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Kruskal's Algorithm (Python)
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| parent = dict() | |
| rank = dict() | |
| def make_set(vertice): | |
| parent[vertice] = vertice | |
| rank[vertice] = 0 | |
| def find(vertice): | |
| if parent[vertice] != vertice: | |
| parent[vertice] = find(parent[vertice]) | |
| return parent[vertice] | |
| def union(vertice1, vertice2): | |
| root1 = find(vertice1) | |
| root2 = find(vertice2) | |
| if root1 != root2: | |
| if rank[root1] > rank[root2]: | |
| parent[root2] = root1 | |
| else: | |
| parent[root1] = root2 | |
| if rank[root1] == rank[root2]: rank[root2] += 1 | |
| def kruskal(graph): | |
| for vertice in graph['vertices']: | |
| make_set(vertice) | |
| minimum_spanning_tree = set() | |
| edges = list(graph['edges']) | |
| edges.sort() | |
| #print edges | |
| for edge in edges: | |
| weight, vertice1, vertice2 = edge | |
| if find(vertice1) != find(vertice2): | |
| union(vertice1, vertice2) | |
| minimum_spanning_tree.add(edge) | |
| return sorted(minimum_spanning_tree) | |
| graph = { | |
| 'vertices': ['A', 'B', 'C', 'D', 'E', 'F', 'G'], | |
| 'edges': set([ | |
| (7, 'A', 'B'), | |
| (5, 'A', 'D'), | |
| (7, 'B', 'A'), | |
| (8, 'B', 'C'), | |
| (9, 'B', 'D'), | |
| (7, 'B', 'E'), | |
| (8, 'C', 'B'), | |
| (5, 'C', 'E'), | |
| (5, 'D', 'A'), | |
| (9, 'D', 'B'), | |
| (7, 'D', 'E'), | |
| (6, 'D', 'F'), | |
| (7, 'E', 'B'), | |
| (5, 'E', 'C'), | |
| (15, 'E', 'D'), | |
| (8, 'E', 'F'), | |
| (9, 'E', 'G'), | |
| (6, 'F', 'D'), | |
| (8, 'F', 'E'), | |
| (11, 'F', 'G'), | |
| (9, 'G', 'E'), | |
| (11, 'G', 'F'), | |
| ]) | |
| } | |
| print kruskal(graph) |
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