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pre-commit-ci[bot] 2024-10-25 16:01:29 +00:00
parent da0717b9ae
commit 18319a8733
1 changed files with 34 additions and 33 deletions
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37
graphs/johnson_graph.py
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@ -2,26 +2,27 @@ from collections import deque
import heapq import heapq
import sys import sys
#First implementation of johnson algorithm
# First implementation of johnson algorithm
class JohnsonGraph: class JohnsonGraph:
def __init__(self): def __init__(self):
self.edges = [] self.edges = []
self.graph = {} self.graph = {}
#add vertices for a graph # add vertices for a graph
def add_vertices(self, u): def add_vertices(self, u):
self.graph[u] = [] self.graph[u] = []
#assign weights for each edges formed of the directed graph # assign weights for each edges formed of the directed graph
def add_edge(self, u, v, w): def add_edge(self, u, v, w):
self.edges.append((u, v, w)) self.edges.append((u, v, w))
self.graph[u].append((v,w)) self.graph[u].append((v, w))
#perform a dijkstra algorithm on a directed graph # perform a dijkstra algorithm on a directed graph
def dijkstra(self, s): def dijkstra(self, s):
no_v = len(self.graph) no_v = len(self.graph)
distances = {vertex: sys.maxsize-1 for vertex in self.graph} distances = {vertex: sys.maxsize - 1 for vertex in self.graph}
pq = [(0,s)] pq = [(0, s)]
distances[s] = 0 distances[s] = 0
while pq: while pq:
@ -31,28 +32,27 @@ class JohnsonGraph:
continue continue
for node, w in self.graph[v]: for node, w in self.graph[v]:
if distances[v]+w < distances[node]: if distances[v] + w < distances[node]:
distances[node] = distances[v]+w distances[node] = distances[v] + w
heapq.heappush(pq, (distances[node], node)) heapq.heappush(pq, (distances[node], node))
return distances return distances
#carry out the bellman ford algorithm for a node and estimate its distance vector # carry out the bellman ford algorithm for a node and estimate its distance vector
def bellman_ford(self, s): def bellman_ford(self, s):
no_v = len(self.graph) no_v = len(self.graph)
distances = {vertex: sys.maxsize-1 for vertex in self.graph} distances = {vertex: sys.maxsize - 1 for vertex in self.graph}
distances[s] = 0 distances[s] = 0
for u in self.graph: for u in self.graph:
for u, v, w in self.edges: for u, v, w in self.edges:
if distances[u] != sys.maxsize-1 and distances[u]+w<distances[v]: if distances[u] != sys.maxsize - 1 and distances[u] + w < distances[v]:
distances[v] = distances[u]+w distances[v] = distances[u] + w
return distances return distances
#perform the johnson algorithm to handle the negative weights that could not be handled by either the dijkstra # perform the johnson algorithm to handle the negative weights that could not be handled by either the dijkstra
#or the bellman ford algorithm efficiently # or the bellman ford algorithm efficiently
def johnson_algo(self): def johnson_algo(self):
self.add_vertices("#") self.add_vertices("#")
for v in self.graph: for v in self.graph:
if v != "#": if v != "#":
@ -74,13 +74,14 @@ class JohnsonGraph:
for u in self.graph: for u in self.graph:
new_dist = self.dijkstra(u) new_dist = self.dijkstra(u)
for v in self.graph: for v in self.graph:
if new_dist[v] < sys.maxsize-1: if new_dist[v] < sys.maxsize - 1:
new_dist[v] += n[v] - n[u] new_dist[v] += n[v] - n[u]
distances.append(new_dist) distances.append(new_dist)
return distances return distances
g = JohnsonGraph() g = JohnsonGraph()
#this a complete connected graph # this a complete connected graph
g.add_vertices("A") g.add_vertices("A")
g.add_vertices("B") g.add_vertices("B")
g.add_vertices("C") g.add_vertices("C")