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| import heapq from collections import namedtuple
class UnionFind(object): def __init__(self, nodes): self.parent = {v: -1 for v in nodes} self.rank = {r: 0 for r in nodes}
def get_root(self, i): if self.parent[i] == -1: return i self.parent[i] = self.get_root(self.parent[i]) return self.parent[i]
def union(self, i, j): i_root = self.get_root(i) j_root = self.get_root(j)
if i_root != j_root: if self.rank[i_root] == self.rank[j_root]: self.parent[i_root] = j_root self.rank[j_root] += 1 elif self.rank[i_root] > self.rank[j_root]: self.parent[j_root] = i_root else: self.parent[i_root] = j_root
def is_connected(self, i, j): return self.get_root(i) == self.get_root(j)
class MyHeap(object): def __init__(self, initial = None, key = None): if not key: self.key = lambda x: x.weight
if initial: self._data = [(key(item), item) for item in initial] heapq.heapify(self._data) else: self._data = []
def push(self, item): heapq.heappush(self._data, (self.key(item), item))
def pop(self): return heapq.heappop(self._data)[1]
def empty(self): return False if self._data else True
def kruskal(graph):
edge = namedtuple("edge",('u','v','weight')) heap = MyHeap() union_find = UnionFind(graph.keys())
path = [] weight = 0
for u in graph: for v in graph[u]: heap.push(edge(u,v,graph[u][v]))
while len(path) < len(graph)-1: edge = heap.pop() if not union_find.is_connected(edge.u, edge.v): path.append(edge) weight += edge.weight union_find.union(edge.u,edge.v)
return weight,path
def prim(graph, root):
prev = None path = [] total = 0 visited = set() Node = namedtuple("Node",("v","weight")) heap = MyHeap() heap.push(Node(root,0)) while not heap.empty(): cur_node = heap.pop() if cur_node.v not in visited: visited.add(cur_node.v) total += cur_node.weight if prev: path.append((prev,cur_node.v,cur_node.weight)) prev = cur_node.v for neighbour in graph[cur_node.v]: if neighbour not in visited: heap.push(Node(neighbour, graph[cur_node.v][neighbour]))
return total,path
return weight,path
if __name__ == '__main__': graph_dict = { "v1":{"v2": 32, "v4": 17}, "v2":{"v1":32, "v5": 45}, "v3":{"v7":5,"v4":18}, "v4":{"v3":18,"v1":17, "v5":10,"v8":3}, "v5":{"v4":10,"v2":45,"v9":25,"v6":28}, "v6":{"v5":28,"v10":6}, "v7":{"v3":5,"v8":59}, "v8":{"v4":3,"v7":59,"v9":4}, "v9":{"v8":4,"v5":25,"v10":12}, "v10":{"v9":12,"v6":6} }
weight,path = prim(graph_dict, 'v1') print(weight) print(path)
weight,path = kruskal(graph_dict) print(weight) print(path)
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