git.sesse.net Git - nms/blob - tsp/tsp.cpp

   1 #include <stdio.h>
   2 #include <limits.h>
   3 #include <vector>
   4 #include <set>
   5 #include <algorithm>
   6
   7 #define MIN_ROW 1
   8 #define MAX_ROW 75
   9 #define MIN_SWITCH 1
  10 #define MAX_SWITCH 6
  11 #define HEAP_MST 0
  12
  13 static const unsigned num_cache_elem = (MAX_ROW * MAX_SWITCH * 2) * (MAX_ROW * MAX_SWITCH * 2);
  14 static unsigned short dist_cache[(MAX_ROW * MAX_SWITCH * 2) * (MAX_ROW * MAX_SWITCH * 2)],
  15         opt_dist_cache[MAX_ROW * MAX_SWITCH * MAX_ROW * MAX_SWITCH],
  16         pess_dist_cache[MAX_ROW * MAX_SWITCH * MAX_ROW * MAX_SWITCH];
  17
  18 inline unsigned short &cache(
  19         unsigned row_from, unsigned switch_from, unsigned side_from,
  20         unsigned row_to, unsigned switch_to, unsigned side_to)
  21 {
  22         return dist_cache[(row_from * MAX_SWITCH * 2 + switch_from * 2 + side_from) * (MAX_ROW * MAX_SWITCH * 2) +
  23                 row_to * MAX_SWITCH * 2 + switch_to * 2 + side_to];
  24 }
  25
  26 inline unsigned short &opt_cache(
  27         unsigned row_from, unsigned switch_from,
  28         unsigned row_to, unsigned switch_to)
  29 {
  30         return opt_dist_cache[(row_from * MAX_SWITCH + switch_from) * (MAX_ROW * MAX_SWITCH) +
  31                 row_to * MAX_SWITCH + switch_to];
  32 }
  33
  34 inline unsigned short &pess_cache(
  35         unsigned row_from, unsigned switch_from,
  36         unsigned row_to, unsigned switch_to)
  37 {
  38         return pess_dist_cache[(row_from * MAX_SWITCH + switch_from) * (MAX_ROW * MAX_SWITCH) +
  39                 row_to * MAX_SWITCH + switch_to];
  40 }
  41
  42 struct order {
  43         unsigned row, num;
  44         int side;
  45         int cost;
  46
  47         bool operator< (const order &other) const
  48         {
  49                 return (cost < other.cost);
  50         }
  51 };
  52
  53 static unsigned best_so_far = UINT_MAX;
  54 order *best_tour;
  55
  56 int distance_switch(unsigned from, unsigned to)
  57 {
  58         /* on the same side of the middle? 9.6m per switch. */
  59         if ((from > 3) == (to > 3)) {
  60                 return abs(from - to) * 96;
  61         }
  62
  63         /* have to cross the border? 25.8m from sw3->sw4 => 16.2m extra gap. */
  64         /* that's _got_ to be wrong. say it's 3m. */
  65         return abs(from - to) * 96 + 30;
  66 }
  67
  68 int distance_middle(unsigned sw, unsigned middle)
  69 {
  70         /* symmetry: 4-5-6 are just mirrored 3-2-1. */
  71         if (middle == 2) {
  72                 if (sw > 3)
  73                         sw = 7 - sw;
  74
  75                 /* estimate 25.8m/2 = 12.9m from sw3 to the middle */
  76                 return 129 + (3 - sw) * 96;
  77         }
  78
  79         /* more symmetry -- getting from 1-6 to the top is like getting from 6-1 to the bottom. */
  80         if (middle == 3) {
  81                 middle = 1;
  82                 sw = 7 - sw;
  83         }
  84
  85         /* guesstimate 4.8m extra to get to the bottom */
  86         if (sw > 3)
  87                 return 48 + 162 + (sw - 1) * 96;
  88         else
  89                 return 48 + (sw - 1) * 96;
  90 }
  91
  92 int distance_row(unsigned from, unsigned to)
  93 {
  94         /* don't calculate gaps here just yet, just estimate 4.1m per double row */
  95         return 41 * abs(from - to);
  96 }
  97
  98 int pessimistic_distance(int row_from, int switch_from, int row_to, int switch_to)
  99 {
 100         /* we'll need to go to one of the three middles */
 101         int best2 = distance_middle(switch_from, 2) + distance_middle(switch_to, 2);
 102         int distrow = distance_row(row_from, row_to);
 103         if ((switch_from > 3) != (switch_to > 3))
 104                 return best2 + distrow;
 105         if (switch_from > 3) {
 106                 int best3 = distance_middle(switch_from, 3) + distance_middle(switch_to, 3);
 107                 return std::min(best2, best3) + distrow;
 108         } else {
 109                 int best1 = distance_middle(switch_from, 1) + distance_middle(switch_to, 1);
 110                 return std::min(best2, best1) + distrow;
 111         }
 112 }
 113
 114 int distance(int row_from, int switch_from, int side_from, int row_to, int switch_to, int side_to)
 115 {
 116         /* can we just walk directly? */
 117         if (row_from == row_to && side_from == side_to) {
 118                 return distance_switch(switch_from, switch_to);
 119         }
 120
 121         /* can we just switch sides? */
 122         if (row_from + 1 == row_to && side_from == 1 && side_to == 0) {
 123                 return distance_switch(switch_from, switch_to);
 124         }
 125         if (row_from == row_to + 1 && side_from == 0 && side_to == 1) {
 126                 return distance_switch(switch_from, switch_to);
 127         }
 128
 129         return pessimistic_distance(row_from, switch_from, row_to, switch_to);
 130 }
 131
 132 int optimistic_distance(int row_from, int switch_from, int row_to, int switch_to)
 133 {
 134         if (abs(row_from - row_to) <= 1)
 135                 return distance_switch(switch_from, switch_to);
 136         else
 137                 return pessimistic_distance(row_from, switch_from, row_to, switch_to);
 138 }
 139
 140 #if HEAP_MST
 141 // this is, surprisingly enough, _slower_ than the naive variant below, so it's not enabled
 142 struct prim_queue_val {
 143         std::pair<unsigned, unsigned> dst;
 144         int cost;
 145
 146         bool operator< (const prim_queue_val &other) const
 147         {
 148                 return (cost > other.cost);
 149         }
 150 };
 151
 152 // standard O(V^2 log v) prim
 153 int prim_mst(std::set<std::pair<unsigned, unsigned> > &in)
 154 {
 155         std::set<std::pair<unsigned, unsigned> > set2;
 156         std::priority_queue<prim_queue_val> queue;
 157
 158         // pick the first one
 159         std::set<std::pair<unsigned, unsigned> >::iterator start = in.begin();
 160
 161         unsigned row = start->first;
 162         unsigned num = start->second;
 163
 164         set2.insert(*start);
 165
 166         // find all the edges out from it
 167         for (std::set<std::pair<unsigned, unsigned> >::iterator j = in.begin(); j != in.end(); ++j) {
 168                 if (set2.count(*j))
 169                         continue;
 170
 171                 unsigned d = opt_cache(row, num, j->first, j->second);
 172                 prim_queue_val val = { *j, d };
 173                 queue.push(val);
 174         }
 175
 176         unsigned total_cost = 0;
 177         while (set2.size() != in.size()) {
 178 invalid:
 179                 prim_queue_val val = queue.top();
 180                 queue.pop();
 181
 182                 // check if dst is already moved
 183                 if (set2.count(val.dst))
 184                         goto invalid;
 185
 186                 unsigned row = val.dst.first;
 187                 unsigned num = val.dst.second;
 188                 set2.insert(val.dst);
 189
 190                 total_cost += val.cost;
 191
 192                 // find all the edges from this new node
 193                 for (std::set<std::pair<unsigned, unsigned> >::iterator j = in.begin(); j != in.end(); ++j) {
 194                         if (set2.count(*j))
 195                                 continue;
 196
 197                         unsigned d = opt_cache(row, num, j->first, j->second);
 198                         prim_queue_val val = { *j, d };
 199                         queue.push(val);
 200                 }
 201         }
 202
 203         return total_cost;
 204 }
 205 #else
 206 // extremely primitive O(V^3) prim
 207 int prim_mst(std::set<std::pair<unsigned, unsigned> > &set1)
 208 {
 209         std::set<std::pair<unsigned, unsigned> > set2;
 210
 211         // pick the first one
 212         std::set<std::pair<unsigned, unsigned> >::iterator start = set1.begin();
 213         set2.insert(*start);
 214         set1.erase(start);
 215
 216         unsigned total_cost = 0;
 217         while (set1.size() > 0) {
 218                 unsigned best_this_cost = UINT_MAX;
 219                 std::set<std::pair<unsigned, unsigned> >::iterator best_set1;
 220
 221                 for (std::set<std::pair<unsigned, unsigned> >::iterator i = set1.begin(); i != set1.end(); ++i) {
 222                         for (std::set<std::pair<unsigned, unsigned> >::iterator j = set2.begin(); j != set2.end(); ++j) {
 223                                 unsigned d = opt_cache(i->first, i->second, j->first, j->second);
 224                                 if (d < best_this_cost) {
 225                                         best_this_cost = d;
 226                                         best_set1 = i;
 227                                 }
 228                         }
 229                 }
 230
 231                 set2.insert(*best_set1);
 232                 set1.erase(best_set1);
 233                 total_cost += best_this_cost;
 234         }
 235
 236         return total_cost;
 237 }
 238 #endif
 239
 240 void print_tour(std::vector<std::pair<unsigned, unsigned> > &points)
 241 {
 242         std::set<std::pair<unsigned, unsigned> > points_left;
 243         for (unsigned i = 0; i < points.size(); ++i) {
 244                 points_left.insert(points[i]);
 245         }
 246
 247         for (unsigned i = 0; i < points.size(); ++i) {
 248                 if (best_tour[i].side == 0)
 249                         printf("%2u-%u (left side)  ", best_tour[i].row, best_tour[i].num);
 250                 else
 251                         printf("%2u-%u (right side) ", best_tour[i].row, best_tour[i].num);
 252                 if (i == 0) {
 253                         printf("           ");
 254                 } else {
 255                         printf("cost=%4u  ", best_tour[i].cost);
 256                 }
 257
 258                 // let's see how good the MST heuristics are
 259                 if (i != points.size() - 1) {
 260                         std::set<std::pair<unsigned, unsigned> > mst_tree = points_left;
 261                         printf("mst_bound=%5u, ", prim_mst(mst_tree));
 262
 263                         unsigned rest_cost = 0;
 264                         for (unsigned j = i + 1; j < points.size(); ++j) {
 265                                 rest_cost += best_tour[j].cost;
 266                         }
 267
 268                         printf("rest_cost=%5u", rest_cost);
 269                 }
 270
 271                 printf("\n");
 272
 273                 std::set<std::pair<unsigned, unsigned> >::iterator j = points_left.find(std::make_pair(best_tour[i].row, best_tour[i].num));
 274                 points_left.erase(j);
 275         }
 276 }
 277
 278 unsigned do_tsp(std::vector<std::pair<unsigned, unsigned> > &points, std::set<std::pair<unsigned, unsigned> > &points_left, order *ord, order *temp, unsigned ind, unsigned cost_so_far)
 279 {
 280         if (cost_so_far >= best_so_far)
 281                 return UINT_MAX;
 282         if (ind == points.size()) {
 283                 memcpy(best_tour, ord, sizeof(order) * points.size());
 284                 printf("\nNew best tour found! cost=%u\n", cost_so_far);
 285                 print_tour(points);
 286                 best_so_far = cost_so_far;
 287                 return 0;
 288         }
 289
 290         /*
 291          * Simple heuristic: always search for the closest points from this one first; that
 292          * will give us a sizable cutoff.
 293          */
 294         unsigned toi = 0;
 295         unsigned last_row = ord[ind-1].row;
 296         unsigned last_switch = ord[ind-1].num;
 297         unsigned last_side = ord[ind-1].side;
 298
 299         std::set<std::pair<unsigned, unsigned> > mst_set = points_left;
 300         mst_set.insert(std::make_pair(last_row, last_switch));
 301
 302         for (std::set<std::pair<unsigned, unsigned> >::iterator i = points_left.begin(); i != points_left.end(); ++i) {
 303                 /* try both sides */
 304                 temp[toi].row = i->first;
 305                 temp[toi].num = i->second;
 306                 temp[toi].side = 0;
 307                 temp[toi].cost = cache(last_row, last_switch, last_side, i->first, i->second, 0);
 308                 ++toi;
 309
 310                 temp[toi].row = i->first;
 311                 temp[toi].num = i->second;
 312                 temp[toi].side = 1;
 313                 temp[toi].cost = cache(last_row, last_switch, last_side, i->first, i->second, 1);
 314                 ++toi;
 315         }
 316
 317         unsigned min_rest_cost = prim_mst(mst_set);
 318         if (cost_so_far + min_rest_cost >= best_so_far) {
 319                 return UINT_MAX;
 320         }
 321
 322         std::sort(temp, temp + toi);
 323
 324         unsigned best_this_cost = UINT_MAX;
 325         for (unsigned i = 0; i < toi; ++i)
 326         {
 327                 ord[ind] = temp[i];
 328
 329                 std::set<std::pair<unsigned, unsigned> >::iterator j = points_left.find(std::make_pair(temp[i].row, temp[i].num));
 330                 points_left.erase(j);
 331                 unsigned cost_rest = do_tsp(points, points_left, ord, temp + points.size() * 2, ind + 1, cost_so_far + temp[i].cost);
 332                 points_left.insert(std::make_pair(temp[i].row, temp[i].num));
 333
 334                 best_this_cost = std::min(best_this_cost, cost_rest);
 335         }
 336
 337         return best_this_cost;
 338 }
 339
 340 int main()
 341 {
 342         std::vector<std::pair<unsigned, unsigned> > points;
 343         std::set<std::pair<unsigned, unsigned> > points_left;
 344
 345         for ( ;; ) {
 346                 unsigned row, sw;
 347                 if (scanf("%u-%u", &row, &sw) != 2)
 348                         break;
 349
 350                 if (row < MIN_ROW || row > MAX_ROW || sw < MIN_SWITCH || sw > MAX_SWITCH) {
 351                         fprintf(stderr, "%u-%u is out of bounds!\n", row, sw);
 352                         exit(1);
 353                 }
 354
 355                 points.push_back(std::make_pair(row, sw));
 356                 if (points.size() != 1)
 357                         points_left.insert(std::make_pair(row, sw));
 358         }
 359
 360         // precalculate all distances
 361         for (unsigned i = 0; i < points.size(); ++i) {
 362                 for (unsigned j = 0; j < points.size(); ++j) {
 363                         cache(points[i].first, points[i].second, 0, points[j].first, points[j].second, 0) =
 364                                 distance(points[i].first, points[i].second, 0, points[j].first, points[j].second, 0);
 365
 366                         cache(points[i].first, points[i].second, 0, points[j].first, points[j].second, 1) =
 367                                 distance(points[i].first, points[i].second, 0, points[j].first, points[j].second, 1);
 368
 369                         cache(points[i].first, points[i].second, 1, points[j].first, points[j].second, 0) =
 370                                 distance(points[i].first, points[i].second, 1, points[j].first, points[j].second, 0);
 371
 372                         cache(points[i].first, points[i].second, 1, points[j].first, points[j].second, 1) =
 373                                 distance(points[i].first, points[i].second, 1, points[j].first, points[j].second, 1);
 374
 375                         opt_cache(points[i].first, points[i].second, points[j].first, points[j].second) =
 376                                 optimistic_distance(points[i].first, points[i].second, points[j].first, points[j].second);
 377
 378                         pess_cache(points[i].first, points[i].second, points[j].first, points[j].second) =
 379                                 pessimistic_distance(points[i].first, points[i].second, points[j].first, points[j].second);
 380                 }
 381         }
 382
 383         order *ord = new order[points.size()];
 384         best_tour = new order[points.size()];
 385         order *temp = new order[points.size() * points.size() * 4];
 386
 387         /* always start at the first one, left side (hack) */
 388         ord[0].row = points[0].first;
 389         ord[0].num = points[0].second;
 390         ord[0].side = 0;
 391
 392         do_tsp(points, points_left, ord, temp, 1, 0);
 393         printf("All done.\n");
 394 }
 395
 396