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Add proof of working for Kruskal's.py and Update Readme
I added the .txt file showing the I/O of the test with a graph of 21 edges and 10 vertex's. And this graph and its MST is shown in the .jpg, both named Kruskal_test. I removed the query for the maximum value of the edge weights As we are not using counting sort. If needed we should find it from the edges that we recive. I updated the README.md with information about the last two scripts that I added to the repo. Signed-off-by: Aditya Prasad <[email protected]>
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‎Kruskal's.py

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@@ -125,10 +125,11 @@ def __iter__(self):
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# add the edge with this info
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the_graph.addEdge(node1_key,node2_key,cost)
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the_graph.addEdge(node2_key,node1_key,cost)
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"""
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AS we wont be using counting sort
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print "enter the maximum weight possible for any of edges in the graph"
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max_weight=int(raw_input())
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"""
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# graph DONE - start MST finding
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# step 1 : Take all edges and sort them
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print " \n\nIn the graph with these vertex's"
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print the_graph.getVertices()
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print "\n With these "+str(len(MST))+" edges between the vertexes given above, we obtain a Minimal Spanning Tree\n"
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print "\nWith these "+str(len(MST))+" edges between the vertexes given above, we obtain a Minimal Spanning Tree\n"
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print MST
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print "\n Please note this is a dictionary with key as the weight of the edge and value as the key's of the two vertex's involved in this edge"
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print "\nPlease note this is a dictionary with key as the weight of the edge and value as the key's of the two vertex's involved in this edge"
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# I HAVE TESTED THIS IMPLEMENTATION WITH THE SAMPLE PROBLEM GIVEN IN WIKIPEDIA
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# THE IMAGE OF THE GRAPH AND THE ONLY MST IS INCLUDED IN THE REPO, ALONG WITH THE

‎Kruskal_test.jpg

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‎Kruskal_test.txt

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Python 2.7.8 (default, Jun 30 2014, 16:08:48) [MSC v.1500 64 bit (AMD64)] on win32
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Type "copyright", "credits" or "license()" for more information.
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>>> ================================ RESTART ================================
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>>>
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enter the number of nodes in the graph
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10
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enter the Node no:1's key
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a
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enter the Node no:2's key
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b
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enter the Node no:3's key
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c
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enter the Node no:4's key
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d
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enter the Node no:5's key
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e
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enter the Node no:6's key
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f
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enter the Node no:7's key
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g
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enter the Node no:8's key
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h
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enter the Node no:9's key
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i
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enter the Node no:10's key
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j
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enter the number of edges in the graph
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21
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For the Edge no:1
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of the 2 nodes involved in this edge
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enter the first Node's key
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a
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enter the second Node's key
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b
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enter the cost (or weight) of this edge (or arc) - an integer
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9
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For the Edge no:2
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of the 2 nodes involved in this edge
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enter the first Node's key
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a
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enter the second Node's key
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c
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enter the cost (or weight) of this edge (or arc) - an integer
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9
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For the Edge no:3
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of the 2 nodes involved in this edge
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enter the first Node's key
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a
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enter the second Node's key
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f
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enter the cost (or weight) of this edge (or arc) - an integer
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8
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For the Edge no:4
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of the 2 nodes involved in this edge
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enter the first Node's key
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a
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enter the second Node's key
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j
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enter the cost (or weight) of this edge (or arc) - an integer
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18
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For the Edge no:5
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of the 2 nodes involved in this edge
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enter the first Node's key
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b
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enter the second Node's key
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c
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enter the cost (or weight) of this edge (or arc) - an integer
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3
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For the Edge no:6
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of the 2 nodes involved in this edge
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enter the first Node's key
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b
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enter the second Node's key
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e
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enter the cost (or weight) of this edge (or arc) - an integer
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6
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For the Edge no:7
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of the 2 nodes involved in this edge
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enter the first Node's key
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c
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enter the second Node's key
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e
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enter the cost (or weight) of this edge (or arc) - an integer
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4
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For the Edge no:8
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of the 2 nodes involved in this edge
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enter the first Node's key
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c
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enter the second Node's key
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d
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enter the cost (or weight) of this edge (or arc) - an integer
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2
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For the Edge no:9
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of the 2 nodes involved in this edge
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enter the first Node's key
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c
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enter the second Node's key
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f
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enter the cost (or weight) of this edge (or arc) - an integer
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9
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For the Edge no:10
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of the 2 nodes involved in this edge
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enter the first Node's key
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d
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enter the second Node's key
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e
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enter the cost (or weight) of this edge (or arc) - an integer
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2
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For the Edge no:11
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of the 2 nodes involved in this edge
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enter the first Node's key
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d
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enter the second Node's key
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f
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enter the cost (or weight) of this edge (or arc) - an integer
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8
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For the Edge no:12
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of the 2 nodes involved in this edge
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enter the first Node's key
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d
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enter the second Node's key
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g
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enter the cost (or weight) of this edge (or arc) - an integer
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9
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For the Edge no:13
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of the 2 nodes involved in this edge
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enter the first Node's key
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e
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enter the second Node's key
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g
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enter the cost (or weight) of this edge (or arc) - an integer
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9
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For the Edge no:14
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of the 2 nodes involved in this edge
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enter the first Node's key
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f
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enter the second Node's key
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g
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enter the cost (or weight) of this edge (or arc) - an integer
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7
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For the Edge no:15
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of the 2 nodes involved in this edge
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enter the first Node's key
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f
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enter the second Node's key
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i
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enter the cost (or weight) of this edge (or arc) - an integer
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9
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For the Edge no:16
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of the 2 nodes involved in this edge
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enter the first Node's key
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f
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enter the second Node's key
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j
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enter the cost (or weight) of this edge (or arc) - an integer
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10
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For the Edge no:17
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of the 2 nodes involved in this edge
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enter the first Node's key
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g
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enter the second Node's key
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i
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enter the cost (or weight) of this edge (or arc) - an integer
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5
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For the Edge no:18
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of the 2 nodes involved in this edge
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enter the first Node's key
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g
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enter the second Node's key
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h
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enter the cost (or weight) of this edge (or arc) - an integer
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4
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For the Edge no:19
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of the 2 nodes involved in this edge
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enter the first Node's key
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h
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enter the second Node's key
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i
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enter the cost (or weight) of this edge (or arc) - an integer
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1
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For the Edge no:20
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of the 2 nodes involved in this edge
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enter the first Node's key
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h
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enter the second Node's key
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j
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enter the cost (or weight) of this edge (or arc) - an integer
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4
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For the Edge no:21
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of the 2 nodes involved in this edge
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enter the first Node's key
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i
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enter the second Node's key
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j
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enter the cost (or weight) of this edge (or arc) - an integer
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3
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enter the maximum weight possible for any of edges in the graph
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20
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The edges with thier unsorted weights are
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{('g', 'e'): [9], ('b', 'c'): [3], ('e', 'd'): [2], ('h', 'i'): [1], ('d', 'e'): [2], ('i', 'h'): [1], ('f', 'd'): [8], ('c', 'b'): [3], ('e', 'c'): [4], ('a', 'b'): [9], ('g', 'd'): [9], ('c', 'f'): [9], ('f', 'a'): [8], ('e', 'g'): [9], ('d', 'f'): [8], ('d', 'g'): [9], ('c', 'a'): [9], ('h', 'j'): [4], ('e', 'b'): [6], ('i', 'g'): [5], ('d', 'c'): [2], ('c', 'e'): [4], ('g', 'h'): [4], ('b', 'a'): [9], ('i', 'j'): [3], ('j', 'h'): [4], ('a', 'f'): [8], ('j', 'a'): [18], ('i', 'f'): [9], ('f', 'j'): [10], ('c', 'd'): [2], ('h', 'g'): [4], ('f', 'c'): [9], ('g', 'i'): [5], ('j', 'f'): [10], ('g', 'f'): [7], ('j', 'i'): [3], ('b', 'e'): [6], ('f', 'g'): [7], ('a', 'c'): [9], ('a', 'j'): [18], ('f', 'i'): [9]}
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After sorting
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[(('h', 'i'), [1]), (('i', 'h'), [1]), (('e', 'd'), [2]), (('d', 'e'), [2]), (('d', 'c'), [2]), (('c', 'd'), [2]), (('b', 'c'), [3]), (('c', 'b'), [3]), (('i', 'j'), [3]), (('j', 'i'), [3]), (('e', 'c'), [4]), (('h', 'j'), [4]), (('c', 'e'), [4]), (('g', 'h'), [4]), (('j', 'h'), [4]), (('h', 'g'), [4]), (('i', 'g'), [5]), (('g', 'i'), [5]), (('e', 'b'), [6]), (('b', 'e'), [6]), (('g', 'f'), [7]), (('f', 'g'), [7]), (('f', 'd'), [8]), (('f', 'a'), [8]), (('d', 'f'), [8]), (('a', 'f'), [8]), (('g', 'e'), [9]), (('a', 'b'), [9]), (('g', 'd'), [9]), (('c', 'f'), [9]), (('e', 'g'), [9]), (('d', 'g'), [9]), (('c', 'a'), [9]), (('b', 'a'), [9]), (('i', 'f'), [9]), (('f', 'c'), [9]), (('a', 'c'), [9]), (('f', 'i'), [9]), (('f', 'j'), [10]), (('j', 'f'), [10]), (('j', 'a'), [18]), (('a', 'j'), [18])]
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In the graph with these vertex's
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['a', 'c', 'b', 'e', 'd', 'g', 'f', 'i', 'h', 'j']
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With these edges between the vertexes given above, we obtain a Minimal Spanning Tree
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{('b', 'c'): [3], ('g', 'f'): [7], ('e', 'd'): [2], ('h', 'i'): [1], ('g', 'h'): [4], ('f', 'd'): [8], ('f', 'a'): [8], ('d', 'c'): [2], ('i', 'j'): [3]}
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Please note this is a dictionary with key as the weight of the edge and value as the key's of the two vertex's involved in this edge
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>>>

‎README.md

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This was the first real usefull python script I wrote, It was just after I had heard about
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BeautifulSoup and I wanted to make a program which downloads manga.
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* **Maximum_subarray.py**
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This is the solution to the problem of finding the subarray with maximum sum,
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It has been solved in this script using both the dynamic programming approach (O(n)) as well
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as the divide and conquer approach (O(nlog(n)). I have explained the whole thing in
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my [Blog][2]
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* **Kruskal's.py**
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This is a script to find the [Minimal Spanning Tree][3] of a connected, undirected graph,
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using Kruskal's algorithm which is a greedy algorithm. I have also included the I/O of
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a test I conducted with a graph and the image of the graph and its only MST.
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These are the Kruskal\_test.txt and Kruskal\_test.jpg
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I have used part of this code to answer [this question][4]
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[1]: https://superuser.com/questions/330297/automate-logging-in-through-sonicwall/785792?noredirect=1#comment1023176_785792
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[2]: http://relativetoaditya.blogspot.in/2014/12/maximum-subarray.html
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[3]: https://en.wikipedia.org/wiki/Minimum_spanning_tree
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[4]: https://stackoverflow.com/questions/14369739/creating-adjacency-lists-from-dicts-in-python/27380835#27380835

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