Question
program with Phython on Sypder you will create a Python program that implements Prim's algorithm to find a Minimal Weight Spanning tree for a weighted
program with Phython on Sypder
you will create a Python program that implements Prim's algorithm to find a Minimal Weight Spanning tree for a weighted graph G. Attached to this assignment, you will find 3 files
1. Weighted_Graph.py : A class to create a weighted graph object. 2. test.txt : A text file defining a weighted graph 3. Prim_Template.py: A template of the python program to implement Prim's algorithm.
Update Prim_Template.py with the python code to create a weighted graph object from test.txt , impletment Prim's algorithm to find a minimal spanning tree for weighted graph, and display the spanning tree.
Wheighed_Graph.py (P.S.!!!!!! this py file should stay un edited!!!!!!) and ignore the untitled py file its just a black open py file
continuation of Wheighed_Graph.py
********(P.S. this is just the context of the picture just incase its too blurry)********
#!/usr/bin/env python3 # -*- coding: utf-8 -*- """ Discrete Mathematical Structures
In this python script we define a simple and weighted graph class object. This object should be used to write Prim's and Kruskal's algorithms. """
import numpy as np import networkx as nx import matplotlib.pyplot as plt
class Weighted_Graph(object): def __init__(self, edge_list_file): """ Set the edge list directory address """ self.edge_list_file = edge_list_file def edge_dict(self): """ Reads in the edge list from the provided directory address and creates a edge dictionary where the keys are the edges and values are the corresponding edge weights. In particular, to access the value of edge (a,b), simply type edge_dict[(a,b)]""" edge_dict = dict() # dict()=empty dictionary edge_list = np.loadtxt(self.edge_list_file, int) # numpy 2-d array for row in edge_list: edge_dict[(row[0], row[1])] = row[2] # Assign keys and values return edge_dict def edge_set(self): """ Returns the set of edges """ return set(self.edge_dict().keys()) def vertex_set(self): """ Returns the set of vertices """ vertex_set = set() # set()= the empty set for e in self.edge_set(): for v in e: vertex_set.add(v) return vertex_set def draw_graph(self): """ This function is used to visualize your weighted graph. The functions used inside are from the networkx library. """ G = nx.read_edgelist(self.edge_list_file, nodetype=int, data=(('weight',float),)) e=[(u,v) for (u,v,d) in G.edges(data=True)] pos=nx.spring_layout(G) # positions for all nodes nx.draw_networkx_nodes(G,pos,node_size=250) # nodes nx.draw_networkx_edges(G,pos,edgelist=e,width=1) # edges # labels labels = nx.get_edge_attributes(G,'weight') nx.draw_networkx_labels(G,pos,font_size=10,font_family='sans-serif') nx.draw_networkx_edge_labels(G,pos,edge_labels=labels) plt.axis('off') plt.show() def draw_subgraph(self, H): """ This function is used to visualize your weighted graph. The functions used inside are from the networkx library. """ G = nx.read_edgelist(self.edge_list_file, nodetype=int, data=(('weight',float),)) e1=[(u,v) for (u,v,d) in G.edges(data=True)] e2= [e for e in e1 if e in H[1]] v1 =[v for v in H[0]] pos=nx.spring_layout(G) # positions for all nodes nx.draw_networkx_nodes(G,pos,node_size=250) # nodes nx.draw_networkx_nodes(G,pos, nodelist = v1,node_size=400) nx.draw_networkx_edges(G,pos,edgelist=e1,width=1) # edges nx.draw_networkx_edges(G,pos,edgelist=e2, color = 'red' ,width=5) # labels labels = nx.get_edge_attributes(G,'weight') nx.draw_networkx_labels(G,pos,font_size=10,font_family='sans-serif') nx.draw_networkx_edge_labels(G,pos,edge_labels=labels) plt.axis('off') plt.show()
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Prim_Template.py (P.S. !! this is where the code should go, following the hints / comments)
continuation of Prim_Template.py
********(P.S. this is just the context of the picture just incase its too blurry)********
''' import Weighted_Graph '''
''' Use Prim's algorithm to find a MST for the graph G ''' def prim(G): ''' Initialize tree T with a single vertex and no edges '''
''' while the vertex set of T is smaller than the vertex set of G, find the edge e with minimum weight so that T+e is a tree. Then update T = T+e '''
''' return T '''
''' return the edge e from graph G with minimum weight where T+e is a tree ''' def minValidEdge(G,T): ''' get a set all edges e in G where T+e is a tree'''
''' initialize minEdge to be a random edge in valid '''
''' check all edges e in valid. if the weight of e is less than the weight of minEdge, update minEdge = e '''
''' return minEdge'''
''' return the weight of an edge in a weighted graph G ''' def weight(e,G):
''' return the set of all edges e from G where T+e is a tree and e is not already an edge of T''' def validEdges(G,T): ''' get a set incident of all edges in G incident with T''' ''' initialize an empty set valid ''' ''' check all edges e in incident. if T+e is a tree, add e to valid'''
''' return validEdges '''
''' return the set of all edges from graph G that are incident with tree T''' def incidentEdges(G,T): ''' initialize an empty set incident ''' ''' for every vertex v in T check all edges e in G. if v is an endpoint of e, add e to incident'''
''' return indicent'''
''' initialize the weighted graph G from the file test.txt. Find a MST for G using prim(). display T (the MST) '''
if __name__ == "__main__":
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Test.txt : (the Text file should just a .txt containing these numbers below)
0 1 2 0 2 3 1 3 2 1 4 4 2 3 11 2 5 2 3 4 10 4 5 3 4 6 4 5 6 2ile dit Search Source Hun Uecua Consoles Projects ools View Help ax Help C urbtc.pyWerhled Groph.ayPrim Templebo.py l/usr/bin/eny pythons Usage 2# -*- coding: utt-8-1. 4Discrete Mathematical Structures 5 In this python script we define a sinple and weighted graph class object. This Here you can get help of any object by pressing Ctrl+I in front of it, cither on the Edilor or the Console. 7 object should be used to write Prin's and Kruskal's algorithms 18 import nurpy as np 11 inport netuorkx as nx 12 import natplotlib.pyplot as plt 13 14class Heighted Graph(abject): Help can also be shown automatically after writir a lelt Fytron console 16 def init__(self, edgc list rile): 17 Set the edge ist directary address self.edgelist file - edge list file 19 2e 21 22 def edge_dict(sclJ Python 3.6.4Anaconda, Tnc(detault, an 16 2013, 10:22:32) [MSC v.1900 64 bit CAMD64)1 Typ "cpyright", "credits or licensr" for more information Reads in the edge list tron the provided directory address and creates a edge dictionary where the keys are the edges and values are the corresponding edge weights. In particular, to access the value ot edge (a,b), simply type edgr dictL(a,b)l TPythan 6.2.1 -- An enhanced Tnteractive Pythen 26 edge dict- dict() edge-list-np. loadtxt(self,edec-list-rile, tor r in edge_list: dict()-empty dicti # nunpy 2 d array int) 28 29 30 edge dict (row[], ro[1])]-ro2] tAssign keys ond volues return edee dict 34 def edge set(sel) Returns the set ot edges return set(self.edge dict).keys)) 37 39 def vertex set(self): 41 Rcturns the sct of vertices set()- the empty vertex set set) for e in self.edge set(): 43for vin Permissins: R Fnd-af-lines: LF Encding: UI-8 line: 1 Column: 1 Memory 34% 843 AM /26/2013 ile dit Search Source Hun Uecua Consoles Projects ools View Help ax Help C urbtc.pyWerhled Groph.ayPrim Templebo.py l/usr/bin/eny pythons Usage 2# -*- coding: utt-8-1. 4Discrete Mathematical Structures 5 In this python script we define a sinple and weighted graph class object. This Here you can get help of any object by pressing Ctrl+I in front of it, cither on the Edilor or the Console. 7 object should be used to write Prin's and Kruskal's algorithms 18 import nurpy as np 11 inport netuorkx as nx 12 import natplotlib.pyplot as plt 13 14class Heighted Graph(abject): Help can also be shown automatically after writir a lelt Fytron console 16 def init__(self, edgc list rile): 17 Set the edge ist directary address self.edgelist file - edge list file 19 2e 21 22 def edge_dict(sclJ Python 3.6.4Anaconda, Tnc(detault, an 16 2013, 10:22:32) [MSC v.1900 64 bit CAMD64)1 Typ "cpyright", "credits or licensr" for more information Reads in the edge list tron the provided directory address and creates a edge dictionary where the keys are the edges and values are the corresponding edge weights. In particular, to access the value ot edge (a,b), simply type edgr dictL(a,b)l TPythan 6.2.1 -- An enhanced Tnteractive Pythen 26 edge dict- dict() edge-list-np. loadtxt(self,edec-list-rile, tor r in edge_list: dict()-empty dicti # nunpy 2 d array int) 28 29 30 edge dict (row[], ro[1])]-ro2] tAssign keys ond volues return edee dict 34 def edge set(sel) Returns the set ot edges return set(self.edge dict).keys)) 37 39 def vertex set(self): 41 Rcturns the sct of vertices set()- the empty vertex set set) for e in self.edge set(): 43for vin Permissins: R Fnd-af-lines: LF Encding: UI-8 line: 1 Column: 1 Memory 34% 843 AM /26/2013
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