khenaidoo | ac63710 | 2019-01-14 15:44:34 -0500 | [diff] [blame] | 1 | package goraph |
| 2 | |
| 3 | import ( |
| 4 | "container/heap" |
| 5 | "math" |
| 6 | "sort" |
| 7 | ) |
| 8 | |
| 9 | // Kruskal finds the minimum spanning tree with disjoint-set data structure. |
| 10 | // (http://en.wikipedia.org/wiki/Kruskal%27s_algorithm) |
| 11 | // |
| 12 | // 0. Kruskal(G) |
| 13 | // 1. |
| 14 | // 2. A = ∅ |
| 15 | // 3. |
| 16 | // 4. for each vertex v in G: |
| 17 | // 5. MakeDisjointSet(v) |
| 18 | // 6. |
| 19 | // 7. edges = get all edges |
| 20 | // 8. sort edges in ascending order of weight |
| 21 | // 9. |
| 22 | // 10. for each edge (u, v) in edges: |
| 23 | // 11. if FindSet(u) ≠ FindSet(v): |
| 24 | // 12. A = A ∪ {(u, v)} |
| 25 | // 13. Union(u, v) |
| 26 | // 14. |
| 27 | // 15. return A |
| 28 | // |
| 29 | func Kruskal(g Graph) (map[Edge]struct{}, error) { |
| 30 | |
| 31 | // A = ∅ |
| 32 | A := make(map[Edge]struct{}) |
| 33 | |
| 34 | // disjointSet maps a member Node to a represent. |
| 35 | // (https://en.wikipedia.org/wiki/Disjoint-set_data_structure) |
| 36 | forests := NewForests() |
| 37 | |
| 38 | // for each vertex v in G: |
| 39 | for _, nd := range g.GetNodes() { |
| 40 | // MakeDisjointSet(v) |
| 41 | MakeDisjointSet(forests, nd.String()) |
| 42 | } |
| 43 | |
| 44 | // edges = get all edges |
| 45 | edges := []Edge{} |
| 46 | foundEdge := make(map[string]struct{}) |
| 47 | for id1, nd1 := range g.GetNodes() { |
| 48 | tm, err := g.GetTargets(id1) |
| 49 | if err != nil { |
| 50 | return nil, err |
| 51 | } |
| 52 | for id2, nd2 := range tm { |
| 53 | weight, err := g.GetWeight(id1, id2) |
| 54 | if err != nil { |
| 55 | return nil, err |
| 56 | } |
| 57 | edge := NewEdge(nd1, nd2, weight) |
| 58 | if _, ok := foundEdge[edge.String()]; !ok { |
| 59 | edges = append(edges, edge) |
| 60 | foundEdge[edge.String()] = struct{}{} |
| 61 | } |
| 62 | } |
| 63 | |
| 64 | sm, err := g.GetSources(id1) |
| 65 | if err != nil { |
| 66 | return nil, err |
| 67 | } |
| 68 | for id3, nd3 := range sm { |
| 69 | weight, err := g.GetWeight(id3, id1) |
| 70 | if err != nil { |
| 71 | return nil, err |
| 72 | } |
| 73 | edge := NewEdge(nd3, nd1, weight) |
| 74 | if _, ok := foundEdge[edge.String()]; !ok { |
| 75 | edges = append(edges, edge) |
| 76 | foundEdge[edge.String()] = struct{}{} |
| 77 | } |
| 78 | } |
| 79 | } |
| 80 | |
| 81 | // sort edges in ascending order of weight |
| 82 | sort.Sort(EdgeSlice(edges)) |
| 83 | |
| 84 | // for each edge (u, v) in edges: |
| 85 | for _, edge := range edges { |
| 86 | // if FindSet(u) ≠ FindSet(v): |
| 87 | if FindSet(forests, edge.Source().String()).represent != FindSet(forests, edge.Target().String()).represent { |
| 88 | |
| 89 | // A = A ∪ {(u, v)} |
| 90 | A[edge] = struct{}{} |
| 91 | |
| 92 | // Union(u, v) |
| 93 | // overwrite v's represent with u's represent |
| 94 | Union(forests, FindSet(forests, edge.Source().String()), FindSet(forests, edge.Target().String())) |
| 95 | } |
| 96 | } |
| 97 | |
| 98 | return A, nil |
| 99 | } |
| 100 | |
| 101 | // Prim finds the minimum spanning tree with min-heap (priority queue). |
| 102 | // (http://en.wikipedia.org/wiki/Prim%27s_algorithm) |
| 103 | // |
| 104 | // 0. Prim(G, source) |
| 105 | // 1. |
| 106 | // 2. let Q be a priority queue |
| 107 | // 3. distance[source] = 0 |
| 108 | // 4. |
| 109 | // 5. for each vertex v in G: |
| 110 | // 6. |
| 111 | // 7. if v ≠ source: |
| 112 | // 8. distance[v] = ∞ |
| 113 | // 9. prev[v] = undefined |
| 114 | // 10. |
| 115 | // 11. Q.add_with_priority(v, distance[v]) |
| 116 | // 12. |
| 117 | // 13. |
| 118 | // 14. while Q is not empty: |
| 119 | // 15. |
| 120 | // 16. u = Q.extract_min() |
| 121 | // 17. |
| 122 | // 18. for each adjacent vertex v of u: |
| 123 | // 19. |
| 124 | // 21. if v ∈ Q and distance[v] > weight(u, v): |
| 125 | // 22. distance[v] = weight(u, v) |
| 126 | // 23. prev[v] = u |
| 127 | // 24. Q.decrease_priority(v, weight(u, v)) |
| 128 | // 25. |
| 129 | // 26. |
| 130 | // 27. return tree from prev |
| 131 | // |
| 132 | func Prim(g Graph, src ID) (map[Edge]struct{}, error) { |
| 133 | |
| 134 | // let Q be a priority queue |
| 135 | minHeap := &nodeDistanceHeap{} |
| 136 | |
| 137 | // distance[source] = 0 |
| 138 | distance := make(map[ID]float64) |
| 139 | distance[src] = 0.0 |
| 140 | |
| 141 | // for each vertex v in G: |
| 142 | for id := range g.GetNodes() { |
| 143 | |
| 144 | // if v ≠ src: |
| 145 | if id != src { |
| 146 | // distance[v] = ∞ |
| 147 | distance[id] = math.MaxFloat64 |
| 148 | |
| 149 | // prev[v] = undefined |
| 150 | // prev[v] = "" |
| 151 | } |
| 152 | |
| 153 | // Q.add_with_priority(v, distance[v]) |
| 154 | nds := nodeDistance{} |
| 155 | nds.id = id |
| 156 | nds.distance = distance[id] |
| 157 | |
| 158 | heap.Push(minHeap, nds) |
| 159 | } |
| 160 | |
| 161 | heap.Init(minHeap) |
| 162 | prev := make(map[ID]ID) |
| 163 | |
| 164 | // while Q is not empty: |
| 165 | for minHeap.Len() != 0 { |
| 166 | |
| 167 | // u = Q.extract_min() |
| 168 | u := heap.Pop(minHeap).(nodeDistance) |
| 169 | uID := u.id |
| 170 | |
| 171 | // for each adjacent vertex v of u: |
| 172 | tm, err := g.GetTargets(uID) |
| 173 | if err != nil { |
| 174 | return nil, err |
| 175 | } |
| 176 | for vID := range tm { |
| 177 | |
| 178 | isExist := false |
| 179 | for _, one := range *minHeap { |
| 180 | if vID == one.id { |
| 181 | isExist = true |
| 182 | break |
| 183 | } |
| 184 | } |
| 185 | |
| 186 | // weight(u, v) |
| 187 | weight, err := g.GetWeight(uID, vID) |
| 188 | if err != nil { |
| 189 | return nil, err |
| 190 | } |
| 191 | |
| 192 | // if v ∈ Q and distance[v] > weight(u, v): |
| 193 | if isExist && distance[vID] > weight { |
| 194 | |
| 195 | // distance[v] = weight(u, v) |
| 196 | distance[vID] = weight |
| 197 | |
| 198 | // prev[v] = u |
| 199 | prev[vID] = uID |
| 200 | |
| 201 | // Q.decrease_priority(v, weight(u, v)) |
| 202 | minHeap.updateDistance(vID, weight) |
| 203 | heap.Init(minHeap) |
| 204 | } |
| 205 | } |
| 206 | |
| 207 | sm, err := g.GetSources(uID) |
| 208 | if err != nil { |
| 209 | return nil, err |
| 210 | } |
| 211 | vID := uID |
| 212 | for uID := range sm { |
| 213 | |
| 214 | isExist := false |
| 215 | for _, one := range *minHeap { |
| 216 | if vID == one.id { |
| 217 | isExist = true |
| 218 | break |
| 219 | } |
| 220 | } |
| 221 | |
| 222 | // weight(u, v) |
| 223 | weight, err := g.GetWeight(uID, vID) |
| 224 | if err != nil { |
| 225 | return nil, err |
| 226 | } |
| 227 | |
| 228 | // if v ∈ Q and distance[v] > weight(u, v): |
| 229 | if isExist && distance[vID] > weight { |
| 230 | |
| 231 | // distance[v] = weight(u, v) |
| 232 | distance[vID] = weight |
| 233 | |
| 234 | // prev[v] = u |
| 235 | prev[vID] = uID |
| 236 | |
| 237 | // Q.decrease_priority(v, weight(u, v)) |
| 238 | minHeap.updateDistance(vID, weight) |
| 239 | heap.Init(minHeap) |
| 240 | } |
| 241 | } |
| 242 | } |
| 243 | |
| 244 | tree := make(map[Edge]struct{}) |
| 245 | for k, v := range prev { |
| 246 | weight, err := g.GetWeight(v, k) |
| 247 | if err != nil { |
| 248 | return nil, err |
| 249 | } |
| 250 | tree[NewEdge(g.GetNode(v), g.GetNode(k), weight)] = struct{}{} |
| 251 | } |
| 252 | return tree, nil |
| 253 | } |
| 254 | |
| 255 | type nodeDistance struct { |
| 256 | id ID |
| 257 | distance float64 |
| 258 | } |
| 259 | |
| 260 | // container.Heap's Interface needs sort.Interface, Push, Pop to be implemented |
| 261 | |
| 262 | // nodeDistanceHeap is a min-heap of nodeDistances. |
| 263 | type nodeDistanceHeap []nodeDistance |
| 264 | |
| 265 | func (h nodeDistanceHeap) Len() int { return len(h) } |
| 266 | func (h nodeDistanceHeap) Less(i, j int) bool { return h[i].distance < h[j].distance } // Min-Heap |
| 267 | func (h nodeDistanceHeap) Swap(i, j int) { h[i], h[j] = h[j], h[i] } |
| 268 | |
| 269 | func (h *nodeDistanceHeap) Push(x interface{}) { |
| 270 | *h = append(*h, x.(nodeDistance)) |
| 271 | } |
| 272 | |
| 273 | func (h *nodeDistanceHeap) Pop() interface{} { |
| 274 | heapSize := len(*h) |
| 275 | lastNode := (*h)[heapSize-1] |
| 276 | *h = (*h)[0 : heapSize-1] |
| 277 | return lastNode |
| 278 | } |
| 279 | |
| 280 | func (h *nodeDistanceHeap) updateDistance(id ID, val float64) { |
| 281 | for i := 0; i < len(*h); i++ { |
| 282 | if (*h)[i].id == id { |
| 283 | (*h)[i].distance = val |
| 284 | break |
| 285 | } |
| 286 | } |
| 287 | } |