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graph.py
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graph.py
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#Graph Implementation
#Author : Sayan Paul
import heapq,collections
class PriorityQueue:
"""
Implements a priority queue data structure.
"""
def __init__(self):
self.heap = []
self.count = 0
def push(self, item, priority):
entry = (priority, self.count, item)
heapq.heappush(self.heap, entry)
self.count += 1
def pop(self):
(_, _, item) = heapq.heappop(self.heap)
return item
def isEmpty(self):
return len(self.heap) == 0
def search(self,element):
for priority,count,item in self.heap:
if item == element:
return True
return False
def update(self,element,priorityNew):
l=[]
for priority,count,item in self.heap:
if item == element:
l.append(tuple([priorityNew,count,item]))
else : l.append(tuple([priority,count,item]))
self.heap=l
heapq.heapify(self.heap)
class Graph(object):
"Undirected Unweighted Graph container"
def __init__(self):
self.nodes=list()
self.edge=dict()
self.color=dict()
self.par=dict()
self.time=0
self.d=dict()
self.f=dict()
self.dfsl=list()
self.bfsl=list()
def insert(self,a,b):
"Insert edges into graph"
if not (a in self.nodes):
self.nodes.append(a)
self.edge[a]=list()
if not (b in self.nodes):
self.nodes.append(b)
self.edge[b]=list()
self.edge[a].append(b)
self.edge[b].append(a)
def succ(self,a):
"""Returns list of successors of cuurent node if present in graph
else returns None"""
try:
return self.edge[a]
except:
return []
def getnodes(self):
"Returns list of nodes in graph"
return self.nodes
def dfs(self):
"Depth first search algorithm"
if not self.dfsl==[]:
return
for u in self.nodes:
self.color[u]="white"
self.par[u]=None
self.time=0
for u in self.nodes:
if self.color[u]=="white":
self.dfs_visit(u)
def dfs_visit(self,u):
self.time+=1
self.dfsl.append(u)## node Discovered
self.dist=self.time
self.color[u]="grey"
for v in self.succ(u):
if self.color[v]=="white":
self.par[v]=u
self.dfs_visit(v)
self.color[u]="black"
self.time+=1
self.f[u]=self.time
def bfs(self,s):
q=list()
for u in self.nodes:
self.color[u]="white"
self.par[u]=None
self.color[s]="grey"
self.d[s]=0
q.append(s)
while q!=[]:
u=q.pop(0)
for v in self.succ(u):
if self.color[v]=="white":
self.color[v]="grey"
self.d[v]=self.d[u]+1
self.par[v]=u
q.append(v)
self.color[u]="black"
self.bfsl.append(u)
class UWGraph(Graph):
"Undirected Weighted Graph container"
def __init__(self):
self.nodes=list()
self.edge=dict()
self.color=dict()
self.par=dict()
self.time=0
self.d=dict()
self.f=dict()
self.dfsl=list()
self.bfsl=list()
self.rank=dict()
self.edges_w=list()
self.key=dict()
def succ(self,a):
"""Returns list of successors of cuurent node if present in graph
else returns None"""
try:
return self.edge[a].keys()
except:
return []
def succ_w(self,a):
"""Returns list of successors of cuurent node with weight if present in graph
else returns None"""
try:
return self.edge[a]
except:
return {}
def insert(self,a,b,w):
"Insert edges into graph"
if not (a in self.nodes):
self.nodes.append(a)
self.edge[a]=dict()
if not (b in self.nodes):
self.nodes.append(b)
self.edge[b]=dict()
self.edge[a][b]=w
self.edge[b][a]=w
self.edges_w.append(tuple([a,b,w]))
def find(self,v):
"Returns root of tree to which v belongs"
if self.par[v]!=v:
self.par[v]=self.find(self.par[v])
return self.par[v]
def union(self,v1,v2):
"Joins the trees to which v1 and v2 belong"
r1=self.find(v1)
r2=self.find(v2)
if r1!=r2:
if self.rank[r1]>self.rank[r2]:
self.par[r2]=r1
else:
self.par[r1]=r2
if self.rank[r1]==self.rank[r2]:
self.rank[r2]+=1
def kruskal(self):
"Kruskal's Algorithm"
rank=dict()
for v in self.nodes:
self.par[v]=v
self.rank[v]=0
mst=set()
self.edges_w.sort(key=lambda x : x[2])
for edge in self.edges_w:
v1,v2,w=edge
if self.find(v1)!=self.find(v2):
self.union(v1,v2)
mst.add(edge)
return mst
def prim(self,r):
"Prim's Algorithm"
q=PriorityQueue()
for v in self.nodes:
self.key[v]=10**6 #this chosen as the upper limit of weights [Can be changed as required]
self.par[v]=None
if v!=r:
q.push(v,self.key[v])
self.key[r]=0
q.push(r,self.key[r])
while not q.isEmpty():
u=q.pop()
adj=self.succ_w(u)
for v in adj:
if q.search(v) and adj[v]<self.key[v]:
self.par[v]=u
self.key[v]=adj[v]
q.update(v,self.key[v])
print str(self.par)
def Floyd_Warshall(self):
dis=dict()
for u in self.nodes:
t=dict()
adj=self.succ_w(u)
for v in self.nodes:
if v==u:
t[v]=0
else:
try:t[v]=adj[v]
except : t[v]=10**7
dis[u]=dict(t)
for k in self.nodes:
for i in self.nodes:
for j in self.nodes:
if dis[i][k] + dis[k][j] < dis[i][j]:
dis[i][j] = dis[i][k] + dis[k][j]
print "Distance Matrix :"
for u in dis.keys():
print u ,str(dis[u])
class DUGraph(Graph):
"Directed Unweighted Graph Container"
def insert(self,a,b):
"Insert edges into graph"
if not (a in self.nodes):
self.nodes.append(a)
self.edge[a]=list()
if not (b in self.nodes):
self.nodes.append(b)
self.edge[b]=list()
self.edge[a].append(b)
class DWGraph(UWGraph):
"Directed Weighted Graph Container"
def insert(self,a,b,w):
"Insert edges into graph"
if not (a in self.nodes):
self.nodes.append(a)
self.edge[a]=dict()
if not (b in self.nodes):
self.nodes.append(b)
self.edge[b]=dict()
self.edge[a][b]=w
self.edges_w.append(tuple([a,b,w]))
def Bellman_Ford(self,s):
"""This implementation takes in a graph, represented as lists of vertices and edges,
and fills two arrays (distance and predecessor) with shortest-path information"""
for v in self.nodes:
if v==s:
self.d[v]=0
else:
self.d[v]=10**7
self.par[v]=None
for i in range(1,len(self.nodes)):
for u,v,w in self.edges_w:
if self.d[v]>self.d[u]+w:
self.d[v]=self.d[u]+w
self.par[v]=u
for u,v,w in self.edges_w:
if self.d[v]>self.d[u]+w:
print "[ERROR] Graph contains a negative-weight cycle"
return
print "Parent list:",str(self.par)
print "Distance from source:",str(self.d)
def Dijkstra(self,r):
"Dijksta's Algorithm for single source shortest path"
q=PriorityQueue()
for v in self.nodes:
self.d[v]=10**6 #this chosen as the upper limit of weights [Can be changed as required]
self.par[v]=None
if v!=r:
q.push(v,self.d[v])
self.d[r]=0
q.push(r,self.d[r])
while not q.isEmpty():
u=q.pop()
if self.d[u]==10**6:
break
adj=self.succ_w(u)
for v in adj:
if self.d[v]>self.d[u]+adj[v]:
self.d[v]=self.d[u]+adj[v]
self.par[v]=u
q.update(v,self.d[v])
print "Parent list:",str(self.par)
print "Distance from source:",str(self.d)
## Driver code
if __name__=='__main__':
n=input("""Enter Choice:\n1. Undirected Unweighted Graph\n2. Undirected Weighted Graph
3. Directed Unweighted Graph\n4. Directed Weighted Graph\n\n$Graph\_ """)
if n==1:
graph=Graph()
print "Enter edges of graph [Enter 0 0 to end]"
while True:
a,b=raw_input().split()
if a=='0' or b =='0' :
break
graph.insert(a,b)
## print graph.getnodes()
## print [graph.succ(x) for x in graph.nodes]
m=input("Enter Choice:\n1. Depth First Search\n2. Breadth First Search\n\n$Graph\_ ")
if m==1:
graph.dfs()
print "Depth First Search:",graph.dfsl
elif m==2:
graph.bfs(graph.nodes[0])
print "Breadth First Search:",graph.bfsl
elif n==2:
graph=UWGraph()
print "Enter edges of graph [Enter 0 0 0 to end]"
while True:
a,b,w=raw_input().split()
if a=='0' or b =='0' or w=='0':
break
graph.insert(a,b,int(w))
#print [graph.succ_w(x) for x in graph.nodes]
m=input("""Enter Choice:\n1. Depth First Search
2. Breadth First Search\n3. Kruskal Minimum Spanning Tree\n4. Prim's Minimum Spanning Tree\n5. Floyd Warshall Algorithm
\n\n$Graph\_ """)
if m==1:
graph.dfs()
print "Depth First Search:",graph.dfsl
elif m==2:
graph.bfs(graph.nodes[0])
print "Breadth First Search:",graph.bfsl
elif m==3:
print "Minimum Spanning Tree [Edge list]:\n",graph.kruskal()
elif m==4:
print "Minimum Spanning Tree [Parent list]:\n"
graph.prim(graph.nodes[0])
elif m==5:
graph.Floyd_Warshall()
elif n==3:
graph=DUGraph()
print "Enter edges of graph [Enter 0 0 to end]"
while True:
a,b=raw_input().split()
if a=='0' or b =='0' :
break
graph.insert(a,b)
## print graph.getnodes()
## print [graph.succ(x) for x in graph.nodes]
m=input("Enter Choice:\n1. Depth First Search\n2. Breadth First Search\n\n$Graph\_ ")
if m==1:
graph.dfs()
print "Depth First Search:",graph.dfsl
elif m==2:
graph.bfs(graph.nodes[0])
print "Breadth First Search:",graph.bfsl
elif n==4:
graph=DWGraph()
print "Enter edges of graph [Enter 0 0 0 to end]"
while True:
a,b,w=raw_input().split()
if a=='0' or b =='0' or w=='0':
break
graph.insert(a,b,int(w))
#print [graph.succ_w(x) for x in graph.nodes]
m=input("""Enter Choice:\n1. Depth First Search
2. Breadth First Search\n3. Bellman Ford Single Source Shortest Path\n4. Dijkstra Single Source Shortest Path\n5. Floyd Warshall Algorithm\n\n$Graph\_ """)
if m==1:
graph.dfs()
print "Depth First Search:",graph.dfsl
elif m==2:
graph.bfs(graph.nodes[0])
print "Breadth First Search:",graph.bfsl
elif m==3:
c=raw_input("Enter source: ")
graph.Bellman_Ford(c)
elif m==4:
c=raw_input("Enter source: ")
graph.Dijkstra(c)
elif m==5:
graph.Floyd_Warshall()