 308 |
|
1414 00:15:46,205 --> 00:15:48,470 |
|
1415 So we can just |
|
1416 replace it by that. |
|
1417 |
|
1418 309 |
|
1419 00:15:48,470 --> 00:15:51,920 |
|
1420 And yes, now we can be |
|
1421 pretty sure they'll |
|
1422 |
|
1423 310 |
|
1424 00:15:51,920 --> 00:15:55,310 |
|
1425 work for all the n times |
|
1426 regular expressions. |
|
1427 |
|
1428 311 |
|
1429 00:15:55,310 --> 00:15:57,860 |
|
1430 And leave that to |
|
1431 the calculation for |
|
1432 |
|
1433 312 |
|
1434 00:15:57,860 --> 00:16:02,570 |
|
1435 maybe R to the four to you. |
|
1436 |
|
1437 313 |
|
1438 00:16:02,570 --> 00:16:04,490 |
|
1439 And the reason why I do it |
|
1440 |
|
1441 314 |
|
1442 00:16:04,490 --> 00:16:06,605 |
|
1443 in such a detail, |
|
1444 this calculation, |
|
1445 |
|
1446 315 |
|
1447 00:16:06,605 --> 00:16:08,960 |
|
1448 this is really meant |
|
1449 to help you with |
|
1450 |
|
1451 316 |
|
1452 00:16:08,960 --> 00:16:13,200 |
|
1453 the coursework which is |
|
1454 coming up this week. |
|
1455 |
|
1456 317 |
|
1457 00:16:13,210 --> 00:16:16,250 |
|
1458 I'm now back in our |
|
1459 implementation. |
|
1460 |
|
1461 318 |
|
1462 00:16:16,250 --> 00:16:20,660 |
|
1463 In this Reto, said We have |
|
1464 this explicit constructor now |
|
1465 |
|
1466 319 |
|
1467 00:16:20,660 --> 00:16:25,535 |
|
1468 for n times b can now fill |
|
1469 in the cases for nullable. |
|
1470 |
|
1471 320 |
|
1472 00:16:25,535 --> 00:16:27,635 |
|
1473 So if we have R in times, |
|
1474 |
|
1475 321 |
|
1476 00:16:27,635 --> 00:16:30,995 |
|
1477 if this n is equal to |
|
1478 0, we return true. |
|
1479 |
|
1480 322 |
|
1481 00:16:30,995 --> 00:16:34,190 |
|
1482 Otherwise we have to test |
|
1483 whether eyes nullable. |
|
1484 |
|
1485 323 |
|
1486 00:16:34,190 --> 00:16:37,565 |
|
1487 And in the derivative case, oi, |
|
1488 |
|
1489 324 |
|
1490 00:16:37,565 --> 00:16:40,339 |
|
1491 if this n is equal to 0, |
|
1492 |
|
1493 325 |
|
1494 00:16:40,339 --> 00:16:43,564 |
|
1495 the return this 0 |
|
1496 wreck expression. |
|
1497 |
|
1498 326 |
|
1499 00:16:43,564 --> 00:16:46,700 |
|
1500 Otherwise we return the |
|
1501 sequence of the derivative |
|
1502 |
|
1503 327 |
|
1504 00:16:46,700 --> 00:16:50,270 |
|
1505 of psi of r four by n times of r, |
|
1506 |
|
1507 328 |
|
1508 00:16:50,270 --> 00:16:54,545 |
|
1509 but n minus one times and |
|
1510 everything else stays the same. |
|
1511 |
|
1512 329 |
|
1513 00:16:54,545 --> 00:16:56,510 |
|
1514 Here's the function for strings, |
|
1515 |
|
1516 330 |
|
1517 00:16:56,510 --> 00:16:58,430 |
|
1518 derivative function for strings. |
|
1519 |
|
1520 331 |
|
1521 00:16:58,430 --> 00:17:01,595 |
|
1522 In the main mantra |
|
1523 function as all the same. |
|
1524 |
|
1525 332 |
|
1526 00:17:01,595 --> 00:17:04,820 |
|
1527 We still require this |
|
1528 definition because |
|
1529 |
|
1530 333 |
|
1531 00:17:04,820 --> 00:17:06,050 |
|
1532 we haven't done anything about |
|
1533 |
|
1534 334 |
|
1535 00:17:06,050 --> 00:17:08,090 |
|
1536 the optional record |
|
1537 expression yet. |
|
1538 |
|
1539 335 |
|
1540 00:17:08,090 --> 00:17:10,670 |
|
1541 And we have now at this |
|
1542 |
|
1543 336 |
|
1544 00:17:10,670 --> 00:17:13,250 |
|
1545 either warm and evil |
|
1546 2-break expression. |
|
1547 |
|
1548 337 |
|
1549 00:17:13,250 --> 00:17:15,290 |
|
1550 And let's test it. And let's be |
|
1551 |
|
1552 338 |
|
1553 00:17:15,290 --> 00:17:17,000 |
|
1554 a bit more ambitious. |
|
1555 Be testing it. |
|
1556 |
|
1557 339 |
|
1558 00:17:17,000 --> 00:17:20,315 |
|
1559 The strings between 01000 |
|
1560 |
|
1561 340 |
|
1562 00:17:20,315 --> 00:17:22,580 |
|
1563 and let's see what the time say. |
|
1564 |
|
1565 341 |
|
1566 00:17:22,580 --> 00:17:26,210 |
|
1567 I'm testing this again |
|
1568 inside the ammonite rebel. |
|
1569 |
|
1570 342 |
|
1571 00:17:26,210 --> 00:17:30,180 |
|
1572 And you'll see it should |
|
1573 be now much quicker. |
|
1574 |
|
1575 343 |
|
1576 00:17:30,610 --> 00:17:34,640 |
|
1577 Okay, it might slow |
|
1578 down also around 600. |
|
1579 |
|
1580 344 |
|
1581 00:17:34,640 --> 00:17:40,490 |
|
1582 700 needs two seconds, |
|
1583 three seconds, 4800. |
|
1584 |
|
1585 345 |
|
1586 00:17:40,490 --> 00:17:43,940 |
|
1587 Let's see about it |
|
1588 needs 4 thousand. |
|
1589 |
|
1590 346 |
|
1591 00:17:43,940 --> 00:17:47,435 |
|
1592 But you have to remember |
|
1593 Ruby and Python. |
|
1594 |
|
1595 347 |
|
1596 00:17:47,435 --> 00:17:51,530 |
|
1597 They needed half a |
|
1598 minute to just 43 TAs. |
|
1599 |
|
1600 348 |
|
1601 00:17:51,530 --> 00:17:54,485 |
|
1602 We need a little bit |
|
1603 more than six seconds, |
|
1604 |
|
1605 349 |
|
1606 00:17:54,485 --> 00:17:57,110 |
|
1607 but we are processing a string of |
|
1608 |
|
1609 350 |
|
1610 00:17:57,110 --> 00:18:00,575 |
|
1611 1000 days so that success. |
|
1612 |
|
1613 351 |
|
1614 00:18:00,575 --> 00:18:04,775 |
|
1615 So this speed is also explained |
|
1616 if you look at the sizes. |
|
1617 |
|
1618 352 |
|
1619 00:18:04,775 --> 00:18:08,975 |
|
1620 Since we now have this explicit |
|
1621 and times constructor, |
|
1622 |
|
1623 353 |
|
1624 00:18:08,975 --> 00:18:11,930 |
|
1625 it doesn't really matter |
|
1626 how big this n is. |
|
1627 |
|
1628 354 |
|
1629 00:18:11,930 --> 00:18:14,540 |
|
1630 This evil one reg |
|
1631 expression will always be |
|
1632 |
|
1633 355 |
|
1634 00:18:14,540 --> 00:18:17,195 |
|
1635 of this size seven, |
|
1636 the beginning. |
|
1637 |
|
1638 356 |
|
1639 00:18:17,195 --> 00:18:20,315 |
|
1640 And you can also see if you |
|
1641 now build the derivatives, |
|
1642 |
|
1643 357 |
|
1644 00:18:20,315 --> 00:18:22,550 |
|
1645 they still grow in size, |
|
1646 |
|
1647 358 |
|
1648 00:18:22,550 --> 00:18:24,740 |
|
1649 but much more moderately. |
|
1650 |
|
1651 359 |
|
1652 00:18:24,740 --> 00:18:28,100 |
|
1653 And let's try out this |
|
1654 example, this 20 a. |
|
1655 |
|
1656 360 |
|
1657 00:18:28,100 --> 00:18:31,685 |
|
1658 So we build the derivative |
|
1659 according to 20 character A's. |
|
1660 |
|
1661 361 |
|
1662 00:18:31,685 --> 00:18:33,890 |
|
1663 In the earlier example, |
|
1664 |
|
1665 362 |
|
1666 00:18:33,890 --> 00:18:35,780 |
|
1667 we ended up this a |
|
1668 wreck expression which |
|
1669 |
|
1670 363 |
|
1671 00:18:35,780 --> 00:18:37,895 |
|
1672 had like 8 million plus nodes. |
|
1673 |
|
1674 364 |
|
1675 00:18:37,895 --> 00:18:39,830 |
|
1676 And if we do this now, |
|
1677 |
|
1678 365 |
|
1679 00:18:39,830 --> 00:18:43,205 |
|
1680 then we just have a wreck |
|
1681 expression with 211 nodes. |
|
1682 |
|
1683 366 |
|
1684 00:18:43,205 --> 00:18:44,750 |
|
1685 And that is much smaller and |
|
1686 |
|
1687 367 |
|
1688 00:18:44,750 --> 00:18:47,165 |
|
1689 all the calculations |
|
1690 would be much quicker. |
|
1691 |
|
1692 368 |
|
1693 00:18:47,165 --> 00:18:49,550 |
|
1694 So yeah, there's |
|
1695 |
|
1696 369 |
|
1697 00:18:49,550 --> 00:18:52,205 |
|
1698 this push off CKY algorithm |
|
1699 and this improvement. |
|
1700 |
|
1701 370 |
|
1702 00:18:52,205 --> 00:18:54,890 |
|
1703 We're now running |
|
1704 circles around Ruby and |
|
1705 |
|
1706 371 |
|
1707 00:18:54,890 --> 00:18:58,445 |
|
1708 Python because they're just |
|
1709 stuck here at the beginning. |
|
1710 |
|
1711 372 |
|
1712 00:18:58,445 --> 00:19:00,230 |
|
1713 Because they need already |
|
1714 |
|
1715 373 |
|
1716 00:19:00,230 --> 00:19:02,975 |
|
1717 like half a minute |
|
1718 for just 30 a's. |
|
1719 |
|
1720 374 |
|
1721 00:19:02,975 --> 00:19:05,930 |
|
1722 We now can do something |
|
1723 like thousand a's. |
|
1724 |
|
1725 375 |
|
1726 00:19:05,930 --> 00:19:07,580 |
|
1727 And in reasonable time. |
|
1728 |
|
1729 376 |
|
1730 00:19:07,580 --> 00:19:09,740 |
|
1731 I think this must be |
|
1732 timing I obtained with |
|
1733 |
|
1734 377 |
|
1735 00:19:09,740 --> 00:19:12,635 |
|
1736 my older laptop some time ago. |
|
1737 |
|
1738 378 |
|
1739 00:19:12,635 --> 00:19:14,210 |
|
1740 Because remember we |
|
1741 had something like |
|
1742 |
|
1743 379 |
|
1744 00:19:14,210 --> 00:19:16,670 |
|
1745 six seconds here, it says 15. |
|
1746 |
|
1747 380 |
|
1748 00:19:16,670 --> 00:19:18,080 |
|
1749 So you always have to take |
|
1750 |
|
1751 381 |
|
1752 00:19:18,080 --> 00:19:20,885 |
|
1753 these times with |
|
1754 the pinch of salt. |
|
1755 |
|
1756 382 |
|
1757 00:19:20,885 --> 00:19:22,670 |
|
1758 It's essentially only the trend, |
|
1759 |
|
1760 383 |
|
1761 00:19:22,670 --> 00:19:25,100 |
|
1762 but it's clear we are |
|
1763 much, much better. |
|
1764 |
|
1765 384 |
|
1766 00:19:25,100 --> 00:19:27,065 |
|
1767 So we have worked a lot, |
|
1768 |
|
1769 385 |
|
1770 00:19:27,065 --> 00:19:30,720 |
|
1771 but we also got something |
|
1772 for it in return. |