Minimum weight cycle in an undirected weighted graph in python
Python program for Minimum weight cycle in an undirected weighted graph. Here problem description and explanation.
import sys
# Python 3 program for
# Minimum weight cycle in an undirected graph
class AjlistNode :
# Vertices node key
def __init__(self, id, weight) :
# Set value of node key
self.id = id
self.weight = weight
self.next = None
class Vertices :
def __init__(self, data) :
self.data = data
self.next = None
self.last = None
class Graph :
# Number of Vertices
def __init__(self, size) :
# Set value
self.size = size
self.result = 0
self.node = [None] * (size)
self.setData()
# Set initial node value
def setData(self) :
if (self.size <= 0) :
print("\nEmpty Graph")
else :
index = 0
while (index < self.size) :
# Set initial node value
self.node[index] = Vertices(index)
index += 1
def connection(self, start, last, weight) :
# Safe connection
edge = AjlistNode(last, weight)
if (self.node[start].next == None) :
self.node[start].next = edge
else :
# Add edge at the end
self.node[start].last.next = edge
# Get last edge
self.node[start].last = edge
# Handling the request of adding new edge
def addEdge(self, start, last, weight) :
if (start >= 0 and start < self.size and
last >= 0 and last < self.size) :
# Connect edge with weight
self.connection(start, last, weight)
self.connection(last, start, weight)
else :
# When invalid nodes
print("\nNode missing (", start ," ", last ,")", end = "")
def printGraph(self) :
if (self.size > 0) :
index = 0
# Print graph ajlist
while (index < self.size) :
print("\nAdjacency list of vertex ", index ," :", end = "")
edge = self.node[index].next
while (edge != None) :
# Display graph node value and weight
print(" ", self.node[edge.id].data ,
"[", edge.weight ,"]", end = "")
# Visit to next edge
edge = edge.next
index += 1
def minimumCycle(self, start, last, visit, sum, length) :
if (start >= self.size or last >= self.size or
start < 0 or last < 0 or self.size <= 0) :
return
if (visit[start] == True) :
# Here length are indicate loop length
if (length > 2 and start == last and sum < self.result) :
# Here length is indicate number of nodes
# Because graph is undirected so we consider all cycle
# Which contains more than 2 node
# ---------------------
# When find a new min weight cycle
self.result = sum
return
# Here modified the value of visited node
visit[start] = True
# This is used to iterate nodes edges
edge = self.node[start].next
while (edge != None) :
# Find solution using recursion
self.minimumCycle(edge.id, last, visit,
sum + (edge.weight), length + 1)
# Visit to next edge
edge = edge.next
# Reset the value of visited node status
visit[start] = False
def minWeightCycle(self) :
if (self.size <= 0) :
# Empty graph
return
# Auxiliary space which is used to store
# information about visited node
# Set initial visited node status
visit = [False] * (self.size)
self.result = sys.maxsize
i = 0
while (i < self.size) :
# Check cycle of node i to i
# Here initial cycle weight is zero
self.minimumCycle(i, i, visit, 0, 0)
i += 1
# Display result
print("\nMin weight cycle : ", self.result)
def main() :
# 6 implies the number of nodes in graph
g = Graph(6)
# Connect node with an edge
# First and second parameter indicate node
# Last parameter is indicate weight
g.addEdge(0, 1, 3)
g.addEdge(0, 3, -3)
g.addEdge(0, 4, 7)
g.addEdge(0, 5, 1)
g.addEdge(1, 2, 11)
g.addEdge(1, 4, 8)
g.addEdge(2, 3, 1)
g.addEdge(2, 5, 4)
g.addEdge(3, 4, 2)
g.addEdge(4, 5, 8)
g.addEdge(5, 1, 0)
# Print graph element
g.printGraph()
# Test
g.minWeightCycle()
if __name__ == "__main__": main()
Output
Adjacency list of vertex 0 : 1 [ 3 ] 3 [ -3 ] 4 [ 7 ] 5 [ 1 ]
Adjacency list of vertex 1 : 0 [ 3 ] 2 [ 11 ] 4 [ 8 ] 5 [ 0 ]
Adjacency list of vertex 2 : 1 [ 11 ] 3 [ 1 ] 5 [ 4 ]
Adjacency list of vertex 3 : 0 [ -3 ] 2 [ 1 ] 4 [ 2 ]
Adjacency list of vertex 4 : 0 [ 7 ] 1 [ 8 ] 3 [ 2 ] 5 [ 8 ]
Adjacency list of vertex 5 : 0 [ 1 ] 2 [ 4 ] 4 [ 8 ] 1 [ 0 ]
Min weight cycle : 3
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