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arboles.py
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arboles.py
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import networkx as nx
from distances import print_nodes, print_Ubitmap
import random
from numpy import Inf
def print_etiquetas(dist):
print("(E(·), ·):|", end="")
for d in dist.values():
print(d, "|", end='')
print("\n")
def dfs_arbol_generador(G, v):
print("INICIO DETERMINACION DFS RECURSIVO DE UN ARBOL GENERADOR")
T = nx.Graph()
for node in G.nodes():
T.add_node(node)
estado = {}
for w in G.nodes():
estado[w] = 0
dfsrec(G, v, T, estado)
return T
def dfsrec(G, v, T, estado):
estado[v] = 1
neighbours = sorted(list(G.neighbors(v)))
for w in neighbours:
if estado[w] == 0:
T.add_edge(w, v)
dfsrec(G, w, T, estado)
def bfs_arbol_generador(G, v):
print("INICIO DETERMINACION BFS DE UN ARBOL GENERADOR")
Q = []
A = []
T = nx.Graph()
for node in G.nodes():
T.add_node(node)
estado = {}
for w in G.nodes():
estado[w] = 0
estado[v] = 1
Q.append(v)
print("===")
print("Q", Q)
print("Aristas añadidas -")
print("A(T)", A)
while not not Q:
w = Q[0]
neighbours = sorted(list(G.neighbors(w)))
for u in neighbours:
if estado[u] == 0:
Q.append(u)
estado[u] = 1
T.add_edge(w, u)
A.append((w, u))
print("Q", Q)
print("Aristas añadidas ", (w, u))
print("A(T)", A)
Q = Q[1:]
print("Q", Q)
print("Aristas añadidas -")
print("A(T)", A)
print("===")
return T
def kruskal(G, minimal=True):
print("INICIO KRUSKAL")
T = nx.Graph()
E = sorted(G.edges(data=True), key=lambda t: t[2].get('weight', 1), reverse=not minimal)
for edge in E:
T.add_edge(edge[0], edge[1], weight=edge[2]['weight'])
if not nx.is_forest(T):
print("Arista {}".format(edge))
T.remove_edge(edge[0], edge[1])
else:
print("Arista {} *".format(edge))
print("Peso total", T.size(weight="weight"))
return T
def prim(G, v_inicial=None):
print("BEGIN PRIM")
T = nx.Graph()
for node in G.nodes():
T.add_node(node)
n = len(G.nodes)
if v_inicial is None:
v = random.choice(list(G.nodes))
else:
v = v_inicial
U = []
dist = {}
etiquetas = {}
E = {}
for node in G.nodes:
E[node] = Inf
etiquetas[node] = (E[node], v)
E[v] = 0
etiquetas[v] = (0, v)
print_nodes(G)
print_Ubitmap(U, G)
print_etiquetas(etiquetas)
U.append(v)
print("chose ", v)
while len(U) != n:
print("====")
print_nodes(G)
print_Ubitmap(U, G)
edges_from_node = sorted(G.edges(v, data=True), key=lambda t: t[2].get('weight', 1))
for edge in edges_from_node:
tgt = edge[1]
if edge[2]['weight'] < etiquetas[tgt][0] and tgt not in U:
etiquetas[tgt] = (edge[2]['weight'], v)
print_etiquetas(etiquetas)
print("====")
can_choose = []
for node in G.nodes():
if node not in U:
can_choose.append(node)
min_aw = Inf
for node in reversed(can_choose):
if etiquetas[node][0] <= min_aw:
min_aw = etiquetas[node][0]
chosen_node = node
print("chose ", chosen_node)
T.add_edge(chosen_node, etiquetas[chosen_node][1], weight=G.get_edge_data(etiquetas[chosen_node][1], chosen_node)['weight'])
U.append(chosen_node)
v = chosen_node
print("====")
print_nodes(G)
print_Ubitmap(U, G)
print_etiquetas(etiquetas)
print("====")
print("Peso total", T.size(weight="weight"))
print("Aristas de T", T.edges(data=True))
return T
def find_root(T):
return [n for n,d in T.in_degree() if d==0][0]
def preorden(T):
raiz = find_root(T)
print(raiz)
succ = list(T.successors(raiz))
if len(succ) == 2:
# Dos hijos
r1, r2 = succ
elif len(succ) == 1:
r1 = succ[0]
r2 = None
elif len(succ) == 0:
# Hoja
return None
T_uno = nx.DiGraph()
T_uno.add_node(r1)
T_uno.add_edges_from(T.edges(r1))
for node in nx.descendants(T, r1):
T_uno.add_edges_from(T.edges(node))
preorden(T_uno)
if r2 is not None:
T_dos = nx.DiGraph()
T_dos.add_node(r2)
T_dos.add_edges_from(T.edges(r2))
for node in nx.descendants(T, r2):
T_dos.add_edges_from(T.edges(node))
preorden(T_dos)
def inorden(T):
raiz = find_root(T)
succ = list(T.successors(raiz))
if len(succ) == 2:
# Dos hijos
r1, r2 = succ
elif len(succ) == 1:
r1 = succ[0]
r2 = None
elif len(succ) == 0:
# Hoja
print(raiz)
return None
T_uno = nx.DiGraph()
T_uno.add_node(r1)
T_uno.add_edges_from(T.edges(r1))
for node in nx.descendants(T, r1):
T_uno.add_edges_from(T.edges(node))
inorden(T_uno)
print(raiz)
if r2 is not None:
T_dos = nx.DiGraph()
T_dos.add_node(r2)
T_dos.add_edges_from(T.edges(r2))
for node in nx.descendants(T, r2):
T_dos.add_edges_from(T.edges(node))
inorden(T_dos)
def postorden(T):
raiz = find_root(T)
succ = list(T.successors(raiz))
if len(succ) == 2:
# Dos hijos
r1, r2 = succ
elif len(succ) == 1:
r1 = succ[0]
r2 = None
elif len(succ) == 0:
# Hoja
print(raiz)
return None
T_uno = nx.DiGraph()
T_uno.add_node(r1)
T_uno.add_edges_from(T.edges(r1))
for node in nx.descendants(T, r1):
T_uno.add_edges_from(T.edges(node))
postorden(T_uno)
if r2 is not None:
T_dos = nx.DiGraph()
T_dos.add_node(r2)
T_dos.add_edges_from(T.edges(r2))
for node in nx.descendants(T, r2):
T_dos.add_edges_from(T.edges(node))
postorden(T_dos)
print(raiz)
def digraph_from_dict_of_lists(adj):
G = nx.DiGraph()
for node, neighs in adj.items():
for n in neighs:
G.add_edges_from([(node, n)])
return G
if __name__ == '__main__':
adjs = {
1: [2, 5],
2: [5],
3: [2, 4, 5],
4: [5, 6],
}
G = nx.from_dict_of_lists(adjs)
bfs_arbol_generador(G, 1)
dfs_arbol_generador(nx.petersen_graph(), 0)
w = {
1 : {
2 : {'weight': 2},
3 : {'weight': 4},
4 : {'weight': 1}
},
2 : {
4 : {'weight': 3},
5 : {'weight': 10}
},
3 : {
4 : {'weight': 2},
6 : {'weight': 5}
},
4 : {
5 : {'weight': 2},
6 : {'weight': 8},
7 : {'weight': 4}
},
5 : {
7 : {'weight': 6}
},
6 : {
7 : {'weight': 1},
}
}
Gw = nx.from_dict_of_dicts(w)
kruskal(Gw, minimal=True)
prim(Gw, 1)
alt = {
'A' : {
'B' : {'weight' : 3},
'D' : {'weight' : 4},
'E' : {'weight' : 4},
},
'B' : {
'C' : {'weight' : 10},
'E' : {'weight' : 2},
'F' : {'weight' : 3},
},
'C' : {
'F' : {'weight' : 6},
'G' : {'weight' : 1},
},
'D' : {
'E' : {'weight' : 5},
'H' : {'weight' : 6},
},
'E' : {
'F' : {'weight' : 11},
'H' : {'weight' : 2},
'I' : {'weight' : 1},
},
'F' : {
'G' : {'weight' : 2},
'I' : {'weight' : 3},
'J' : {'weight' : 11},
},
'G' : {
'J' : {'weight' : 8},
},
'H' : {
'I' : {'weight' : 4},
},
'I' : {
'J' : {'weight' : 7},
}
}
Galt = nx.from_dict_of_dicts(alt)
kruskal(Galt)
prim(Galt, 'A')
# Ejercicio 28
letras = {
'A' : ['B', 'F'],
'B' : ['-', 'C'],
'C' : ['D', 'G'],
'D' : ['-', 'E'],
'E' : ['-', '-'],
'F' : ['-', '-'],
'G' : ['-', '-'],
}
G = digraph_from_dict_of_lists(letras)
print("PREORDEN")
preorden(G)
print("INORDEN")
inorden(G)
print("POSTORDEN")
postorden(G)