def topo_sort_dfs(g:Graph):
#找出有入度的节点
in_nodes = set()
for v in g:
for nbr in v.getConnections():
in_nodes.add(nbr.id)
#找出起始节点
start_nodes = []
for node in g.getVertices():
if node not in list(in_nodes):
start_nodes.append(node)
'''
对递归版dfs做点改变
'''
def dfs(node:Vertex,path=''):
if not node.getConnections():
paths.append(path + node.id)
return
for nbr in node.getConnections():
dfs(nbr,path + node.id)
return
paths = []
for node in start_nodes:
dfs(g.getVertex(node))
#打印结果
for str in paths:
for char in str:
print(char,end=' ')
print()
def topo_sort_bfs(g:Graph):
#建立入度表
in_degrees = {}
for v in g:
if v.id not in in_degrees:
in_degrees[v.id] = 0
for nbr in v.getConnections():
in_degrees[nbr.id] = in_degrees.get(nbr.id,0) + 1
# print(in_degrees)
#找起始节点
queue = []
for key,value in in_degrees.items():
if value == 0:
queue.append(key)
#拓扑排序
tuopu = []
while queue:
cur_id = queue.pop(0)
tuopu.append(cur_id)
for nbr in g.getVertex(cur_id).getConnections():
in_degrees[nbr.id] = in_degrees.get(nbr.id) - 1
if in_degrees[nbr.id] == 0:
queue.append(nbr.id)
#返回结果
return tuopu if len(tuopu) == len(g.getVertices()) else []
def createBoard(size=8):
game = Graph()
for row in range(size):
for col in range(size):
ID = (row * size) + col
pos = moves(row, col, size)
for i in pos:
nid = (i[0] * size) + i[1]
game.addEdge(ID, nid)
return game
def generate_connected_weighted_undirected_graph(number_of_vertices: int,
maximum_edge_weight: int,
edges_per_vertex: int):
graph = Graph()
indexes = [index for index in range(number_of_vertices)]
for index in indexes:
for neighbor_vertex_index in choices(indexes, k=randrange(1, min(number_of_vertices, edges_per_vertex))):
graph.addEdge(index, neighbor_vertex_index, randrange(1, maximum_edge_weight))
graph.addEdge(neighbor_vertex_index, index, randrange(1, maximum_edge_weight))
return graph
def knightGraph( size ):
"""在每个格子上 knightGraph 函数调用 genLegalMoves 辅助函数来创建一个当 前这个格子上骑士所有合法移动的列表。
所有的合法移动都被转换为图上的边。"""
knightGrh = Graph()
for row in range(size):
for col in range(size):
location = posToNodeId( row, col, size )
legalList = genLegalMoves( row, col, size)
for legal in legalList:
legal_loc = posToNodeId(legal[0], legal[1], size)
knightGrh.addEdge(location, legal_loc)
return knightGrh
def buildGraph(wordFile):
d = {}
g = Graph()
wfile = open(wordFile,'r')
# create buckets of words that differ by one letter
for line in wfile:
word = line[:-1]
for i in range(len(word)):
bucket = word[:i] + '_' + word[i+1:]
if bucket in d:
d[bucket].append(word)
else:
d[bucket] = [word]
# add vertices and edges for words in the same bucket
for bucket in d.keys():
for word1 in d[bucket]:
for word2 in d[bucket]:
if word1 != word2:
g.addEdge(word1,word2)
return g
def buildGraph(wordFile):
d = {}
g = Graph()
wfile = open(wordFile, 'r')
# create buckets of words that differ by one letter
for line in wfile:
word = line[:-1]
for i in range(len(word)):
bucket = word[:i] + '_' + word[i + 1:]
if bucket in d:
d[bucket].append(word)
else:
d[bucket] = [word]
# add vertices and edges for words in the same bucket
for bucket in d.keys():
for word1 in d[bucket]:
for word2 in d[bucket]:
if word1 != word2:
g.addEdge(word1, word2)
return g
def test_model(self):
number_of_vertices, maximum_edge_weight, edges_per_vertex = (10, 10, 3)
# graph = RandomGraphGenerator.generate_connected_weighted_undirected_graph(number_of_vertices,
# maximum_edge_weight,
# edges_per_vertex)
graph = Graph()
graph.addEdge(0, 1, 1)
graph.addEdge(1, 0, 1)
graph.addEdge(0, 2, 2)
graph.addEdge(2, 0, 2)
thorup = ThorupModel(graph)
thorup.construct_minimum_spanning_tree(KruskalMstAlgorithm)
thorup.construct_other_data_structures()
result = thorup.find_shortest_paths(0)
self.assertEquals([0, 1, 2], result)
def spawn_tree(source_graph: Graph) -> Graph:
union_find_nodes = [
UnionFindNode(i) for i in range(source_graph.numVertices)
]
sorted_edges = KruskalMstAlgorithm.sorts_edges_by_weights(source_graph)
msb_minimum_spanning_tree = Graph()
while sorted_edges: # msb_minimum_spanning_tree.numVertices < ((source_graph.numVertices - 1) * 2):
edge = sorted_edges.pop(0)
source_id = UnionFindStructureTarjan\
.find(union_find_nodes[edge.source]).item
target_id = UnionFindStructureTarjan\
.find(union_find_nodes[edge.target]).item
if source_id != target_id:
msb_minimum_spanning_tree.addEdge(source_id, target_id,
edge.weight)
msb_minimum_spanning_tree.addEdge(target_id, source_id,
edge.weight)
UnionFindStructureTarjan.union(union_find_nodes[source_id],
union_find_nodes[target_id])
return msb_minimum_spanning_tree
#!/usr/bin/env python
import argparse
import re
import subprocess, sys, os
from pythonds import Queue, Graph, Vertex
vertices = []
consumes = Graph()
is_consumed = Graph()
blacklisted_modules_id = []
class MyVertex(Vertex):
WHITE = 0
GRAY = 1
BLACK = 2
def __init__(self,num):
self.color = MyVertex.WHITE
super().__init__(num)
def bfs(graph, start, debug=False):
"""
Breadth First Search (BFS)
Given a node in a graph, BFS will find all nodes connected to this
node. The distance between nodes is measured in HOPS. It will find
all nodes at distance 'k' before finding any nodes at a further
distance. It will return the full list of connected nodes.
PseudoCode:
BFS(G,s)
for each vertex u in V[G] - {s} do
state[u] = WHITE
else:
d[bucket] = [word]
# add vertices and edges for words in the same bucket
for bucket in d.keys():
for word1 in d[bucket]:
for word2 in d[bucket]:
if word1 != word2:
g.addEdge(word1,word2)
return g
line = "pool cool fool foil fail "
word = line[:-1]
d = {}
g = Graph()
for i in range(len(word)):
bucket = word[:i] + '_' + word[i+1:]
if bucket in d:
d[bucket].append(word)
else:
d[bucket] = [word]
for bucket in d.keys():
for word1 in d[bucket]:
for word2 in d[bucket]:
if word1 != word2:
g.addEdge(word1,word2)
# O(V)
pq.buildHeap([(v.getDistance(), v) for v in G])
while not pq.isEmpty():
closest = pq.delMin()
for n in closest.getConnections():
newCost = closest.getWeight(n)
if n in pq and newCost < n.getDistance():
n.setPred(closest)
n.setDistance(newCost)
pq.decreaseKey(n, newCost)
return G
g = Graph()
g.addVertex(0)
g.addVertex(1)
g.addVertex(2)
g.addVertex(3)
g.addEdge(0, 1, 10)
g.addEdge(1, 0, 10)
g.addEdge(0, 2, 6)
g.addEdge(2, 0, 6)
g.addEdge(0, 3, 5)
g.addEdge(3, 0, 5)
g.addEdge(1, 3, 15)
g.addEdge(3, 1, 15)
g.addEdge(2, 3, 4)
g.addEdge(3, 2, 4)
# O(V)
pq.buildHeap([(v.getDistance(), v) for v in g])
while not pq.isEmpty():
# O(logV) * O(V) = O(V*logV)
closest = pq.delMin()
for n in closest.getConnections():
new_distance = closest.getDistance() + closest.getWeight(n)
if new_distance < n.getDistance():
n.setDistance(new_distance)
n.setPred(closest)
# O(E*logV)
pq.decreaseKey(n, new_distance)
g = Graph()
g.addVertex(0)
g.addVertex(1)
g.addVertex(2)
g.addVertex(3)
g.addEdge(0, 1, 10)
g.addEdge(0, 2, 6)
g.addEdge(0, 3, 5)
g.addEdge(1, 3, 15)
g.addEdge(2, 3, 4)
d = dijsktras(g, g.getVertex(0))
print('Distances from {}: '.format(0), end="\n")
print("********************")
for v in d:
print('Distance to {}: {}'.format(v.getId(), d[v]))
def dfs_modified(g, start, visited, s):
visited.append(start)
for v in g.getVertex(start).getConnections():
if v.id not in visited:
dfs_modified(g, v.id, visited, s)
s.append(start)
def topological_sort(g, n):
visited = []
s = []
for i in range(n):
if i not in visited:
dfs_modified(g, i, visited, s)
print(s[::-1])
g = Graph()
g.addEdge(5, 2)
g.addEdge(5, 0)
g.addEdge(4, 0)
g.addEdge(4, 1)
g.addEdge(2, 3)
g.addEdge(3, 1)
topological_sort(g, 6)
distance[v][v] = 0
for n in v.getConnections():
distance[v][n] = v.getWeight(n)
for k in g:
for i in g:
for j in g:
distance[i][j] = min(distance[i][j],
distance[i][k] + distance[k][j])
print_shortest_distance(distance, g)
def print_shortest_distance(d, g):
for i in d:
for j in g:
print(f"{i.getId()} --> {j.getId()} {d[i][j]}")
g = Graph()
g.addVertex(0)
g.addVertex(1)
g.addVertex(2)
g.addVertex(3)
g.addEdge(0, 1, 5)
g.addEdge(0, 3, 10)
g.addEdge(1, 2, 3)
g.addEdge(2, 3, 1)
floyd_warshall(g)
from pythonds import Graph, Vertex
def dfs(g, start, visited=None):
if not visited:
visited = []
visited.append(start)
for v in g.getVertex(start).getConnections():
if v.id not in visited:
dfs(g, v.id, visited)
return visited
g = Graph()
for i in range(1, 7):
g.addVertex(i)
g.addEdge(1,2)
g.addEdge(1,3)
g.addEdge(2,4)
g.addEdge(2,5)
g.addEdge(3,5)
g.addEdge(3,6)
a = dfs(g, 1)
print(a)
from pythonds import Graph
import timeit
from algorithms import Prims
from Stats import Display
graph = Graph()
Display.creategraph(Display, graph)
v = graph.getVertex(1)
testing = 10
exe = 0
exe2 = 0
# Prim 1
for i in range(testing):
start_time = timeit.default_timer()
Prims.prim1(Prims, graph, v)
time = timeit.default_timer() - start_time
exe += time
average = exe / testing
print("Prim 1 took:", average, 'on average')
'''
# Prim 2
for x in range(testing):
start_time = timeit.default_timer()
Prims.prim2(Prims, graph, v)
time = timeit.default_timer() - start_time
exe2 += time
average = exe2 / testing
print("Prim 2 took:", average, 'on average')
else:
d[bucket] = [word]
# add vertices and edges for words in the same bucket
for bucket in d.keys():
for word1 in d[bucket]:
for word2 in d[bucket]:
if word1 != word2:
g.addEdge(word1, word2)
return g
line = "pool cool fool foil fail "
word = line[:-1]
d = {}
g = Graph()
for i in range(len(word)):
bucket = word[:i] + '_' + word[i + 1:]
if bucket in d:
d[bucket].append(word)
else:
d[bucket] = [word]
for bucket in d.keys():
for word1 in d[bucket]:
for word2 in d[bucket]:
if word1 != word2:
g.addEdge(word1, word2)
if t not in self.vertList:
self.addVertex(t)
self.vertList[f].addNeighbor(self.vertList[t], cost)
def getVertices(self):
return self.vertList.keys()
def __contains__(self, key):
return key in self.vertList
def __iter__(self):
return iter(self.vertList.values())
#测试
g = Graph()
for i in range(4):
g.addVertex(i)
g.addEdge(0, 1, 5)
g.addEdge(0, 2, 4)
g.addEdge(1, 2, 3)
g.addEdge(1, 3, 3)
g.addEdge(2, 4, 1)
g.addEdge(2, 5, 2)
# for v in g:
# print(v)
# print(g.getVertex(1))
'''
2.图的遍历(非强连通图也可以)
2.1 BFS
if newDist < nextV.getDistance():
nextV.setDistance(newDist)
nextV.setPred(curV)
pq.decreaseKey(nextV,newDist) #这个方法应该是内部调用了percUp(),有调整堆的味道
#初始化图
v = ['u','v','x','w','y','z']
#无向图一定要这样创建吗？
edge = [('u','v',2),('u','w',5),('u','x',1),
('v','u',2),('v','x',2),('v','w',3),
('x','u',1),('x','v',2),('x','w',3),('x','y',1),
('w','v',2),('w','u',5),('w','x',3),('w','y',1),('w','z',5),
('y','x',1),('y','w',1),('y','z',1),
('z','w',5),('z','y',1)]
g = Graph()
g.addVertex(v for v in v)
for cur,nbr,weight in edge:
g.addEdge(cur, nbr, weight)
# print(g.getVertex('w'))
# #测试
# dijkstra(g,g.getVertex('u'))
# for v in v[1:]:
# print('u到%s的最短距离：%i' % (v,g.getVertex(v).getDistance()))
'''
4.最小生成树
注：同Dijkstra算法很相似
'''