Add baumzerlegte_graphen

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hal8174 2025-01-21 20:42:15 +01:00
parent cd4f7c1ad9
commit 394e14cef4
21 changed files with 131300 additions and 0 deletions

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s td 96 71 410
b 1 311 314 325 331 343 351 352 353 354 355 356 357 358 359 360 396 397 398 402 404
b 2 311 314 325 331 343 351 352 353 354 355 356 357 358 359 360 364 370 397
b 3 311 325 331 343 351 352 353 354 355 356 357 358 359 360 393 394 396 397 398 400 402 404
b 4 287 311 314 325 331 343 351 352 353 354 355 356 357 358 359 360 363 364 368 370 371 372
b 5 311 325 331 343 351 352 353 354 355 356 357 358 359 360 393 394 396 397 400 402 403 404
b 6 325 343 351 352 354 356 357 358 359 360 393 394 396 397 398 400 401 402 404 405
b 7 266 287 311 313 314 325 331 343 351 353 354 355 356 357 358 360 363 364 368 370 371 372 373
b 8 311 325 331 343 351 352 353 354 355 356 357 358 359 360 364 370 409
b 9 311 325 331 343 351 352 353 354 355 356 357 358 359 360 364 370 406
b 10 287 311 325 331 343 351 352 353 354 355 356 357 358 360 363 364 368 370 371 372 374
b 11 325 343 351 352 354 356 357 358 359 360 393 394 395 396 397 399 400 401 402 404 405
b 12 266 287 311 313 314 325 331 343 353 354 356 357 358 361 362 363 364 365 366 367 368 369 370 371 372 373
b 13 325 343 352 356 358 360 395 396 397 399 400 401 402 404 405 408
b 14 325 343 352 356 358 360 395 396 397 399 400 401 402 404 405 407
b 15 266 287 311 313 314 318 319 325 331 333 341 343 344 345 354 356 357 358 361 362 363 364 365 366 367 368 369 370 371 372
b 16 325 352 356 358 360 395 396 397 400 401 402 404 405 408 410
b 17 266 287 311 313 314 318 319 324 325 331 333 341 343 344 345 354 357 361 362 363 364 365 366 367 368 369 370 371 372
b 18 266 287 311 313 314 318 319 324 325 331 333 341 343 344 345 350 354 357 362 363 364 365 366 367 368 369 370 371
b 19 266 287 307 311 312 313 314 316 317 318 319 320 323 324 325 329 330 331 332 333 337 340 341 343 344 345 350 357 364 367 368 370
b 20 266 287 307 311 312 313 314 316 317 318 319 320 321 323 324 325 326 329 330 331 332 333 334 335 337 340 341 343 344 345 348 350 357 367 368
b 21 266 287 307 308 311 312 313 314 316 317 318 319 320 321 323 324 325 326 329 330 331 332 333 334 335 337 339 340 341 343 344 345 348 350 357
b 22 266 287 307 308 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 329 330 331 332 333 334 335 336 337 338 339 340 341 343 344 345 348 357
b 23 141 266 277 287 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 328 329 330 331 332 333 334 335 336 337 338 339 340 341 343 344 345 348
b 24 141 266 277 287 307 308 309 310 311 312 313 315 316 317 318 319 320 321 322 323 324 325 326 327 329 330 331 332 333 334 335 336 337 338 339 340 341
b 25 266 287 307 308 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 328 329 330 331 332 333 334 335 336 337 338 339 340 341 343 344 345 348 349
b 26 141 149 266 277 287 307 309 312 316 318 319 320 325 327 329 333 337 340 341
b 27 141 149 262 266 277 287 307 320
b 28 141 149 266 277 287 307 309 312 316 319 320 325 327 329 333 337 340 341 342
b 29 119 141 149 163 166 232 233 234 235 237 238 240 241 242 243 245 246 247 248 249 250 251 252 253 254 255 256 257 258 260 261 262 263 264 265 266 267 268 269 270 271 272 273 275 277 279 282 284 287 288 292 295
b 30 119 141 149 163 166 232 233 234 235 237 238 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 275 277 281 282 284 288 292 293 294 295
b 31 119 141 149 163 166 232 233 234 235 237 238 240 241 242 243 245 246 247 248 249 250 251 252 253 254 255 256 257 258 260 261 262 263 264 265 266 267 268 269 270 271 272 273 275 277 279 282 285 286 287 288 295
b 32 119 141 149 163 166 232 233 234 235 236 237 238 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 277 281 284 288 292 293 294 295
b 33 119 141 149 163 166 232 233 234 235 237 238 240 241 242 243 245 246 247 248 249 250 251 252 253 254 255 256 257 258 260 261 262 263 264 265 266 267 268 269 270 271 272 273 275 277 279 280 282 285 286 287
b 34 119 141 149 163 166 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 277 281 284 288 293 294 295
b 35 119 141 149 163 166 232 233 234 237 238 240 241 242 243 245 246 247 248 249 250 251 252 253 254 255 256 257 258 260 261 262 263 264 265 266 267 268 269 270 271 272 273 275 277 278 279 280 282 283 285 286 287 289 290
b 36 119 141 144 149 163 166 167 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 277 281 284 293 294
b 37 141 149 163 232 233 234 237 238 240 241 243 248 251 252 253 256 257 258 260 262 263 264 266 267 268 269 271 273 277 278 280 282 283 285 286 287 289 290 306
b 38 53 105 119 141 144 149 163 166 167 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 277 284
b 39 119 141 149 163 166 232 233 234 235 236 237 241 242 244 245 246 247 249 250 251 252 254 255 257 258 259 260 261 262 263 264 265 266 268 269 270 271 272 274 275 281 291 293 294
b 40 238 240 243 248 253 256 260 263 266 267 269 273 280 282 285 286 287 289 306 347
b 41 53 105 119 141 144 149 163 166 167 170 232 233 234 235 236 237 239 241 242 244 245 246 247 249 250 251 252 254 255 257 258 259 260 261 262 263 264 265 266 268 269 270 271 272 274 275 277 284
b 42 53 105 109 119 141 144 149 163 166 167 169 170 171 228 229 230 231 232 233 234 235 236 237 239 241 242 244 245 246 247 249 250 251 252 254 255 257 258 259 260 261 262 263 264 265 266 268 269 270 271 272 274 275
b 43 277 346
b 44 53 105 109 111 119 141 144 145 149 163 166 167 169 170 171 205 228 229 230 231 232 234 249 262 271
b 45 53 105 109 111 119 141 144 145 149 160 163 166 167 169 170 171 205 228 229 230 231 232 234 262 271
b 46 53 104 105 109 111 119 141 144 145 149 157 160 163 164 166 167 169 170 171 205 228 229 230 231 271
b 47 53 104 105 109 111 119 141 144 145 149 157 160 163 164 166 167 169 170 171 172 176 205 271
b 48 53 55 97 104 105 109 111 116 119 121 125 127 129 132 133 136 138 141 144 145 149 157 160 162 163 164 166 167 169 170 171 172 175 176 205
b 49 53 55 90 91 97 101 102 104 105 108 109 111 113 116 118 119 120 121 123 125 127 129 130 132 133 136 137 138 141 142 143 144 145 146 148 149 154 157 160 162 163 164 166 167 169 170 171 172 175 176
b 50 53 55 90 91 92 97 101 102 104 105 108 109 111 113 116 118 119 120 121 123 124 125 127 129 130 132 133 136 137 138 141 142 143 144 145 146 148 149 154 157 160 161 162 163 164 166 167 169 170 171 172 176
b 51 53 55 90 91 97 101 102 104 105 108 109 111 113 118 119 120 121 123 125 127 129 130 132 133 136 137 138 141 142 143 144 145 146 148 149 154 157 160 162 163 166 167 169 170 171 173 174 175
b 52 53 55 90 91 92 97 101 102 104 105 108 109 111 113 116 118 119 120 121 122 123 124 125 127 129 130 132 133 136 137 138 139 141 142 143 144 145 146 147 148 149 154 157 160 161 162 163 164 166 167 169 170 171 176
b 53 53 105 109 119 141 144 149 163 166 167 169 170 171 172 176 276
b 54 53 55 90 91 92 97 101 102 103 104 105 108 109 110 111 113 116 118 119 120 121 122 123 124 125 127 129 130 132 133 135 136 137 138 139 141 142 143 144 145 146 147 148 149 153 154 157 160 161 162 163 164 166 167 170 176
b 55 2 8 34 53 55 73 80 90 91 92 95 96 97 98 101 102 103 104 105 108 109 110 111 113 116 118 119 120 121 122 123 124 125 126 127 129 130 132 133 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 151 153 154 156 157 159 160 161 162 163 164 166 167
b 56 2 8 29 32 34 53 55 73 75 80 90 91 92 95 96 97 98 101 103 104 105 109 110 111 117 118 119 121 124 125 126 130 131 132 133 135 136 138 139 140 143 144 146 147 148 151 153 154 157 161 162 163 164 166 167 168
b 57 2 8 53 55 80 90 91 92 96 97 98 101 102 103 104 105 108 109 110 111 113 116 118 119 120 121 122 123 124 125 126 127 129 130 132 133 136 137 138 139 140 141 142 143 144 145 146 147 148 149 151 153 154 155 156 157 159 160 161 162 163 164 166 167
b 58 2 8 29 32 34 53 55 73 75 80 90 91 92 95 96 97 98 103 104 105 106 109 110 111 117 118 121 124 126 130 131 132 133 135 136 138 139 140 143 144 146 147 148 151 153 154 157 161 162 163 164 166 167 168
b 59 2 8 24 29 32 34 45 53 55 58 73 75 80 90 91 92 93 95 96 97 98 99 100 103 104 105 106 107 109 110 112 114 115 117 118 121 124 126 128 130 131 132 133 136 138 139 140 143 144 146 147 148 150 151 153 154 157 158 161 162 163 164 165 166 167 168
b 60 2 8 24 27 29 32 34 40 45 52 53 55 58 64 67 68 73 75 80 86 90 91 92 93 95 96 97 98 99 100 103 104 105 106 107 109 110 112 114 115 117 118 121 124 128 130 131 132 133 136 138 139 143 144 146 147 148 150 151 153 154 157 158 161 162 163 164 165 166 167 168
b 61 2 8 24 27 29 32 34 40 45 52 53 55 58 64 67 68 73 75 80 86 93 95 96 99 100 107 112 114 115 117 128 131 134 138 150 151 158 165 168
b 62 2 6 8 24 27 29 32 34 40 45 52 53 55 58 64 67 68 73 75 80 86 93 95 96 99 100 104 105 106 107 109 112 114 115 117 118 124 128 130 131 138 144 150 151 153 158 165 167 168
b 63 2 6 8 24 25 27 29 32 34 38 39 40 45 46 52 53 55 58 64 67 68 71 73 75 80 85 86 93 95 96 99 100 105 106 107 109 112 114 115 117 118 128 130 131 138 144 150 151 153 158 165 167 168
b 64 2 6 8 12 21 24 25 27 29 31 32 34 38 39 40 41 45 46 50 51 52 53 55 58 63 64 67 68 71 72 73 75 78 79 80 85 86 93 95 96 99 100 106 107 112 114 115 117 128 131 138 144 150 151 153 158 165 167 168
b 65 2 8 12 21 24 25 27 29 31 32 34 38 39 40 41 45 46 50 51 52 53 55 58 63 64 67 68 71 72 73 75 78 79 80 85 86 93 95 96 99 100 106 107 112 114 115 117 128 131 138 144 150 151 152 158 165 167 168
b 66 2 6 8 12 21 24 25 27 29 31 32 34 38 39 40 41 45 46 50 51 52 53 55 56 58 63 64 67 68 71 72 73 75 78 79 80 85 86 87 93 95 99 100 107 112 114 115 117 128 131 138 150 151 153 158 165 168
b 67 2 6 8 12 21 24 25 27 29 31 32 34 38 39 40 41 45 46 49 50 51 52 53 55 56 58 63 64 67 68 71 72 73 75 78 79 80 85 86 87 95 114 151 153 158
b 68 2 6 8 12 14 21 22 24 25 27 29 31 32 34 38 39 40 41 45 46 49 50 51 52 53 55 56 58 63 64 67 68 71 72 73 75 76 78 79 80 85 86 87 95 114 151 158
b 69 1 2 6 8 11 12 14 17 18 19 21 22 23 24 25 27 29 30 31 32 34 36 37 38 39 40 41 42 43 45 46 48 49 50 51 52 53 54 55 56 58 63 64 65 67 68 69 71 72 73 75 76 78 79 80 81 82 85 86 87
b 70 2 8 42 76 94
b 71 1 2 6 8 10 11 14 17 18 19 21 22 23 27 29 30 32 34 37 41 42 43 48 49 52 54 55 59 62 63 65 67 69 72 73 75 76 78 80 81 82 83 85 87
b 72 1 2 5 6 8 9 10 11 14 17 18 19 21 22 23 27 28 29 30 32 34 37 41 42 43 47 48 49 52 54 59 63 65 67 69 70 72 73 75 76 78 80 81 82 85 87
b 73 1 2 3 5 6 8 9 10 11 13 14 15 16 17 18 19 21 22 23 27 28 29 30 32 34 37 41 42 43 47 48 49 52 54 59 63 65 67 69 70 72 73 75 76 78 80 81 85 87 88
b 74 1 2 3 5 6 7 8 9 10 13 14 15 16 17 18 19 20 21 22 23 26 27 28 29 30 32 33 34 35 37 41 42 47 48 49 52 54 59 60 61 63 65 66 67 69 70 72 73 74 75 76 78 80 81 84 85 87 88 89
b 75 15 33 61 206
b 76 1 2 3 4 5 6 7 8 9 10 13 14 15 16 17 18 19 20 22 23 26 27 28 29 30 32 33 34 35 37 42 44 47 48 49 52 54 57 60 61 65 66 67 69 70 72 73 74 75 76 77 81 84 85 87 88 89
b 77 3 4 5 7 9 10 13 14 15 16 17 18 19 20 23 26 27 28 29 32 33 34 35 37 47 48 52 54 57 60 61 65 66 67 69 70 72 73 74 75 77 81 84 85 87 88 89 182 184 191 198
b 78 3 4 5 7 9 10 13 15 16 17 20 26 27 28 29 32 33 34 35 47 48 52 54 57 60 61 66 67 70 72 73 74 75 77 84 85 87 88 89 182 184 191 195 198
b 79 3 4 5 7 9 13 15 16 17 20 26 27 28 29 32 33 34 35 47 48 52 54 57 60 61 66 67 70 72 73 74 75 77 84 85 87 88 89 182 184 189 191 195 198
b 80 3 4 5 7 9 13 15 16 17 20 26 27 28 33 34 35 47 48 52 54 57 60 61 66 67 70 72 73 74 77 84 85 88 89 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198
b 81 5 15 17 27 28 34 48 52 54 61 67 70 72 73 85 88 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 207
b 82 5 17 27 28 34 48 52 54 67 70 72 73 85 88 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 207
b 83 199 200 201 202 203 204 392
b 84 17 27 34 48 52 67 72 73 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 193 194 195 196 197 198 199 200 201 202 203 204 207 213 214 215 216 219
b 85 17 27 34 48 52 67 72 73 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 193 194 195 196 197 198 199 201 204 207 213 214 215 216 219 222 224 225 226
b 86 17 34 48 72 73 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 193 194 195 196 197 198 199 207 208 209 210 211 212 213 214 215 216 217 218 219 220 222 224 225 226
b 87 17 34 48 72 73 178 180 181 182 184 186 187 189 190 191 193 194 195 196 197 198 199 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226
b 88 17 34 48 72 73 178 180 181 186 187 189 190 193 194 195 196 197 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227
b 89 34 73 178 180 181 186 187 190 193 194 195 196 197 207 213 214 215 216 219 221 222 223 224 225 226 296 297 299 300 302 303 304 305
b 90 34 73 178 180 181 186 187 190 193 194 195 196 197 213 214 215 216 219 221 222 223 224 225 226 296 297 298 299 300 301 302 303 304 305
b 91 178 180 181 186 187 190 193 194 195 196 197 207 213 215 219 221 222 223 224 225 226 296 297 299 300 302 303 304 305 375 376 377 378 379 380 381
b 92 180 181 186 194 195 196 197 207 215 219 221 222 223 224 225 226 296 297 299 300 302 303 304 305 375 376 377 378 379 380 381 384 385
b 93 180 181 186 194 195 196 197 207 221 222 223 224 225 226 296 297 299 300 302 303 304 305 375 376 377 378 379 380 381 383 384 385
b 94 180 195 196 207 221 223 296 297 299 300 302 303 304 305 375 376 377 378 379 380 381 382 383 384 385
b 95 180 195 196 207 297 303 375 376 377 378 379 380 382 383 384 385 386 387 388 389
b 96 180 195 196 207 297 303 375 376 377 378 379 380 382 383 384 385 386 387 389 390 391
1 2
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p tw 5 6
1 2
1 3
2 3
2 4
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2 5

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0
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4

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s td 3 3 5
b 1 1 2 3
b 2 2 3 4
b 3 2 5
1 2
2 3

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use clap::Parser;
use std::{
collections::{HashMap, HashSet},
fmt::Debug,
io::{BufWriter, Write},
path::{Path, PathBuf},
};
#[derive(Parser)]
struct Args {
filename: PathBuf,
}
type NodeType = u16;
struct Baumzerlegung {
nodes: NodeType,
edges: HashMap<NodeType, HashSet<NodeType>>,
bags: Vec<HashSet<NodeType>>,
bag_edges: HashMap<NodeType, HashSet<NodeType>>,
tree_width: NodeType,
}
impl Baumzerlegung {
fn edge(&self, a: NodeType, b: NodeType) -> bool {
if let Some(e) = self.edges.get(&a) {
e.contains(&b)
} else {
false
}
}
}
fn parse_input(path: impl AsRef<Path>) -> Baumzerlegung {
let gr_string = std::fs::read_to_string(path.as_ref().with_extension("gr")).unwrap();
let td_string = std::fs::read_to_string(path.as_ref().with_extension("td")).unwrap();
let mut gr_lines = gr_string.lines();
let mut td_lines = td_string.lines();
let nodes = gr_lines
.next()
.unwrap()
.split(' ')
.nth(2)
.unwrap()
.parse::<NodeType>()
.unwrap();
let mut edges: HashMap<u16, HashSet<u16>> = HashMap::new();
gr_lines
.flat_map(|l| {
let (a, b) = l.split_once(' ').unwrap();
let a = a.parse::<NodeType>().unwrap() - 1;
let b = b.parse::<NodeType>().unwrap() - 1;
[(a, b), (b, a)]
})
.for_each(|(a, b)| match edges.entry(a) {
std::collections::hash_map::Entry::Occupied(mut occupied_entry) => {
occupied_entry.get_mut().insert(b);
}
std::collections::hash_map::Entry::Vacant(vacant_entry) => {
vacant_entry.insert(HashSet::from([b]));
}
});
let mut first_line = td_lines.next().unwrap().split(' ');
let num_bags = first_line.nth(2).unwrap().parse::<usize>().unwrap();
let tree_width = first_line.next().unwrap().parse::<NodeType>().unwrap();
let bags = td_lines
.by_ref()
.take(num_bags)
.map(|l| {
l.strip_prefix("b ")
.unwrap()
.trim()
.split(' ')
.skip(1)
.map(|c| c.parse::<NodeType>().unwrap() - 1)
.collect()
})
.collect();
let mut bag_edges: HashMap<u16, HashSet<u16>> = HashMap::new();
td_lines
.map(|l| {
let (a, b) = l.split_once(' ').unwrap();
(
a.parse::<NodeType>().unwrap() - 1,
b.parse::<NodeType>().unwrap() - 1,
)
})
.for_each(|(a, b)| match bag_edges.entry(a) {
std::collections::hash_map::Entry::Occupied(mut occupied_entry) => {
occupied_entry.get_mut().insert(b);
}
std::collections::hash_map::Entry::Vacant(vacant_entry) => {
vacant_entry.insert(HashSet::from([b]));
}
});
Baumzerlegung {
nodes,
edges,
bags,
bag_edges,
tree_width,
}
}
fn walk_dp<D: DP>(node: NodeType, td: &Baumzerlegung) -> D {
if let Some(children) = td.bag_edges.get(&node) {
children
.iter()
.map(|&c| {
let mut cd = walk_dp::<D>(c, td);
for &f in td.bags[c as usize].difference(&td.bags[node as usize]) {
cd = cd.forget(f, td);
}
for &i in td.bags[node as usize].difference(&td.bags[c as usize]) {
cd = cd.introduce(i, td);
}
cd
})
.reduce(|a, b| D::join(a, b, td))
.unwrap()
} else {
let mut d = D::init();
for &v in &td.bags[node as usize] {
d = d.introduce(v, td);
}
d
}
}
trait DP {
fn init() -> Self;
fn introduce(self, node: NodeType, graph: &Baumzerlegung) -> Self;
fn forget(self, node: NodeType, graph: &Baumzerlegung) -> Self;
fn join(a: Self, b: Self, graph: &Baumzerlegung) -> Self;
}
#[derive(Debug)]
struct IndependentSet {
current: HashMap<Vec<NodeType>, HashSet<NodeType>>,
}
impl DP for IndependentSet {
fn init() -> Self {
Self {
current: HashMap::from([(Vec::new(), HashSet::new())]),
}
}
fn introduce(mut self, node: NodeType, graph: &Baumzerlegung) -> Self {
for (mut k, mut v) in self.current.clone() {
if !k.iter().any(|&i| graph.edge(i, node)) {
k.push(node);
k.sort();
v.insert(node);
self.current.insert(k, v);
}
}
self
}
fn forget(mut self, node: NodeType, _graph: &Baumzerlegung) -> Self {
let current = self.current.clone();
for (k, h1) in &mut self.current {
if !k.contains(&node) {
let mut klone = k.clone();
klone.push(node);
klone.sort();
if let Some(h2) = current.get(&klone) {
if h2.len() > h1.len() {
*h1 = h2.clone();
}
}
}
}
self.current.retain(|k, _| k.binary_search(&node).is_err());
self
}
fn join(mut a: Self, b: Self, _graph: &Baumzerlegung) -> Self {
for (ka, va) in &mut a.current {
// assert!(b.current.contains_key(ka));
va.extend(&b.current[ka]);
}
// for kb in b.current.keys() {
// assert!(a.current.contains_key(kb));
// }
a
}
}
impl IndependentSet {
fn solution(&self) -> &HashSet<NodeType> {
self.current.values().max_by_key(|h| h.len()).unwrap()
}
}
fn main() {
let mut args = Args::parse();
args.filename.set_extension("");
let td = parse_input(&args.filename);
let s = walk_dp::<IndependentSet>(0, &td);
let f = std::fs::File::create(args.filename.with_extension("solution")).unwrap();
let mut bf = BufWriter::new(f);
let mut s = s.solution().iter().copied().collect::<Vec<_>>();
s.sort();
for i in s {
let _ = writeln!(bf, "{i}");
}
}