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 struct order {
   8         unsigned row, num;
   9         int side;
  10         int cost;
  11
  12         bool operator< (const order &other) const
  13         {
  14                 return (cost < other.cost);
  15         }
  16 };
  17
  18 static unsigned best_so_far = UINT_MAX;
  19 order *best_tour;
  20
  21 int distance_switch(unsigned from, unsigned to)
  22 {
  23         /* on the same side of the middle? 9.6m per switch. */
  24         if ((from > 3) == (to > 3)) {
  25                 return abs(from - to) * 96;
  26         }
  27
  28         /* have to cross the border? 25.8m from sw3->sw4 => 16.2m extra gap. */
  29         /* that's _got_ to be wrong. say it's 3m. */
  30         return abs(from - to) * 96 + 30;
  31 }
  32
  33 int distance_middle(unsigned sw, unsigned middle)
  34 {
  35         /* symmetry: 4-5-6 are just mirrored 3-2-1. */
  36         if (middle == 2) {
  37                 if (sw > 3)
  38                         sw = 7 - sw;
  39
  40                 /* estimate 25.8m/2 = 12.9m from sw3 to the middle */
  41                 return 129 + (3 - sw) * 96;
  42         }
  43
  44         /* more symmetry -- getting from 1-6 to the top is like getting from 6-1 to the bottom. */
  45         if (middle == 3) {
  46                 middle = 1;
  47                 sw = 7 - sw;
  48         }
  49
  50         /* guesstimate 4.8m extra to get to the bottom */
  51         if (sw > 3)
  52                 return 48 + 162 + (sw - 1) * 96;
  53         else
  54                 return 48 + (sw - 1) * 96;
  55 }
  56
  57 int distance_row(unsigned from, unsigned to)
  58 {
  59         /* don't calculate gaps here just yet, just estimate 4.1m per double row */
  60         return 41 * abs(from - to);
  61 }
  62
  63 int distance(int row_from, int switch_from, int side_from, int row_to, int switch_to, int side_to)
  64 {
  65         /* can we just walk directly? */
  66         if (row_from == row_to && side_from == side_to) {
  67                 return distance_switch(switch_from, switch_to);
  68         }
  69
  70         /* can we just switch sides? */
  71         if (row_from + 1 == row_to && side_from == 1 && side_to == -1) {
  72                 return distance_switch(switch_from, switch_to);
  73         }
  74         if (row_from == row_to + 1 && side_from == -1 && side_to == 1) {
  75                 return distance_switch(switch_from, switch_to);
  76         }
  77
  78         /* we'll need to go to one of the three middles */
  79         int best1 = distance_middle(switch_from, 1) + distance_middle(switch_to, 1);
  80         int best2 = distance_middle(switch_from, 2) + distance_middle(switch_to, 2);
  81         int best3 = distance_middle(switch_from, 3) + distance_middle(switch_to, 3);
  82         return std::min(std::min(best1, best2), best3) + distance_row(row_from, row_to);
  83 }
  84
  85 int optimistic_distance(int row_from, int switch_from, int row_to, int switch_to)
  86 {
  87         if (abs(row_from - row_to) == 1)
  88                 return distance_switch(switch_from, switch_to);
  89         else
  90                 return distance(row_from, switch_from, -1, row_to, switch_to, -1);
  91 }
  92
  93 // extremely primitive O(V^2) prim
  94 int prim_mst(std::set<std::pair<unsigned, unsigned> > &set1)
  95 {
  96         std::set<std::pair<unsigned, unsigned> > set2;
  97
  98         // pick the first one
  99         std::set<std::pair<unsigned, unsigned> >::iterator start = set1.begin();
 100         set2.insert(*start);
 101         set1.erase(start);
 102
 103         unsigned total_cost = 0;
 104         while (set1.size() > 0) {
 105                 unsigned best_this_cost = UINT_MAX;
 106                 std::set<std::pair<unsigned, unsigned> >::iterator best_set1;
 107
 108                 for (std::set<std::pair<unsigned, unsigned> >::iterator i = set1.begin(); i != set1.end(); ++i) {
 109                         for (std::set<std::pair<unsigned, unsigned> >::iterator j = set2.begin(); j != set2.end(); ++j) {
 110                                 unsigned d = optimistic_distance(i->first, i->second, j->first, j->second);
 111                                 if (d < best_this_cost) {
 112                                         best_this_cost = d;
 113                                         best_set1 = i;
 114                                 }
 115                         }
 116                 }
 117
 118                 set2.insert(*best_set1);
 119                 set1.erase(best_set1);
 120                 total_cost += best_this_cost;
 121         }
 122
 123         return total_cost;
 124 }
 125
 126
 127 void print_tour(std::vector<std::pair<unsigned, unsigned> > &points)
 128 {
 129         std::set<std::pair<unsigned, unsigned> > points_left;
 130         for (unsigned i = 0; i < points.size(); ++i) {
 131                 points_left.insert(points[i]);
 132         }
 133
 134         for (unsigned i = 0; i < points.size(); ++i) {
 135                 if (best_tour[i].side == -1)
 136                         printf("%2u-%u (left side)  ", best_tour[i].row, best_tour[i].num);
 137                 else
 138                         printf("%2u-%u (right side) ", best_tour[i].row, best_tour[i].num);
 139                 if (i == 0) {
 140                         printf("           ");
 141                 } else {
 142                         printf("cost=%4u  ", best_tour[i].cost);
 143                 }
 144
 145                 // let's see how good the MST heuristics are
 146                 if (i != points.size() - 1) {
 147                         std::set<std::pair<unsigned, unsigned> > mst_tree = points_left;
 148                         printf("mst_bound=%5u, ", prim_mst(mst_tree));
 149
 150                         unsigned rest_cost = 0;
 151                         for (unsigned j = i + 1; j < points.size(); ++j) {
 152                                 rest_cost += best_tour[j].cost;
 153                         }
 154
 155                         printf("rest_cost=%5u", rest_cost);
 156                 }
 157
 158                 printf("\n");
 159
 160                 std::set<std::pair<unsigned, unsigned> >::iterator j = points_left.find(std::make_pair(best_tour[i].row, best_tour[i].num));
 161                 points_left.erase(j);
 162         }
 163 }
 164
 165 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)
 166 {
 167         if (cost_so_far >= best_so_far)
 168                 return UINT_MAX;
 169         if (ind == points.size()) {
 170                 memcpy(best_tour, ord, sizeof(order) * points.size());
 171                 printf("\nNew best tour found! cost=%u\n", cost_so_far);
 172                 print_tour(points);
 173                 best_so_far = cost_so_far;
 174                 return 0;
 175         }
 176
 177         /*
 178          * Simple heuristic: always search for the closest points from this one first; that
 179          * will give us a sizable cutoff.
 180          */
 181         unsigned toi = 0;
 182         unsigned last_row = ord[ind-1].row;
 183         unsigned last_switch = ord[ind-1].num;
 184         unsigned last_side = ord[ind-1].side;
 185
 186         std::set<std::pair<unsigned, unsigned> > mst_set = points_left;
 187         mst_set.insert(std::make_pair(last_row, last_switch));
 188
 189         for (std::set<std::pair<unsigned, unsigned> >::iterator i = points_left.begin(); i != points_left.end(); ++i) {
 190                 /* try both sides */
 191                 temp[toi].row = i->first;
 192                 temp[toi].num = i->second;
 193                 temp[toi].side = -1;
 194                 temp[toi].cost = distance(last_row, last_switch, last_side, i->first, i->second, -1);
 195                 ++toi;
 196
 197                 temp[toi].row = i->first;
 198                 temp[toi].num = i->second;
 199                 temp[toi].side = +1;
 200                 temp[toi].cost = distance(last_row, last_switch, last_side, i->first, i->second, +1);
 201                 ++toi;
 202         }
 203
 204         unsigned min_rest_cost = prim_mst(mst_set);
 205         if (cost_so_far + min_rest_cost >= best_so_far) {
 206                 return UINT_MAX;
 207         }
 208
 209         std::sort(temp, temp + toi);
 210
 211         unsigned best_this_cost = UINT_MAX;
 212         for (unsigned i = 0; i < toi; ++i)
 213         {
 214                 ord[ind] = temp[i];
 215
 216                 std::set<std::pair<unsigned, unsigned> >::iterator j = points_left.find(std::make_pair(temp[i].row, temp[i].num));
 217                 points_left.erase(j);
 218                 unsigned cost_rest = do_tsp(points, points_left, ord, temp + points.size() * 2, ind + 1, cost_so_far + temp[i].cost);
 219                 points_left.insert(std::make_pair(temp[i].row, temp[i].num));
 220
 221                 best_this_cost = std::min(best_this_cost, cost_rest);
 222         }
 223
 224         return best_this_cost;
 225 }
 226
 227 int main()
 228 {
 229         std::vector<std::pair<unsigned, unsigned> > points;
 230         std::set<std::pair<unsigned, unsigned> > points_left;
 231
 232         for ( ;; ) {
 233                 unsigned row, sw;
 234                 if (scanf("%u-%u", &row, &sw) != 2)
 235                         break;
 236
 237                 points.push_back(std::make_pair(row, sw));
 238                 if (points.size() != 1)
 239                         points_left.insert(std::make_pair(row, sw));
 240         }
 241
 242         order *ord = new order[points.size()];
 243         best_tour = new order[points.size()];
 244         order *temp = new order[points.size() * points.size() * 4];
 245
 246         /* always start at the first one, left side (hack) */
 247         ord[0].row = points[0].first;
 248         ord[0].num = points[0].second;
 249         ord[0].side = -1;
 250
 251         do_tsp(points, points_left, ord, temp, 1, 0);
 252         printf("All done.\n");
 253 }
 254
 255