diff --git a/assignment-2/main.pdf b/assignment-2/main.pdf index 3421058..851799f 100644 --- a/assignment-2/main.pdf +++ b/assignment-2/main.pdf @@ -4,8 +4,8 @@ 1 0 obj << /Type /Pages - /Count 1 - /Kids [112 0 R] + /Count 2 + /Kids [385 0 R 390 0 R] >> endobj @@ -13,19 +13,20 @@ endobj << /Type /Outlines /First 3 0 R - /Last 3 0 R - /Count 1 + /Last 7 0 R + /Count 2 >> endobj 3 0 obj << /Parent 2 0 R + /Next 7 0 R /First 4 0 R - /Last 5 0 R - /Count -2 + /Last 6 0 R + /Count -3 /Title (task 1) - /Dest 110 0 R + /Dest 382 0 R >> endobj @@ -34,26 +35,45 @@ endobj /Parent 3 0 R /Next 5 0 R /Title (a\)) - /Dest 108 0 R + /Dest 379 0 R >> endobj 5 0 obj << /Parent 3 0 R + /Next 6 0 R /Prev 4 0 R /Title (b\)) - /Dest 109 0 R + /Dest 380 0 R >> endobj 6 0 obj << - /Nums [0 81 0 R] + /Parent 3 0 R + /Prev 5 0 R + /Title (c\)) + /Dest 381 0 R >> endobj 7 0 obj +<< + /Parent 2 0 R + /Prev 3 0 R + /Title (other) + /Dest 383 0 R +>> +endobj + +8 0 obj +<< + /Nums [0 345 0 R 1 346 0 R] +>> +endobj + +9 0 obj << /Type /StructTreeRoot /RoleMap << @@ -63,118 +83,100 @@ endobj /Strong /Span /Em /Span >> - /K [9 0 R] + /K [12 0 R] /ParentTree << - /Nums [0 73 0 R 1 8 0 R] + /Nums [0 337 0 R 1 10 0 R 2 14 0 R 3 14 0 R 4 14 0 R 5 11 0 R] >> - /ParentTreeNextKey 2 ->> -endobj - -8 0 obj -[80 0 R 80 0 R 79 0 R 76 0 R 74 0 R 72 0 R 72 0 R 73 0 R 72 0 R 72 0 R 72 0 R 72 0 R 71 0 R 69 0 R 69 0 R 68 0 R 66 0 R 67 0 R 64 0 R 62 0 R 63 0 R 60 0 R 58 0 R 59 0 R 56 0 R 54 0 R 55 0 R 49 0 R 51 0 R 51 0 R 51 0 R 49 0 R 50 0 R 50 0 R 50 0 R 50 0 R 49 0 R 43 0 R 48 0 R 43 0 R 43 0 R 47 0 R 43 0 R 43 0 R 46 0 R 46 0 R 46 0 R 46 0 R 43 0 R 43 0 R 45 0 R 43 0 R 44 0 R 43 0 R 43 0 R 41 0 R 42 0 R 41 0 R 41 0 R 40 0 R 40 0 R 40 0 R 40 0 R 40 0 R 40 0 R 40 0 R 40 0 R 40 0 R 40 0 R 40 0 R 40 0 R 40 0 R 40 0 R 40 0 R 40 0 R 40 0 R 40 0 R 40 0 R 39 0 R 37 0 R 38 0 R 37 0 R 37 0 R 36 0 R 35 0 R 35 0 R 35 0 R 35 0 R 35 0 R 35 0 R 35 0 R 35 0 R 35 0 R 35 0 R 35 0 R 35 0 R 35 0 R 35 0 R 35 0 R 32 0 R 31 0 R 31 0 R 31 0 R 31 0 R 31 0 R 31 0 R 31 0 R 31 0 R 31 0 R 31 0 R 31 0 R 31 0 R 27 0 R 27 0 R 26 0 R 25 0 R 25 0 R 25 0 R 25 0 R 25 0 R 25 0 R 25 0 R 25 0 R 25 0 R 25 0 R 25 0 R 25 0 R 25 0 R 25 0 R 25 0 R 25 0 R 25 0 R 25 0 R 25 0 R 25 0 R 25 0 R 25 0 R 25 0 R 25 0 R 25 0 R 25 0 R 25 0 R 25 0 R 25 0 R 25 0 R 25 0 R 25 0 R 25 0 R 25 0 R 25 0 R 25 0 R 25 0 R 24 0 R 18 0 R 23 0 R 18 0 R 22 0 R 22 0 R 22 0 R 22 0 R 22 0 R 22 0 R 22 0 R 18 0 R 21 0 R 18 0 R 18 0 R 20 0 R 18 0 R 19 0 R 19 0 R 19 0 R 19 0 R 19 0 R 19 0 R 19 0 R 18 0 R 18 0 R 18 0 R 17 0 R 12 0 R 12 0 R 15 0 R 15 0 R 15 0 R 15 0 R 15 0 R 15 0 R 12 0 R 12 0 R 14 0 R 14 0 R 14 0 R 14 0 R 12 0 R 12 0 R 13 0 R 13 0 R 13 0 R 13 0 R 12 0 R 12 0 R 12 0 R 11 0 R 10 0 R 10 0 R 10 0 R 10 0 R 10 0 R 10 0 R 10 0 R 10 0 R 10 0 R 10 0 R 10 0 R 10 0 R 10 0 R 10 0 R 10 0 R 10 0 R 10 0 R 10 0 R 10 0 R 10 0 R 10 0 R 10 0 R 10 0 R 10 0 R 10 0 R 10 0 R 10 0 R 10 0 R 10 0 R 10 0 R 10 0 R 10 0 R 10 0 R 10 0 R 10 0 R] -endobj - -9 0 obj -<< - /Type /StructElem - /S /Document - /P 7 0 R - /K [80 0 R 77 0 R 75 0 R 72 0 R 69 0 R 52 0 R 49 0 R 43 0 R 41 0 R 40 0 R 39 0 R 37 0 R 28 0 R 27 0 R 26 0 R 25 0 R 24 0 R 18 0 R 12 0 R 11 0 R 10 0 R] + /ParentTreeNextKey 6 >> endobj 10 0 obj -<< - /Type /StructElem - /S /Formula - /P 9 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238] - /Pg 112 0 R ->> +[344 0 R 344 0 R 343 0 R 340 0 R 338 0 R 336 0 R 336 0 R 337 0 R 336 0 R 336 0 R 336 0 R 336 0 R 335 0 R 333 0 R 333 0 R 332 0 R 330 0 R 331 0 R 328 0 R 326 0 R 327 0 R 324 0 R 322 0 R 323 0 R 320 0 R 318 0 R 319 0 R 313 0 R 315 0 R 315 0 R 315 0 R 313 0 R 314 0 R 314 0 R 314 0 R 314 0 R 313 0 R 307 0 R 312 0 R 307 0 R 307 0 R 311 0 R 307 0 R 307 0 R 310 0 R 310 0 R 310 0 R 310 0 R 307 0 R 307 0 R 309 0 R 307 0 R 308 0 R 307 0 R 307 0 R 305 0 R 306 0 R 305 0 R 305 0 R 304 0 R 304 0 R 304 0 R 304 0 R 304 0 R 304 0 R 304 0 R 304 0 R 304 0 R 304 0 R 304 0 R 304 0 R 304 0 R 304 0 R 304 0 R 304 0 R 304 0 R 304 0 R 304 0 R 303 0 R 301 0 R 302 0 R 301 0 R 301 0 R 300 0 R 299 0 R 299 0 R 299 0 R 299 0 R 299 0 R 299 0 R 299 0 R 299 0 R 299 0 R 299 0 R 299 0 R 299 0 R 299 0 R 299 0 R 299 0 R 296 0 R 295 0 R 295 0 R 295 0 R 295 0 R 295 0 R 295 0 R 295 0 R 295 0 R 295 0 R 295 0 R 295 0 R 295 0 R 291 0 R 291 0 R 290 0 R 289 0 R 289 0 R 289 0 R 289 0 R 289 0 R 289 0 R 289 0 R 289 0 R 289 0 R 289 0 R 289 0 R 289 0 R 289 0 R 289 0 R 289 0 R 289 0 R 289 0 R 289 0 R 289 0 R 289 0 R 289 0 R 289 0 R 289 0 R 289 0 R 289 0 R 289 0 R 289 0 R 289 0 R 289 0 R 289 0 R 289 0 R 289 0 R 289 0 R 289 0 R 289 0 R 289 0 R 289 0 R 288 0 R 282 0 R 287 0 R 282 0 R 286 0 R 286 0 R 286 0 R 286 0 R 286 0 R 286 0 R 286 0 R 282 0 R 285 0 R 282 0 R 282 0 R 284 0 R 282 0 R 283 0 R 283 0 R 283 0 R 283 0 R 283 0 R 283 0 R 283 0 R 282 0 R 282 0 R 282 0 R 281 0 R 276 0 R 276 0 R 279 0 R 279 0 R 279 0 R 279 0 R 279 0 R 279 0 R 276 0 R 276 0 R 278 0 R 278 0 R 278 0 R 278 0 R 276 0 R 276 0 R 277 0 R 277 0 R 277 0 R 277 0 R 276 0 R 276 0 R 276 0 R 275 0 R 274 0 R 274 0 R 274 0 R 274 0 R 274 0 R 274 0 R 274 0 R 274 0 R 274 0 R 274 0 R 274 0 R 274 0 R 274 0 R 274 0 R 274 0 R 274 0 R 274 0 R 274 0 R 274 0 R 274 0 R 274 0 R 274 0 R 274 0 R 274 0 R 274 0 R 274 0 R 274 0 R 274 0 R 274 0 R 274 0 R 274 0 R 274 0 R 274 0 R 274 0 R 274 0 R 273 0 R 271 0 R 271 0 R 271 0 R 270 0 R 270 0 R 270 0 R 270 0 R 267 0 R 265 0 R 264 0 R 264 0 R 263 0 R 263 0 R 263 0 R 262 0 R 260 0 R 256 0 R 256 0 R 255 0 R 254 0 R 254 0 R 253 0 R 252 0 R 250 0 R 246 0 R 245 0 R 244 0 R 244 0 R 244 0 R 244 0 R 244 0 R 244 0 R 244 0 R 242 0 R 243 0 R 240 0 R 234 0 R 234 0 R 233 0 R 232 0 R 231 0 R 230 0 R] endobj 11 0 obj -<< - /Type /StructElem - /S /P - /P 9 0 R - /K [203] - /Pg 112 0 R ->> +[228 0 R 222 0 R 222 0 R 221 0 R 220 0 R 219 0 R 218 0 R 216 0 R 212 0 R 210 0 R 205 0 R 201 0 R 200 0 R 200 0 R 199 0 R 199 0 R 199 0 R 199 0 R 199 0 R 199 0 R 199 0 R 197 0 R 198 0 R 195 0 R 189 0 R 189 0 R 187 0 R 181 0 R 181 0 R 180 0 R 179 0 R 178 0 R 177 0 R 177 0 R 177 0 R 177 0 R 177 0 R 177 0 R 177 0 R 177 0 R 177 0 R 177 0 R 177 0 R 177 0 R 177 0 R 177 0 R 175 0 R 169 0 R 169 0 R 168 0 R 167 0 R 166 0 R 165 0 R 165 0 R 165 0 R 165 0 R 165 0 R 165 0 R 165 0 R 165 0 R 165 0 R 165 0 R 165 0 R 165 0 R 165 0 R 165 0 R 163 0 R 157 0 R 156 0 R 155 0 R 154 0 R 153 0 R 153 0 R 153 0 R 153 0 R 153 0 R 153 0 R 153 0 R 153 0 R 151 0 R 144 0 R 138 0 R 138 0 R 138 0 R 137 0 R 135 0 R 129 0 R 129 0 R 128 0 R 127 0 R 126 0 R 125 0 R 125 0 R 125 0 R 125 0 R 123 0 R 116 0 R 110 0 R 110 0 R 110 0 R 108 0 R 102 0 R 101 0 R 100 0 R 100 0 R 100 0 R 100 0 R 100 0 R 100 0 R 100 0 R 100 0 R 100 0 R 100 0 R 100 0 R 100 0 R 100 0 R 100 0 R 98 0 R 99 0 R 96 0 R 88 0 R 88 0 R 87 0 R 86 0 R 85 0 R 84 0 R 82 0 R 76 0 R 74 0 R 68 0 R 67 0 R 66 0 R 66 0 R 66 0 R 66 0 R 66 0 R 66 0 R 66 0 R 66 0 R 66 0 R 66 0 R 66 0 R 66 0 R 66 0 R 66 0 R 64 0 R 65 0 R 62 0 R 54 0 R 54 0 R 53 0 R 52 0 R 51 0 R 50 0 R 48 0 R 42 0 R 40 0 R 36 0 R 34 0 R 30 0 R 29 0 R 28 0 R 28 0 R 28 0 R 28 0 R 28 0 R 28 0 R 28 0 R 28 0 R 28 0 R 28 0 R 28 0 R 28 0 R 26 0 R 24 0 R 17 0 R 19 0 R 19 0 R 19 0 R 19 0 R 17 0 R 17 0 R 18 0 R 17 0 R 16 0 R 13 0 R 13 0 R 14 0 R 14 0 R 14 0 R] endobj 12 0 obj << /Type /StructElem - /S /P + /S /Document /P 9 0 R - /K [16 0 R 180 181 15 0 R 188 189 14 0 R 194 195 13 0 R 200 201 202] - /Pg 112 0 R + /K [344 0 R 341 0 R 339 0 R 336 0 R 333 0 R 316 0 R 313 0 R 307 0 R 305 0 R 304 0 R 303 0 R 301 0 R 292 0 R 291 0 R 290 0 R 289 0 R 288 0 R 282 0 R 276 0 R 275 0 R 274 0 R 271 0 R 20 0 R 17 0 R 15 0 R 13 0 R] >> endobj 13 0 obj << /Type /StructElem - /S /Formula + /S /P /P 12 0 R - /K [196 197 198 199] - /Pg 112 0 R + /K [185 186 14 0 R] + /Pg 390 0 R >> endobj 14 0 obj << /Type /StructElem - /S /Formula - /P 12 0 R - /K [190 191 192 193] - /Pg 112 0 R + /S /Link + /P 13 0 R + /K [187 << + /Type /OBJR + /Pg 390 0 R + /Obj 387 0 R + >> 188 << + /Type /OBJR + /Pg 390 0 R + /Obj 388 0 R + >> 189 << + /Type /OBJR + /Pg 390 0 R + /Obj 389 0 R + >>] + /Pg 390 0 R >> endobj 15 0 obj << /Type /StructElem - /S /Formula + /S /P /P 12 0 R - /K [182 183 184 185 186 187] - /Pg 112 0 R + /K [16 0 R] >> endobj 16 0 obj << /Type /StructElem - /S /H3 - /P 12 0 R - /T (b\)) - /K [17 0 R] + /S /H2 + /P 15 0 R + /T (other) + /K [184] + /Pg 390 0 R >> endobj 17 0 obj << /Type /StructElem - /S /Strong - /P 16 0 R - /K [179] - /Pg 112 0 R + /S /P + /P 12 0 R + /K [175 19 0 R 180 181 18 0 R 183] + /Pg 390 0 R >> endobj 18 0 obj << /Type /StructElem - /S /P - /P 9 0 R - /K [153 23 0 R 155 22 0 R 163 21 0 R 165 166 20 0 R 168 19 0 R 176 177 178] - /Pg 112 0 R + /S /Formula + /P 17 0 R + /K [182] + /Pg 390 0 R >> endobj @@ -182,316 +184,329 @@ endobj << /Type /StructElem /S /Formula - /P 18 0 R - /K [169 170 171 172 173 174 175] - /Pg 112 0 R + /P 17 0 R + /K [176 177 178 179] + /Pg 390 0 R >> endobj 20 0 obj << /Type /StructElem - /S /Formula - /P 18 0 R - /K [167] - /Pg 112 0 R + /S /Div + /P 12 0 R + /K [268 0 R 21 0 R] >> endobj 21 0 obj << /Type /StructElem - /S /Formula - /P 18 0 R - /K [164] - /Pg 112 0 R + /S /Div + /P 20 0 R + /K [22 0 R] >> endobj 22 0 obj << /Type /StructElem - /S /Formula - /P 18 0 R - /K [156 157 158 159 160 161 162] - /Pg 112 0 R + /S /Div + /P 21 0 R + /K [266 0 R 261 0 R 259 0 R 258 0 R 257 0 R 251 0 R 249 0 R 248 0 R 247 0 R 241 0 R 239 0 R 238 0 R 237 0 R 236 0 R 235 0 R 229 0 R 227 0 R 226 0 R 225 0 R 224 0 R 223 0 R 217 0 R 215 0 R 214 0 R 213 0 R 211 0 R 209 0 R 208 0 R 207 0 R 206 0 R 204 0 R 203 0 R 202 0 R 196 0 R 194 0 R 193 0 R 192 0 R 191 0 R 190 0 R 188 0 R 186 0 R 185 0 R 184 0 R 183 0 R 182 0 R 176 0 R 174 0 R 173 0 R 172 0 R 171 0 R 170 0 R 164 0 R 162 0 R 161 0 R 160 0 R 159 0 R 158 0 R 152 0 R 150 0 R 149 0 R 148 0 R 147 0 R 146 0 R 145 0 R 143 0 R 142 0 R 141 0 R 140 0 R 139 0 R 136 0 R 134 0 R 133 0 R 132 0 R 131 0 R 130 0 R 124 0 R 122 0 R 121 0 R 120 0 R 119 0 R 118 0 R 117 0 R 115 0 R 114 0 R 113 0 R 112 0 R 111 0 R 109 0 R 107 0 R 106 0 R 105 0 R 104 0 R 103 0 R 97 0 R 95 0 R 94 0 R 93 0 R 92 0 R 91 0 R 90 0 R 89 0 R 83 0 R 81 0 R 80 0 R 79 0 R 78 0 R 77 0 R 75 0 R 73 0 R 72 0 R 71 0 R 70 0 R 69 0 R 63 0 R 61 0 R 60 0 R 59 0 R 58 0 R 57 0 R 56 0 R 55 0 R 49 0 R 47 0 R 46 0 R 45 0 R 44 0 R 43 0 R 41 0 R 39 0 R 38 0 R 37 0 R 35 0 R 33 0 R 32 0 R 31 0 R 27 0 R 25 0 R 23 0 R] >> endobj 23 0 obj << /Type /StructElem - /S /Formula - /P 18 0 R - /K [154] - /Pg 112 0 R + /S /Div + /P 22 0 R + /K [24 0 R] >> endobj 24 0 obj << /Type /StructElem - /S /P - /P 9 0 R - /K [152] - /Pg 112 0 R + /S /Strong + /P 23 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [174] + /Pg 390 0 R >> endobj 25 0 obj << /Type /StructElem - /S /Formula - /P 9 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151] - /Pg 112 0 R + /S /Div + /P 22 0 R + /K [26 0 R] >> endobj 26 0 obj << /Type /StructElem - /S /P - /P 9 0 R - /K [114] - /Pg 112 0 R + /S /Span + /P 25 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [173] + /Pg 390 0 R >> endobj 27 0 obj << /Type /StructElem - /S /P - /P 9 0 R - /K [112 113] - /Pg 112 0 R + /S /Div + /P 22 0 R + /K [30 0 R 29 0 R 28 0 R] >> endobj 28 0 obj << /Type /StructElem - /S /L - /P 9 0 R + /S /Formula + /P 27 0 R /A [<< - /O /List - /ListNumbering /Circle + /O /Layout + /Placement /Block >>] - /K [33 0 R 29 0 R] + /K [161 162 163 164 165 166 167 168 169 170 171 172] + /Pg 390 0 R >> endobj 29 0 obj << /Type /StructElem - /S /LI - /P 28 0 R - /K [32 0 R 30 0 R] + /S /Span + /P 27 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [160] + /Pg 390 0 R >> endobj 30 0 obj << /Type /StructElem - /S /LBody - /P 29 0 R - /K [31 0 R] + /S /Strong + /P 27 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [159] + /Pg 390 0 R >> endobj 31 0 obj << /Type /StructElem - /S /Formula - /P 30 0 R - /K [100 101 102 103 104 105 106 107 108 109 110 111] - /Pg 112 0 R + /S /Div + /P 22 0 R + /K [] >> endobj 32 0 obj << /Type /StructElem - /S /Lbl - /P 29 0 R - /K [99] - /Pg 112 0 R + /S /Div + /P 22 0 R + /K [] >> endobj 33 0 obj << /Type /StructElem - /S /LI - /P 28 0 R - /K [36 0 R 34 0 R] + /S /Div + /P 22 0 R + /K [34 0 R] >> endobj 34 0 obj << /Type /StructElem - /S /LBody + /S /Span /P 33 0 R - /K [35 0 R] + /A [<< + /O /Layout + /Placement /Block + >>] + /K [158] + /Pg 390 0 R >> endobj 35 0 obj << /Type /StructElem - /S /Formula - /P 34 0 R - /K [84 85 86 87 88 89 90 91 92 93 94 95 96 97 98] - /Pg 112 0 R + /S /Div + /P 22 0 R + /K [36 0 R] >> endobj 36 0 obj << /Type /StructElem - /S /Lbl - /P 33 0 R - /K [83] - /Pg 112 0 R + /S /Strong + /P 35 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [157] + /Pg 390 0 R >> endobj 37 0 obj << /Type /StructElem - /S /P - /P 9 0 R - /K [79 38 0 R 81 82] - /Pg 112 0 R + /S /Div + /P 22 0 R + /K [] >> endobj 38 0 obj << /Type /StructElem - /S /Formula - /P 37 0 R - /K [80] - /Pg 112 0 R + /S /Div + /P 22 0 R + /K [] >> endobj 39 0 obj << /Type /StructElem - /S /P - /P 9 0 R - /K [78] - /Pg 112 0 R + /S /Div + /P 22 0 R + /K [40 0 R] >> endobj 40 0 obj << /Type /StructElem - /S /Formula - /P 9 0 R + /S /Span + /P 39 0 R /A [<< /O /Layout /Placement /Block >>] - /K [59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77] - /Pg 112 0 R + /K [156] + /Pg 390 0 R >> endobj 41 0 obj << /Type /StructElem - /S /P - /P 9 0 R - /K [55 42 0 R 57 58] - /Pg 112 0 R + /S /Div + /P 22 0 R + /K [42 0 R] >> endobj 42 0 obj << /Type /StructElem - /S /Formula + /S /Strong /P 41 0 R - /K [56] - /Pg 112 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [155] + /Pg 390 0 R >> endobj 43 0 obj << /Type /StructElem - /S /P - /P 9 0 R - /K [37 48 0 R 39 40 47 0 R 42 43 46 0 R 48 49 45 0 R 51 44 0 R 53 54] - /Pg 112 0 R + /S /Div + /P 22 0 R + /K [] >> endobj 44 0 obj << /Type /StructElem - /S /Formula - /P 43 0 R - /K [52] - /Pg 112 0 R + /S /Div + /P 22 0 R + /K [] >> endobj 45 0 obj << /Type /StructElem - /S /Formula - /P 43 0 R - /K [50] - /Pg 112 0 R + /S /Div + /P 22 0 R + /K [] >> endobj 46 0 obj << /Type /StructElem - /S /Formula - /P 43 0 R - /K [44 45 46 47] - /Pg 112 0 R + /S /Div + /P 22 0 R + /K [] >> endobj 47 0 obj << /Type /StructElem - /S /Formula - /P 43 0 R - /K [41] - /Pg 112 0 R + /S /Div + /P 22 0 R + /K [48 0 R] >> endobj 48 0 obj << /Type /StructElem - /S /Formula - /P 43 0 R - /K [38] - /Pg 112 0 R + /S /Span + /P 47 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [154] + /Pg 390 0 R >> endobj 49 0 obj << /Type /StructElem - /S /P - /P 9 0 R - /K [27 51 0 R 31 50 0 R 36] - /Pg 112 0 R + /S /Div + /P 22 0 R + /K [54 0 R 53 0 R 52 0 R 51 0 R 50 0 R] >> endobj @@ -500,260 +515,291 @@ endobj /Type /StructElem /S /Formula /P 49 0 R - /K [32 33 34 35] - /Pg 112 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [153] + /Pg 390 0 R >> endobj 51 0 obj << /Type /StructElem - /S /Formula + /S /Span /P 49 0 R - /K [28 29 30] - /Pg 112 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [152] + /Pg 390 0 R >> endobj 52 0 obj << /Type /StructElem - /S /L - /P 9 0 R + /S /Formula + /P 49 0 R /A [<< - /O /List - /ListNumbering /Circle + /O /Layout + /Placement /Block >>] - /K [65 0 R 61 0 R 57 0 R 53 0 R] + /K [151] + /Pg 390 0 R >> endobj 53 0 obj << /Type /StructElem - /S /LI - /P 52 0 R - /K [56 0 R 54 0 R] + /S /Span + /P 49 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [150] + /Pg 390 0 R >> endobj 54 0 obj << /Type /StructElem - /S /LBody - /P 53 0 R - /K [25 55 0 R] - /Pg 112 0 R + /S /Formula + /P 49 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [148 149] + /Pg 390 0 R >> endobj 55 0 obj << /Type /StructElem - /S /Formula - /P 54 0 R - /K [26] - /Pg 112 0 R + /S /Div + /P 22 0 R + /K [] >> endobj 56 0 obj << /Type /StructElem - /S /Lbl - /P 53 0 R - /K [24] - /Pg 112 0 R + /S /Div + /P 22 0 R + /K [] >> endobj 57 0 obj << /Type /StructElem - /S /LI - /P 52 0 R - /K [60 0 R 58 0 R] + /S /Div + /P 22 0 R + /K [] >> endobj 58 0 obj << /Type /StructElem - /S /LBody - /P 57 0 R - /K [22 59 0 R] - /Pg 112 0 R + /S /Div + /P 22 0 R + /K [] >> endobj 59 0 obj << /Type /StructElem - /S /Formula - /P 58 0 R - /K [23] - /Pg 112 0 R + /S /Div + /P 22 0 R + /K [] >> endobj 60 0 obj << /Type /StructElem - /S /Lbl - /P 57 0 R - /K [21] - /Pg 112 0 R + /S /Div + /P 22 0 R + /K [] >> endobj 61 0 obj << /Type /StructElem - /S /LI - /P 52 0 R - /K [64 0 R 62 0 R] + /S /Div + /P 22 0 R + /K [62 0 R] >> endobj 62 0 obj << /Type /StructElem - /S /LBody + /S /Span /P 61 0 R - /K [19 63 0 R] - /Pg 112 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [147] + /Pg 390 0 R >> endobj 63 0 obj << /Type /StructElem - /S /Formula - /P 62 0 R - /K [20] - /Pg 112 0 R + /S /Div + /P 22 0 R + /K [68 0 R 67 0 R 66 0 R 65 0 R 64 0 R] >> endobj 64 0 obj << /Type /StructElem - /S /Lbl - /P 61 0 R - /K [18] - /Pg 112 0 R + /S /Span + /P 63 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [145] + /Pg 390 0 R >> endobj 65 0 obj << /Type /StructElem - /S /LI - /P 52 0 R - /K [68 0 R 66 0 R] + /S /Strong + /P 63 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [146] + /Pg 390 0 R >> endobj 66 0 obj << /Type /StructElem - /S /LBody - /P 65 0 R - /K [16 67 0 R] - /Pg 112 0 R + /S /Formula + /P 63 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [131 132 133 134 135 136 137 138 139 140 141 142 143 144] + /Pg 390 0 R >> endobj 67 0 obj << /Type /StructElem - /S /Formula - /P 66 0 R - /K [17] - /Pg 112 0 R + /S /Span + /P 63 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [130] + /Pg 390 0 R >> endobj 68 0 obj << /Type /StructElem - /S /Lbl - /P 65 0 R - /K [15] - /Pg 112 0 R + /S /Strong + /P 63 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [129] + /Pg 390 0 R >> endobj 69 0 obj << /Type /StructElem - /S /P - /P 9 0 R - /K [70 0 R 13 14] - /Pg 112 0 R + /S /Div + /P 22 0 R + /K [] >> endobj 70 0 obj << /Type /StructElem - /S /H3 - /P 69 0 R - /T (a\)) - /K [71 0 R] + /S /Div + /P 22 0 R + /K [] >> endobj 71 0 obj << /Type /StructElem - /S /Strong - /P 70 0 R - /K [12] - /Pg 112 0 R + /S /Div + /P 22 0 R + /K [] >> endobj 72 0 obj << /Type /StructElem - /S /P - /P 9 0 R - /K [74 0 R 5 6 73 0 R 8 9 10 11] - /Pg 112 0 R + /S /Div + /P 22 0 R + /K [] >> endobj 73 0 obj << /Type /StructElem - /S /Link - /P 72 0 R - /K [7 << - /Type /OBJR - /Pg 112 0 R - /Obj 111 0 R - >>] - /Pg 112 0 R + /S /Div + /P 22 0 R + /K [74 0 R] >> endobj 74 0 obj << /Type /StructElem - /S /H2 - /P 72 0 R - /T (task 1) - /K [4] - /Pg 112 0 R + /S /Span + /P 73 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [128] + /Pg 390 0 R >> endobj 75 0 obj << /Type /StructElem - /S /P - /P 9 0 R + /S /Div + /P 22 0 R /K [76 0 R] >> endobj @@ -763,8 +809,12 @@ endobj /Type /StructElem /S /Strong /P 75 0 R - /K [3] - /Pg 112 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [127] + /Pg 390 0 R >> endobj @@ -772,8 +822,8 @@ endobj << /Type /StructElem /S /Div - /P 9 0 R - /K [78 0 R] + /P 22 0 R + /K [] >> endobj @@ -781,36 +831,2921 @@ endobj << /Type /StructElem /S /Div - /P 77 0 R - /K [79 0 R] + /P 22 0 R + /K [] >> endobj 79 0 obj << /Type /StructElem - /S /Span - /P 78 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [2] - /Pg 112 0 R + /S /Div + /P 22 0 R + /K [] >> endobj 80 0 obj << /Type /StructElem - /S /P - /P 9 0 R - /K [0 1] - /Pg 112 0 R + /S /Div + /P 22 0 R + /K [] >> endobj 81 0 obj +<< + /Type /StructElem + /S /Div + /P 22 0 R + /K [82 0 R] +>> +endobj + +82 0 obj +<< + /Type /StructElem + /S /Span + /P 81 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [126] + /Pg 390 0 R +>> +endobj + +83 0 obj +<< + /Type /StructElem + /S /Div + /P 22 0 R + /K [88 0 R 87 0 R 86 0 R 85 0 R 84 0 R] +>> +endobj + +84 0 obj +<< + /Type /StructElem + /S /Formula + /P 83 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [125] + /Pg 390 0 R +>> +endobj + +85 0 obj +<< + /Type /StructElem + /S /Span + /P 83 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [124] + /Pg 390 0 R +>> +endobj + +86 0 obj +<< + /Type /StructElem + /S /Formula + /P 83 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [123] + /Pg 390 0 R +>> +endobj + +87 0 obj +<< + /Type /StructElem + /S /Span + /P 83 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [122] + /Pg 390 0 R +>> +endobj + +88 0 obj +<< + /Type /StructElem + /S /Formula + /P 83 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [120 121] + /Pg 390 0 R +>> +endobj + +89 0 obj +<< + /Type /StructElem + /S /Div + /P 22 0 R + /K [] +>> +endobj + +90 0 obj +<< + /Type /StructElem + /S /Div + /P 22 0 R + /K [] +>> +endobj + +91 0 obj +<< + /Type /StructElem + /S /Div + /P 22 0 R + /K [] +>> +endobj + +92 0 obj +<< + /Type /StructElem + /S /Div + /P 22 0 R + /K [] +>> +endobj + +93 0 obj +<< + /Type /StructElem + /S /Div + /P 22 0 R + /K [] +>> +endobj + +94 0 obj +<< + /Type /StructElem + /S /Div + /P 22 0 R + /K [] +>> +endobj + +95 0 obj +<< + /Type /StructElem + /S /Div + /P 22 0 R + /K [96 0 R] +>> +endobj + +96 0 obj +<< + /Type /StructElem + /S /Span + /P 95 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [119] + /Pg 390 0 R +>> +endobj + +97 0 obj +<< + /Type /StructElem + /S /Div + /P 22 0 R + /K [102 0 R 101 0 R 100 0 R 99 0 R 98 0 R] +>> +endobj + +98 0 obj +<< + /Type /StructElem + /S /Span + /P 97 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [117] + /Pg 390 0 R +>> +endobj + +99 0 obj +<< + /Type /StructElem + /S /Strong + /P 97 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [118] + /Pg 390 0 R +>> +endobj + +100 0 obj +<< + /Type /StructElem + /S /Formula + /P 97 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [103 104 105 106 107 108 109 110 111 112 113 114 115 116] + /Pg 390 0 R +>> +endobj + +101 0 obj +<< + /Type /StructElem + /S /Span + /P 97 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [102] + /Pg 390 0 R +>> +endobj + +102 0 obj +<< + /Type /StructElem + /S /Strong + /P 97 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [101] + /Pg 390 0 R +>> +endobj + +103 0 obj +<< + /Type /StructElem + /S /Div + /P 22 0 R + /K [] +>> +endobj + +104 0 obj +<< + /Type /StructElem + /S /Div + /P 22 0 R + /K [] +>> +endobj + +105 0 obj +<< + /Type /StructElem + /S /Div + /P 22 0 R + /K [] +>> +endobj + +106 0 obj +<< + /Type /StructElem + /S /Div + /P 22 0 R + /K [] +>> +endobj + +107 0 obj +<< + /Type /StructElem + /S /Div + /P 22 0 R + /K [108 0 R] +>> +endobj + +108 0 obj +<< + /Type /StructElem + /S /Span + /P 107 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [100] + /Pg 390 0 R +>> +endobj + +109 0 obj +<< + /Type /StructElem + /S /Div + /P 22 0 R + /K [110 0 R] +>> +endobj + +110 0 obj +<< + /Type /StructElem + /S /Span + /P 109 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [97 98 99] + /Pg 390 0 R +>> +endobj + +111 0 obj +<< + /Type /StructElem + /S /Div + /P 22 0 R + /K [] +>> +endobj + +112 0 obj +<< + /Type /StructElem + /S /Div + /P 22 0 R + /K [] +>> +endobj + +113 0 obj +<< + /Type /StructElem + /S /Div + /P 22 0 R + /K [] +>> +endobj + +114 0 obj +<< + /Type /StructElem + /S /Div + /P 22 0 R + /K [] +>> +endobj + +115 0 obj +<< + /Type /StructElem + /S /Div + /P 22 0 R + /K [116 0 R] +>> +endobj + +116 0 obj +<< + /Type /StructElem + /S /Span + /P 115 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [96] + /Pg 390 0 R +>> +endobj + +117 0 obj +<< + /Type /StructElem + /S /Div + /P 22 0 R + /K [] +>> +endobj + +118 0 obj +<< + /Type /StructElem + /S /Div + /P 22 0 R + /K [] +>> +endobj + +119 0 obj +<< + /Type /StructElem + /S /Div + /P 22 0 R + /K [] +>> +endobj + +120 0 obj +<< + /Type /StructElem + /S /Div + /P 22 0 R + /K [] +>> +endobj + +121 0 obj +<< + /Type /StructElem + /S /Div + /P 22 0 R + /K [] +>> +endobj + +122 0 obj +<< + /Type /StructElem + /S /Div + /P 22 0 R + /K [123 0 R] +>> +endobj + +123 0 obj +<< + /Type /StructElem + /S /Span + /P 122 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [95] + /Pg 390 0 R +>> +endobj + +124 0 obj +<< + /Type /StructElem + /S /Div + /P 22 0 R + /K [129 0 R 128 0 R 127 0 R 126 0 R 125 0 R] +>> +endobj + +125 0 obj +<< + /Type /StructElem + /S /Formula + /P 124 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [91 92 93 94] + /Pg 390 0 R +>> +endobj + +126 0 obj +<< + /Type /StructElem + /S /Span + /P 124 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [90] + /Pg 390 0 R +>> +endobj + +127 0 obj +<< + /Type /StructElem + /S /Formula + /P 124 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [89] + /Pg 390 0 R +>> +endobj + +128 0 obj +<< + /Type /StructElem + /S /Span + /P 124 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [88] + /Pg 390 0 R +>> +endobj + +129 0 obj +<< + /Type /StructElem + /S /Formula + /P 124 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [86 87] + /Pg 390 0 R +>> +endobj + +130 0 obj +<< + /Type /StructElem + /S /Div + /P 22 0 R + /K [] +>> +endobj + +131 0 obj +<< + /Type /StructElem + /S /Div + /P 22 0 R + /K [] +>> +endobj + +132 0 obj +<< + /Type /StructElem + /S /Div + /P 22 0 R + /K [] +>> +endobj + +133 0 obj +<< + /Type /StructElem + /S /Div + /P 22 0 R + /K [] +>> +endobj + +134 0 obj +<< + /Type /StructElem + /S /Div + /P 22 0 R + /K [135 0 R] +>> +endobj + +135 0 obj +<< + /Type /StructElem + /S /Span + /P 134 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [85] + /Pg 390 0 R +>> +endobj + +136 0 obj +<< + /Type /StructElem + /S /Div + /P 22 0 R + /K [138 0 R 137 0 R] +>> +endobj + +137 0 obj +<< + /Type /StructElem + /S /Formula + /P 136 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [84] + /Pg 390 0 R +>> +endobj + +138 0 obj +<< + /Type /StructElem + /S /Span + /P 136 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [81 82 83] + /Pg 390 0 R +>> +endobj + +139 0 obj 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R] +>> +endobj + +151 0 obj +<< + /Type /StructElem + /S /Span + /P 150 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [79] + /Pg 390 0 R +>> +endobj + +152 0 obj +<< + /Type /StructElem + /S /Div + /P 22 0 R + /K [157 0 R 156 0 R 155 0 R 154 0 R 153 0 R] +>> +endobj + +153 0 obj +<< + /Type /StructElem + /S /Formula + /P 152 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [71 72 73 74 75 76 77 78] + /Pg 390 0 R +>> +endobj + +154 0 obj +<< + /Type /StructElem + /S /Span + /P 152 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [70] + /Pg 390 0 R +>> +endobj + +155 0 obj +<< + /Type /StructElem + /S /Formula + /P 152 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [69] + /Pg 390 0 R +>> +endobj + +156 0 obj +<< + /Type /StructElem + /S /Span + /P 152 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [68] + /Pg 390 0 R +>> +endobj + +157 0 obj +<< + /Type /StructElem + /S /Formula + /P 152 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [67] + /Pg 390 0 R +>> +endobj + +158 0 obj +<< + /Type /StructElem + /S /Div + /P 22 0 R + /K [] +>> +endobj + +159 0 obj +<< + /Type /StructElem + /S /Div + /P 22 0 R + /K [] +>> +endobj + +160 0 obj +<< + /Type /StructElem + /S /Div + /P 22 0 R + /K [] +>> +endobj + +161 0 obj +<< + /Type /StructElem + /S /Div + /P 22 0 R + /K [] +>> +endobj + +162 0 obj +<< + /Type /StructElem + /S /Div + /P 22 0 R + /K [163 0 R] +>> +endobj + +163 0 obj +<< + /Type /StructElem + /S /Span + /P 162 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [66] + /Pg 390 0 R +>> +endobj + +164 0 obj +<< + /Type /StructElem + /S /Div + /P 22 0 R + /K [169 0 R 168 0 R 167 0 R 166 0 R 165 0 R] +>> +endobj + +165 0 obj +<< + /Type /StructElem + /S /Formula + /P 164 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [52 53 54 55 56 57 58 59 60 61 62 63 64 65] + /Pg 390 0 R +>> +endobj + +166 0 obj +<< + /Type /StructElem + /S /Span + /P 164 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [51] + /Pg 390 0 R +>> +endobj + +167 0 obj +<< + /Type /StructElem + /S /Formula + /P 164 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [50] + /Pg 390 0 R +>> +endobj + +168 0 obj +<< + /Type /StructElem + /S /Span + /P 164 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [49] + /Pg 390 0 R +>> +endobj + +169 0 obj +<< + /Type /StructElem + /S /Formula + /P 164 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [47 48] + /Pg 390 0 R +>> +endobj + +170 0 obj +<< + /Type /StructElem + /S /Div + /P 22 0 R + /K [] +>> +endobj + +171 0 obj +<< + /Type /StructElem + /S /Div + /P 22 0 R + /K [] +>> +endobj + +172 0 obj +<< + /Type /StructElem + /S /Div + /P 22 0 R + /K [] +>> +endobj + +173 0 obj +<< + /Type /StructElem + /S /Div + /P 22 0 R + /K [] +>> +endobj + +174 0 obj +<< + /Type /StructElem + /S /Div + /P 22 0 R + /K [175 0 R] +>> +endobj + +175 0 obj +<< + /Type /StructElem + /S /Span + /P 174 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [46] + 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dd6p}ͧp{=.=<=1}t~.'9"!hIeZd%mN7 xvYHB%ŊE(.V"<`4ZX PO}Mu,h̓rWWr4v8dZunD˩N4ޚc/J3 6[s=^M幐 ٻs KQ`R`AL5pD`a%ՓDJmM6mJ]V_dm{O^ PR͈1;W <W_u;;_=VVEUڼx@¯;%͝ 1ƂEiCD@!wgbkǾ$lY.?7zqS,=}؆ΉocoxE&!8䬰׋HϒDp[ ""ՈH7%/g &uK^!6^߆7^^d%K.yO:9D;(95:z!L0::ò0߽}]t15d\{SSm۹BKݰ2a ʈ_M"=28)GrcdS4Δ We"Hv`sl3tÝf|p`_QRBW"ut߼ -ryD)gRHT뵹9ɩ%ϕ?[Y&.eq"~q L7Vvt3Xu?.dosgydvGF$_> +xX XS׶&Ɠ!ֶZkYjJ'f 9@IVy $Tp:ϼkmնTZ{o[wyEm}}|g[ԿD"RɓƯVŨmK‹/INJOv̧#72/99I;C_rrzee(WL.ZU٦pIg2i4amk4ۢ' -=JVEDŽmUEkUK׭Y$~{JD̚8Q4!<*hb`x&zi艎qx\;~WY1>~tsġ&u/%~ w*f>ج5dtˍqS>`6q)IkvZJ[qRN6 VICuKũ(L7gi`҃GMT4mGZ 6ɬ[:POEAV) +*ű_vU)jbp݃UݜJ&*A_=Sau@crߍA"mk"Yn*C< ;!'] +ڡ|`8@N%≼}%\o}V7gC&˳r*A2)Xȥf%~Z V|CŅGEFwW7ؔr:iD:|InG&cr13sW_0ט!=s*c!.)%=ЗD õLb~zeZ8.`ܱɎN"Z8ɖꑊ!]n=qTBRŏ;7b|b}6/D:r} +Tı:(,AswXD:m=ϔi:6} 7M +4xyǪU!.-,PIП*0=y"BkdoY DNK6|+\(`~ƛ8Dq*j-;?T QW +`iQ2PY$儛QF_irQ)ZJ|ʵ>tS])ۛ)ZV~ L6MiE@J J<- HNgeU T` 4E6>J"Uk6́tjM}1;H2d+p620f0WV;hH)`˨5MvDq5,AݚTz,OPOe G9jɋ֭ioz1O>L_3#1_mbsD1O~uo ;m3s.7렟90 Od2DAz%OvsmSw/0r:0V(H$#Rff5f,H3deiɫ4&FWľ*yDD@)L֕ &3K >יڊ&D@ŢӋ%{ě5]{ eZi5FB(7';s1'C"$&g{s&ȊV Js +ͳWxtF#d7W cEP&H*{K{qj9V+Ƌc)M[8j,10,Ǫ&.Q q !@_rcuZ66oX+! +|!+@dCmEv}/_Ķݭ9@y`1j2BJRªZ%]Da  iMMe6]6`>gźEƎ^uC{X-ӕrz=NKR8M+Wr6*iHWC%Kc}(qT= tU6`rj~@Pod%Rv|t!!+1d. 2 `A`avsh2 +bg3̚lhKAv~Atf!%5%FO"Vs, 2 *+|@wBl!j5$3X3!SRVЦLPE%5A`cvSc@7Jp8nˤ,"#$'#vI{cy-ΘN_qI%@Vҍ ? )Qw&U$З)KS SȦL`ׁP:N4D'J*(IIb]u nK0OAG*DZ +A:]( +LDVӉ>BtDV/\HN&^T+f%N~cʗҾ܄r(ܪ"Dc;Sr&YAc@8wgB$'eiۙI2]ifPe +tEPHlՠv}{ Pp黟+gq.PD2C3|Rwf/ t\+F)|I1 WZ'܃{pύzE//V\ ԓ1wuGPmm􄝼p'b&+!Ű*'t6}1mȀtcR6*/ږ#(}a^EL +{HkDuXtHϤGW_}) ImL𚸅D> @g1A|>V-k|Ǡ+"AAzq#i~߽ރ\b8wtw8!:RԉA75g4~UPrK )k]7.'z)P)7m!u,.:tmdgxvZw=sMF_ +I,Zҿ+'6%zxej`ՕϠ7= pHe lDno]k{R1wfɨ %YU$ +S0 %y +ST T>t],?][zy/jAGI::k:Q)pZU;j QܛrjkO!YeKX6} !/'dw~~[x:3kWn .u\zqBO?o pav d!wD/BVy +6z{k`СwԞ&!,M~kɁ +!,&14m7@9{7si ۠q8\V߹A +E1VxUe~73DOY9ނyٓu5(í5]ι7ț +K|cu7lmh=8;x:R` Uc +\XAcpX;8׷]Ύ"P,97<@šl_'ȂA*cO2*

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(ZXIiNjSycTbjR93qll3jfw==)] + /Size 395 + /Root 394 0 R + /Info 392 0 R + /ID [(Lkg0wJF4aHwoXBBBcQdsGQ==) (yf5uiSqSlldM9ylnKnS6xg==)] >> startxref -40175 +87110 %%EOF \ No newline at end of file diff --git a/assignment-2/main.typ b/assignment-2/main.typ index b740e72..c156ab3 100644 --- a/assignment-2/main.typ +++ b/assignment-2/main.typ @@ -1,6 +1,8 @@ #import "@preview/simple-ntnu-report:0.1.2": ntnu-report, un #import "@preview/zero:0.5.0": num #import "@preview/physica:0.9.8": * +#import "@preview/algorithmic:1.0.7" +#import algorithmic: style-algorithm, algorithm-figure #let text-size = 12pt #let white = rgb("#F8F8F2") @@ -13,6 +15,14 @@ #let purple = rgb("#BD93F9") #let pink = rgb("#FF79C6") +#show: style-algorithm.with( + hlines: ( + grid.hline(stroke: 0.5pt + white), + grid.hline(stroke: 0.5pt + white), + grid.hline(stroke: 0.5pt + white) + ) +) + #set page(fill: black) #set text(size: text-size, fill: white) @@ -102,3 +112,48 @@ $ <=> sum_(v in e) y_e <= c_v \ quad forall v in V, quad y >= 0 $ + +=== c) +to construct a primal-dual algorithm to approximate this problem, we use the formulations given previously. + + +#algorithm-figure( + "Primal-Dual Weighted Vertex Cover Approximation", + vstroke: .5pt + white, { + import algorithmic: * + Procedure( + "Vertex-Cover", + ("G", "c"), { + Comment[initialize primal ($x$) and dual ($y$) variables] + For($v in V, e in E$, + Assign[$y_e$][$0$], + Assign[$x_v$][$0$] + ) + LineBreak + While([there exists an uncovered edge $e = (u, v)$], { + Comment[calculate minimum slack] + Assign[$"slack"_u$][$c_u - sum_(e' in delta(u)) y_(e')$] + Assign[$"slack"_v$][$c_v - sum_(e' in delta(v)) y_(e')$] + Assign[$alpha$][$min("slack"_u, "slack"_v)$] + LineBreak + Comment[increase dual variable for edge $e$] + Assign[$y_e$][$y_e + alpha$] + LineBreak + Comment[Update primal if constraint becomes tight] + If([$sum_(e' in delta(u)) y_(e') = c_u$], + Assign[$x_u$][$1$]) + If([$sum_(e' in delta(v)) y_(e') = c_v$], + Assign[$x_v$][$1$]) + }) + Return[$C = {v in V | x_v = 1}$] + }, + ) + } +) + +where $delta(u)$ means the set of all edges going out of vertex $u$. + +== other + +the rest of the tasks are attached or can be found at +https://git.pvv.ntnu.no/frero-uni/TDT4125/src/branch/main/assignment-2