khenaidoo | ac63710 | 2019-01-14 15:44:34 -0500 | [diff] [blame] | 1 | package goraph |
| 2 | |
| 3 | import ( |
| 4 | "container/heap" |
| 5 | "fmt" |
| 6 | "math" |
| 7 | ) |
| 8 | |
| 9 | // Dijkstra returns the shortest path using Dijkstra |
| 10 | // algorithm with a min-priority queue. This algorithm |
| 11 | // does not work with negative weight edges. |
| 12 | // (https://en.wikipedia.org/wiki/Dijkstra%27s_algorithm) |
| 13 | // |
| 14 | // 0. Dijkstra(G, source, target) |
| 15 | // 1. |
| 16 | // 2. let Q be a priority queue |
| 17 | // 3. distance[source] = 0 |
| 18 | // 4. |
| 19 | // 5. for each vertex v in G: |
| 20 | // 6. |
| 21 | // 7. if v ≠ source: |
| 22 | // 8. distance[v] = ∞ |
| 23 | // 9. prev[v] = undefined |
| 24 | // 10. |
| 25 | // 11. Q.add_with_priority(v, distance[v]) |
| 26 | // 12. |
| 27 | // 13. while Q is not empty: |
| 28 | // 14. |
| 29 | // 15. u = Q.extract_min() |
| 30 | // 16. if u == target: |
| 31 | // 17. break |
| 32 | // 18. |
| 33 | // 19. for each child vertex v of u: |
| 34 | // 20. |
| 35 | // 21. alt = distance[u] + weight(u, v) |
| 36 | // 22. if distance[v] > alt: |
| 37 | // 23. distance[v] = alt |
| 38 | // 24. prev[v] = u |
| 39 | // 25. Q.decrease_priority(v, alt) |
| 40 | // 26. |
| 41 | // 27. reheapify(Q) |
| 42 | // 28. |
| 43 | // 29. |
| 44 | // 30. path = [] |
| 45 | // 31. u = target |
| 46 | // 32. while prev[u] is defined: |
| 47 | // 33. path.push_front(u) |
| 48 | // 34. u = prev[u] |
| 49 | // 35. |
| 50 | // 36. return path, prev |
| 51 | // |
| 52 | func Dijkstra(g Graph, source, target ID) ([]ID, map[ID]float64, error) { |
| 53 | // let Q be a priority queue |
| 54 | minHeap := &nodeDistanceHeap{} |
| 55 | |
| 56 | // distance[source] = 0 |
| 57 | distance := make(map[ID]float64) |
| 58 | distance[source] = 0.0 |
| 59 | |
| 60 | // for each vertex v in G: |
| 61 | for id := range g.GetNodes() { |
| 62 | // if v ≠ source: |
| 63 | if id != source { |
| 64 | // distance[v] = ∞ |
| 65 | distance[id] = math.MaxFloat64 |
| 66 | |
| 67 | // prev[v] = undefined |
| 68 | // prev[v] = "" |
| 69 | } |
| 70 | |
| 71 | // Q.add_with_priority(v, distance[v]) |
| 72 | nds := nodeDistance{} |
| 73 | nds.id = id |
| 74 | nds.distance = distance[id] |
| 75 | |
| 76 | heap.Push(minHeap, nds) |
| 77 | } |
| 78 | |
| 79 | heap.Init(minHeap) |
| 80 | prev := make(map[ID]ID) |
| 81 | |
| 82 | // while Q is not empty: |
| 83 | for minHeap.Len() != 0 { |
| 84 | |
| 85 | // u = Q.extract_min() |
| 86 | u := heap.Pop(minHeap).(nodeDistance) |
| 87 | |
| 88 | // if u == target: |
| 89 | if u.id == target { |
| 90 | break |
| 91 | } |
| 92 | |
| 93 | // for each child vertex v of u: |
| 94 | cmap, err := g.GetTargets(u.id) |
| 95 | if err != nil { |
| 96 | return nil, nil, err |
| 97 | } |
| 98 | for v := range cmap { |
| 99 | |
| 100 | // alt = distance[u] + weight(u, v) |
| 101 | weight, err := g.GetWeight(u.id, v) |
| 102 | if err != nil { |
| 103 | return nil, nil, err |
| 104 | } |
| 105 | alt := distance[u.id] + weight |
| 106 | |
| 107 | // if distance[v] > alt: |
| 108 | if distance[v] > alt { |
| 109 | |
| 110 | // distance[v] = alt |
| 111 | distance[v] = alt |
| 112 | |
| 113 | // prev[v] = u |
| 114 | prev[v] = u.id |
| 115 | |
| 116 | // Q.decrease_priority(v, alt) |
| 117 | minHeap.updateDistance(v, alt) |
| 118 | } |
| 119 | } |
| 120 | heap.Init(minHeap) |
| 121 | } |
| 122 | |
| 123 | // path = [] |
| 124 | path := []ID{} |
| 125 | |
| 126 | // u = target |
| 127 | u := target |
| 128 | |
| 129 | // while prev[u] is defined: |
| 130 | for { |
| 131 | if _, ok := prev[u]; !ok { |
| 132 | break |
| 133 | } |
| 134 | // path.push_front(u) |
| 135 | temp := make([]ID, len(path)+1) |
| 136 | temp[0] = u |
| 137 | copy(temp[1:], path) |
| 138 | path = temp |
| 139 | |
| 140 | // u = prev[u] |
| 141 | u = prev[u] |
| 142 | } |
| 143 | |
| 144 | // add the source |
| 145 | temp := make([]ID, len(path)+1) |
| 146 | temp[0] = source |
| 147 | copy(temp[1:], path) |
| 148 | path = temp |
| 149 | |
| 150 | return path, distance, nil |
| 151 | } |
| 152 | |
| 153 | // BellmanFord returns the shortest path using Bellman-Ford algorithm |
| 154 | // This algorithm works with negative weight edges. |
| 155 | // Time complexity is O(|V||E|). |
| 156 | // (http://courses.csail.mit.edu/6.006/spring11/lectures/lec15.pdf) |
| 157 | // It returns error when there is a negative-weight cycle. |
| 158 | // A negatively-weighted cycle adds up to infinite negative-weight. |
| 159 | // |
| 160 | // 0. BellmanFord(G, source, target) |
| 161 | // 1. |
| 162 | // 2. distance[source] = 0 |
| 163 | // 3. |
| 164 | // 4. for each vertex v in G: |
| 165 | // 5. |
| 166 | // 6. if v ≠ source: |
| 167 | // 7. distance[v] = ∞ |
| 168 | // 8. prev[v] = undefined |
| 169 | // 9. |
| 170 | // 10. |
| 171 | // 11. for 1 to |V|-1: |
| 172 | // 12. |
| 173 | // 13. for every edge (u, v): |
| 174 | // 14. |
| 175 | // 15. alt = distance[u] + weight(u, v) |
| 176 | // 16. if distance[v] > alt: |
| 177 | // 17. distance[v] = alt |
| 178 | // 18. prev[v] = u |
| 179 | // 19. |
| 180 | // 20. |
| 181 | // 21. for every edge (u, v): |
| 182 | // 22. |
| 183 | // 23. alt = distance[u] + weight(u, v) |
| 184 | // 24. if distance[v] > alt: |
| 185 | // 25. there is a negative-weight cycle |
| 186 | // 26. |
| 187 | // 27. |
| 188 | // 28. path = [] |
| 189 | // 29. u = target |
| 190 | // 30. while prev[u] is defined: |
| 191 | // 31. path.push_front(u) |
| 192 | // 32. u = prev[u] |
| 193 | // 33. |
| 194 | // 34. return path, prev |
| 195 | // |
| 196 | func BellmanFord(g Graph, source, target ID) ([]ID, map[ID]float64, error) { |
| 197 | // distance[source] = 0 |
| 198 | distance := make(map[ID]float64) |
| 199 | distance[source] = 0.0 |
| 200 | |
| 201 | // for each vertex v in G: |
| 202 | for id := range g.GetNodes() { |
| 203 | |
| 204 | // if v ≠ source: |
| 205 | if id != source { |
| 206 | // distance[v] = ∞ |
| 207 | distance[id] = math.MaxFloat64 |
| 208 | |
| 209 | // prev[v] = undefined |
| 210 | // prev[v] = "" |
| 211 | } |
| 212 | } |
| 213 | |
| 214 | prev := make(map[ID]ID) |
| 215 | |
| 216 | // for 1 to |V|-1: |
| 217 | for i := 1; i <= g.GetNodeCount()-1; i++ { |
| 218 | |
| 219 | // for every edge (u, v): |
| 220 | for id := range g.GetNodes() { |
| 221 | |
| 222 | cmap, err := g.GetTargets(id) |
| 223 | if err != nil { |
| 224 | return nil, nil, err |
| 225 | } |
| 226 | u := id |
| 227 | for v := range cmap { |
| 228 | // edge (u, v) |
| 229 | weight, err := g.GetWeight(u, v) |
| 230 | if err != nil { |
| 231 | return nil, nil, err |
| 232 | } |
| 233 | |
| 234 | // alt = distance[u] + weight(u, v) |
| 235 | alt := distance[u] + weight |
| 236 | |
| 237 | // if distance[v] > alt: |
| 238 | if distance[v] > alt { |
| 239 | // distance[v] = alt |
| 240 | distance[v] = alt |
| 241 | |
| 242 | // prev[v] = u |
| 243 | prev[v] = u |
| 244 | } |
| 245 | } |
| 246 | |
| 247 | pmap, err := g.GetSources(id) |
| 248 | if err != nil { |
| 249 | return nil, nil, err |
| 250 | } |
| 251 | v := id |
| 252 | for u := range pmap { |
| 253 | // edge (u, v) |
| 254 | weight, err := g.GetWeight(u, v) |
| 255 | if err != nil { |
| 256 | return nil, nil, err |
| 257 | } |
| 258 | |
| 259 | // alt = distance[u] + weight(u, v) |
| 260 | alt := distance[u] + weight |
| 261 | |
| 262 | // if distance[v] > alt: |
| 263 | if distance[v] > alt { |
| 264 | // distance[v] = alt |
| 265 | distance[v] = alt |
| 266 | |
| 267 | // prev[v] = u |
| 268 | prev[v] = u |
| 269 | } |
| 270 | } |
| 271 | } |
| 272 | } |
| 273 | |
| 274 | // for every edge (u, v): |
| 275 | for id := range g.GetNodes() { |
| 276 | |
| 277 | cmap, err := g.GetTargets(id) |
| 278 | if err != nil { |
| 279 | return nil, nil, err |
| 280 | } |
| 281 | u := id |
| 282 | for v := range cmap { |
| 283 | // edge (u, v) |
| 284 | weight, err := g.GetWeight(u, v) |
| 285 | if err != nil { |
| 286 | return nil, nil, err |
| 287 | } |
| 288 | |
| 289 | // alt = distance[u] + weight(u, v) |
| 290 | alt := distance[u] + weight |
| 291 | |
| 292 | // if distance[v] > alt: |
| 293 | if distance[v] > alt { |
| 294 | return nil, nil, fmt.Errorf("there is a negative-weight cycle: %v", g) |
| 295 | } |
| 296 | } |
| 297 | |
| 298 | pmap, err := g.GetSources(id) |
| 299 | if err != nil { |
| 300 | return nil, nil, err |
| 301 | } |
| 302 | v := id |
| 303 | for u := range pmap { |
| 304 | // edge (u, v) |
| 305 | weight, err := g.GetWeight(u, v) |
| 306 | if err != nil { |
| 307 | return nil, nil, err |
| 308 | } |
| 309 | |
| 310 | // alt = distance[u] + weight(u, v) |
| 311 | alt := distance[u] + weight |
| 312 | |
| 313 | // if distance[v] > alt: |
| 314 | if distance[v] > alt { |
| 315 | return nil, nil, fmt.Errorf("there is a negative-weight cycle: %v", g) |
| 316 | } |
| 317 | } |
| 318 | } |
| 319 | |
| 320 | // path = [] |
| 321 | path := []ID{} |
| 322 | |
| 323 | // u = target |
| 324 | u := target |
| 325 | |
| 326 | // while prev[u] is defined: |
| 327 | for { |
| 328 | if _, ok := prev[u]; !ok { |
| 329 | break |
| 330 | } |
| 331 | // path.push_front(u) |
| 332 | temp := make([]ID, len(path)+1) |
| 333 | temp[0] = u |
| 334 | copy(temp[1:], path) |
| 335 | path = temp |
| 336 | |
| 337 | // u = prev[u] |
| 338 | u = prev[u] |
| 339 | } |
| 340 | |
| 341 | // add the source |
| 342 | temp := make([]ID, len(path)+1) |
| 343 | temp[0] = source |
| 344 | copy(temp[1:], path) |
| 345 | path = temp |
| 346 | |
| 347 | return path, distance, nil |
| 348 | } |