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GraphAlgorithms.py
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GraphAlgorithms.py
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from Heap import MinHeap
from collections import OrderedDict
import random
# #######################################################
# apsp - All Points Shortest Paths
#
# given a graph represented as a matrix with
# weighted edges, returns a matrix of
# shortes path lengths between any pair of vertices
# #######################################################
def apsp(W):
#
# Inner Function Definitions
#
def newMatrix(size):
M = []
for _ in range(size):
m = [float('inf')] * size
M.append(m)
return M
def ExtendShortestPaths(L, a, b):
if L[a] is None:
L[a] = ExtendShortestPaths(L, a//2, a - a//2)
if L[b] is None:
L[b] = ExtendShortestPaths(L, b//2, b - b//2)
n = len(L[a])
M = newMatrix(n)
for i in range(n):
for j in range(n):
for k in range(n):
M[i][j] = round(min(M[i][j], L[a][i][k] + L[b][k][j]), 2)
return M
#
# Main function definition
#
n = len(W) -1 # since longest possible path is number of vertices -1
L = [None] * (n+1) # initialzie L, the matrix of Matrix powers
L[1] = W
# Create L[0]
l = newMatrix(n)
for i in range(n):
l[i][i] = 1
L[0] = l
L[n] = ExtendShortestPaths(L, n//2, n - n//2)
return L[-1]
# ############################################################
# prims.py
# the prims() function takes as paremeters:
#
# D: a dictionary of key value pairs
# where the keys are labels of vertices,
# and the values are dictionaries of labels - distance pairs
#
# returns an edge list unless to_graph is set to True
# ############################################################
def prims(D, start = None, to_matrix = False, dist_graph = False):
if start is None:
start = random.choice(list(D.keys()))
visited = [start]
edges = []
id_function = lambda x : x['weight']
heap = MinHeap(item_val = id_function)
for dest,dist in D[start].items():
heap.insert({'origen':start, 'destination':dest, 'weight': dist})
while heap.size > 0:
e = None
while e is None and heap.size > 0:
e = heap.extract()
if e['destination'] in visited:
e = None
if e is not None:
v = e['destination']
visited.append(v)
edges.append(e)
for dest,dist in list(D[v].items()):
if dest in visited:
continue
heap.insert({'origen':v, 'destination':dest, 'weight': dist})
if to_matrix:
# initialize M
M = {}
for k in D.keys():
M[k] = {}
for l in D.keys():
if dist_graph:
M[k][l] = float('inf')
else:
M[k][l] = 0
for e in edges:
if dist_graph:
M[e['origen']][e['destination']] = e['weight']
M[e['destination']][e['origen']] = e['weight']
else:
M[e['origen']][e['destination']] = 1
M[e['destination']][e['origen']] = 1
return M
return [(e['origen'],e['destination']) for e in edges]
def randSpanningTree(initial_list):
""" Returns a random spanning tree from a list of vertices.
Based on prim's, but ignores weights """
edges = []
remaining = initial_list.copy()
visited = [random.choice(remaining)]
remaining.remove(visited[-1])
while len(remaining) > 0:
origen = random.choice(visited)
destination = random.choice(remaining)
remaining.remove(destination)
edges.append((origen,destination))
visited.append(destination)
return edges
def edge2chr(clist, edgelist):
""" takes a list of vertices, and a list of edges,
and returns a list of the degrees of the vertices """
d = OrderedDict()
for c in clist:
d[c] = 0
for s,t in edgelist:
d[s] += 1
d[t] += 1
return list(d.values())
def edge2dict(distances, E):
# initialize M
D = {}
for k in distances.keys():
D[k] = {}
for l in distances.keys():
if k == l:
D[k][l] = 0
else:
D[k][l] = float('inf')
for s,t in E:
D[s][t] = distances[s][t]
D[t][s] = distances[t][s]
return D
def edge2Matrix(D, E):
N = edge2dict(D,E)
M = []
for x in N.values():
M.append(list(x.values()))
return M
def edge_apsp(distances, E):
M = edge2Matrix(distances, E)
return apsp(M)
def edge_apsp_sum(distances, E):
M = edge2Matrix(distances, E)
return sum([sum(x) for x in apsp(M)])