File:KruskalDemo.gif
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KruskalDemo.gif (314 × 323 pixels, file size: 415 KB, MIME type: image/gif, looped, 93 frames, 47 s)
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Summary[edit]
DescriptionKruskalDemo.gif |
English: A demo for Kruskal's algorithm to find minimum spanning tree on a 2D plane. |
Date | |
Source | Own work |
Author | Shiyu Ji |
Python 3 Code[edit]
'''
Minimum Spanning Tree generation (SVG) for Kruskal's algorithm.
Firstly use this code to generate SVG frames.
Then transform to bitmaps and convert to GIF.
'''
# range size
N = 300
margin = 20
def norm(x, y):
return (x*x+y*y)**.5
class Edge(object):
def __init__(self, source, target, points):
self.u = source
self.v = target
self.len = norm(points[source][0]-points[target][0], points[source][1]-points[target][1])
class UnionNode(object):
def __init__(self):
self.next = None
def saveToSVG(nFrames, points, firmed, trying):
f = open('demo_'+'0'*(3-len(str(nFrames)))+str(nFrames)+'.svg', 'w')
f.write("<svg xmlns=\"http://www.w3.org/2000/svg\" version=\"1.1\">\n")
for p in points:
f.write("<circle cx=\"" +str(p[0]+margin)+ "\" cy=\""+ str(N-p[1]+margin) +"\" r=\"5\" fill=\"white\" stroke=\"black\"/>\n")
for L in firmed:
f.write("<line x1=\"" +str(L[0][0]+margin)+ "\" y1=\""+ str(N-L[0][1]+margin) +"\" x2=\"" + str(L[1][0]+margin) + "\" y2=\"" + str(N-L[1][1]+margin) + "\" stroke=\"red\" stroke-width=\"5\"/>\n")
for L in trying:
f.write("<line x1=\"" +str(L[0][0]+margin)+ "\" y1=\""+ str(N-L[0][1]+margin) +"\" x2=\"" + str(L[1][0]+margin) + "\" y2=\"" + str(N-L[1][1]+margin) + "\" stroke=\"blue\" stroke-width=\"5\"/>\n")
f.write("</svg>\n")
f.close()
def generatePoints(n):
import random as r
r.seed(100)
res = []
for i in range(n):
pt = [r.randint(0,N) for _ in [0, 1]]
if [pt] not in res:
res += [pt]
return res
def kruskal(n, points):
n = len(points)
union = [UnionNode() for _ in points]
edges = []
for i in range(n-1):
for j in range(i+1, n):
e = Edge(i, j, points)
edges.append(e)
edges.sort(key = lambda x:-x.len)
mst = []
nframe = 0
saveToSVG(nframe, points, mst, [])
nframe+=1
while len(mst)<n-1:
s = edges[-1].u
t = edges[-1].v
saveToSVG(nframe, points, mst, [[points[s], points[t]]])
nframe+=1
p = union[s]
q = union[t]
while p.next != None: p = p.next
while q.next != None: q = q.next
if p!=q:
newNode = UnionNode()
p.next = q.next = newNode
mst.append([points[s], points[t]])
saveToSVG(nframe, points, mst, [])
nframe+=1
edges.pop()
return mst
# test 30 points temporarily
n = 30
pts = generatePoints(n)
kruskal(n, pts)
Licensing[edit]
I, the copyright holder of this work, hereby publish it under the following license:
This file is licensed under the Creative Commons Attribution-Share Alike 4.0 International license.
- You are free:
- to share – to copy, distribute and transmit the work
- to remix – to adapt the work
- Under the following conditions:
- attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.
File history
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Date/Time | Thumbnail | Dimensions | User | Comment | |
---|---|---|---|---|---|
current | 12:52, 24 December 2016 | 314 × 323 (415 KB) | Shiyu Ji (talk | contribs) | User created page with UploadWizard |
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