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Implementation of David Wilson's Uniform Spanning Tree Algorithm
Raw
readme.md

David Wilson (at Microsoft Research) designed a very simple algorithm for counting uniform spanning trees that mathematicians study as well as theoretical computer scientists. Not entirely sure how UST can be used in software engineering, but we implement it in Python and output the result in d3.js

The paper Trees and Matchings makes for any interesting reading on the cusp between combinatorics, statiscal mechanics and theoretical computer science.

Manually:

  • place all files in the same folder
  • run ust.py (can give you UST of any size, but just use n = 30) which outputs ust.txt
  • open ust.html reads ust.txt and produces a nice iage.
  • possible you need to set up a server due to same-origin-policy issues

If you give me a few minutes, I can write a Bottle.py server that does all this for you.

As it runs now:

  • place all files in the same folder
  • run server.py
  • go to localhost:8080/
Raw
server.py
from bottle import static_file, route, run
import ust
@route('/static/<filename>')
def server_static(filename):
return static_file(filename, root='...')
@route('/')
def sup():
ust.toText(ust.maze(30))
return static_file('ust.html', root='...')
run(host='localhost', port=8080, debug=True)
Raw
ust.html
<!DOCTYPE html>
<html>
<head>
<meta http-equiv="Content-Type" content="text/html;charset=utf-8"/>
<style type="text/css">
svg { background:#888; }
</style>
</head>
<body>
<script src="http://d3js.org/d3.v3.min.js"></script>
<script type="text/javascript">
scale = 20;
width = (30+1)*scale;
height = (30+1)*scale;
var svg = d3.select("body").append("svg:svg")
.attr("width",width)
.attr("height",height);
d3.tsv("/static/ust.txt", function(d){
for(var i= 0; i < d.length; i++){
if(d[i].b == d[i].y){
if(d[i].x - d[i].a > 0){
console.log(d[i].x - d[i].a);
svg.append("rect")
.attr("width", scale*(d[i].x - d[i].a)+10)
.attr("height",10)
.attr("x",scale*d[i].a + 15)
.attr("y",scale*d[i].b + 15)
.attr("fill","yellow");
}
if(d[i].a - d[i].x > 0 ){
console.log(d[i].a - d[i].x);
svg.append("rect")
.attr("width", scale*(d[i].a - d[i].x)+10)
.attr("height",10)
.attr("x",scale*d[i].x + 15)
.attr("y",scale*d[i].y + 15)
.attr("fill","yellow");
}
}
else if(d[i].a == d[i].x){
if(d[i].y - d[i].b > 0){
console.log(d[i].y - d[i].b);
svg.append("rect")
.attr("width", 10)
.attr("height",scale*(d[i].y - d[i].b)+10)
.attr("x",scale*d[i].a+15)
.attr("y",scale*d[i].b+15)
.attr("fill","yellow");
}
if(d[i].b - d[i].y > 0){
console.log(d[i].b - d[i].y);
svg.append("rect")
.attr("width", 10)
.attr("height",scale*(d[i].b - d[i].y)+10)
.attr("x",scale*d[i].x+15)
.attr("y",scale*d[i].y+15)
.attr("fill","yellow");
}
}
}
});
</script>
</body>
</html>
Raw
ust.py
import random
def maze(n):
grid = [[0 for y in range(n)] for x in range(n)]
grid[int(n*random.random())][int(n*random.random())] = 1
tree = []
while(sum([sum(x) for x in grid]) < n*n):
a,b = int(n*random.random()), int(n*random.random())
while(grid[a][b]):
a,b = int(n*random.random()), int(n*random.random())
walk = [(a,b)]
while(True):
c = int(4*random.random())
if(c==0 and a < n-1): a+=1
if(c==1 and a > 0): a-=1
if(c==2 and b < n-1): b+=1
if(c==3 and b > 0): b-=1
if(grid[a][b]):
break
elif(walk[-1] != (a,b)): walk += [(a,b)]
c,d = walk[-1][0], walk[-1][1]
grid[c][d] = 1
tree += [(walk[-1],(a,b))]
return tree
def toText(tree):
s = ""
s += "a\tb\tx\ty\n"
for x in tree[:-1]:
s += "%s\t%s\t%s\t%s\n"% (x[0][0],x[0][1],x[1][0],x[1][1])
s += "%s\t%s\t%s\t%s"% (tree[-1][0][0],tree[-1][0][1],tree[-1][1][0],tree[-1][1][1])
out = file("ust.txt","w")
out.write(s)
return s
if __name__ == "__main__":
#n = input("How large is your grid?\t")
n = 30
tree = maze(n)
Raw
ust.txt
a b x y
18 1 19 1
18 2 18 1
19 2 19 1
20 2 19 2
18 3 18 2
17 3 18 3
16 3 17 3
16 2 16 3
15 3 16 3
20 3 20 2
19 3 18 3
15 4 15 3
14 3 15 3
21 3 20 3
13 3 14 3
19 4 19 3
14 4 15 4
21 2 21 3
12 3 13 3
13 4 13 3
15 2 16 2
20 4 20 3
12 4 13 4
22 2 21 2
11 3 12 3
11 4 12 4
17 4 17 3
11 5 11 4
10 5 11 5
17 5 17 4
11 6 11 5
21 4 20 4
21 1 21 2
21 5 21 4
22 1 21 1
10 6 10 5
19 5 19 4
22 4 21 4
10 7 10 6
20 5 20 4
19 6 19 5
17 6 17 5
10 4 11 4
23 2 22 2
22 5 22 4
10 3 10 4
20 6 19 6
9 4 10 4
23 3 23 2
10 8 10 7
10 9 10 8
9 7 10 7
10 10 10 9
23 4 22 4
10 2 10 3
20 7 20 6
23 5 23 4
24 2 23 2
8 4 9 4
10 11 10 10
24 5 23 5
9 8 10 8
10 12 10 11
11 7 10 7
17 7 17 6
10 13 10 12
11 11 10 11
9 2 10 2
19 7 19 6
23 6 23 5
17 8 17 7
23 7 23 6
12 11 11 11
24 4 24 5
17 9 17 8
9 6 10 6
18 8 17 8
9 9 10 9
18 9 17 9
8 6 9 6
11 8 11 7
25 5 24 5
11 2 11 3
16 9 17 9
8 8 9 8
8 7 8 6
20 8 20 7
24 6 23 6
26 5 25 5
21 8 20 8
16 8 16 9
12 10 12 11
24 1 24 2
9 1 9 2
11 13 10 13
15 9 16 9
11 14 11 13
21 0 21 1
9 12 10 12
9 10 9 9
22 6 23 6
15 10 15 9
17 10 17 9
11 15 11 14
25 1 24 1
8 2 9 2
22 8 21 8
8 12 9 12
15 11 15 10
18 10 18 9
10 15 11 15
11 16 11 15
23 8 22 8
14 2 14 3
12 15 11 15
13 15 12 15
22 9 22 8
13 16 13 15
8 3 8 2
7 4 8 4
22 10 22 9
14 15 13 15
9 15 10 15
20 9 20 8
7 8 8 8
15 15 14 15
13 10 12 10
7 2 8 2
24 3 23 3
12 16 11 16
7 12 8 12
7 9 7 8
14 14 14 15
27 5 26 5
15 14 14 14
10 14 11 14
24 8 23 8
7 3 7 2
12 17 12 16
7 13 7 12
24 9 24 8
6 2 7 2
26 6 26 5
15 12 15 11
16 15 15 15
25 9 24 9
23 10 22 10
14 16 14 15
13 11 12 11
24 10 23 10
16 16 16 15
20 10 20 9
24 0 24 1
18 4 18 3
6 12 7 12
6 9 7 9
9 5 9 4
23 1 22 1
5 12 6 12
17 15 16 15
15 16 16 16
4 12 5 12
28 5 27 5
6 13 6 12
25 10 25 9
16 10 17 10
7 14 7 13
25 11 25 10
14 17 14 16
7 15 7 14
10 16 10 15
13 14 14 14
12 18 12 17
20 11 20 10
13 9 13 10
11 18 12 18
13 17 14 17
16 11 16 10
26 1 25 1
13 18 12 18
26 11 25 11
5 9 6 9
27 6 27 5
17 16 17 15
26 12 26 11
5 2 6 2
12 19 12 18
9 16 9 15
8 16 9 16
25 6 26 6
28 4 28 5
13 19 12 19
14 18 13 18
13 8 13 9
25 7 25 6
3 12 4 12
21 10 20 10
13 20 13 19
27 12 26 12
18 16 17 16
12 8 13 8
12 20 13 20
15 18 14 18
11 20 12 20
7 5 7 4
17 17 17 16
4 13 4 12
5 13 5 12
12 2 11 2
25 12 26 12
19 16 18 16
27 7 27 6
4 14 4 13
17 14 17 15
2 12 3 12
27 1 26 1
2 11 2 12
7 1 7 2
4 15 4 14
12 21 12 20
9 17 9 16
25 2 25 1
16 18 15 18
13 2 12 2
19 17 19 16
18 11 18 10
7 0 7 1
17 18 16 18
19 15 19 16
12 22 12 21
20 17 19 17
1 12 2 12
8 1 9 1
18 18 17 18
6 1 7 1
29 4 28 4
16 12 16 11
13 21 13 20
20 15 19 15
10 20 11 20
12 23 12 22
25 13 25 12
3 15 4 15
21 15 20 15
28 12 27 12
14 20 13 20
9 3 9 4
7 16 7 15
3 14 4 14
27 13 27 12
13 22 13 21
8 13 8 12
17 19 17 18
28 7 27 7
25 14 25 13
6 14 7 14
7 17 7 16
24 11 24 10
14 21 13 21
9 18 9 17
6 17 7 17
15 21 14 21
24 12 25 12
11 22 12 22
12 7 11 7
14 22 13 22
5 14 5 13
3 16 3 15
6 3 7 3
18 14 17 14
17 20 17 19
18 13 18 14
1 13 1 12
7 11 7 12
22 15 21 15
26 13 25 13
17 21 17 20
29 12 28 12
27 4 27 5
22 7 22 8
15 22 15 21
18 20 17 20
18 12 18 11
12 24 12 23
12 25 12 24
2 15 3 15
13 25 12 25
16 22 15 22
17 22 16 22
13 7 13 8
10 17 9 17
15 8 15 9
6 18 6 17
11 24 12 24
13 23 13 22
5 1 6 1
27 14 27 13
11 21 12 21
12 26 12 25
10 1 10 2
11 26 12 26
18 21 18 20
3 17 3 16
20 18 20 17
11 19 11 18
13 24 13 23
11 1 11 2
9 20 10 20
4 9 5 9
13 26 12 26
3 18 3 17
8 20 9 20
13 13 13 14
20 19 20 18
26 14 26 13
6 0 7 0
6 5 7 5
10 0 10 1
10 26 11 26
8 0 7 0
6 6 6 5
9 11 9 12
5 18 6 18
23 11 23 10
19 19 20 19
11 25 11 26
27 0 27 1
7 6 7 5
14 25 13 25
13 27 13 26
9 26 10 26
5 0 5 1
10 27 10 26
10 21 10 20
17 23 17 22
5 3 6 3
10 25 10 26
25 15 25 14
3 19 3 18
7 20 8 20
19 20 19 19
20 16 20 15
24 15 25 15
8 26 9 26
14 11 13 11
4 2 5 2
20 20 19 20
6 16 7 16
17 12 16 12
11 27 10 27
19 14 19 15
7 10 7 11
21 20 20 20
18 22 18 21
13 28 13 27
28 1 27 1
14 28 13 28
21 21 21 20
3 9 4 9
28 8 28 7
20 1 19 1
25 16 25 15
18 23 18 22
5 19 5 18
21 17 20 17
27 11 26 11
22 20 21 20
8 27 8 26
1 11 2 11
22 21 21 21
1 10 1 11
16 23 17 23
16 21 17 21
23 20 22 20
4 3 5 3
4 4 4 3
17 1 18 1
2 9 3 9
3 20 3 19
21 14 21 15
22 19 22 20
14 27 13 27
16 24 16 23
8 25 8 26
14 9 15 9
16 14 16 15
17 24 17 23
1 15 2 15
12 13 13 13
10 28 10 27
29 13 29 12
9 19 9 20
7 25 8 25
7 27 8 27
8 28 8 27
28 6 28 7
2 18 3 18
11 12 11 11
0 12 1 12
7 24 7 25
4 11 4 12
4 0 5 0
19 21 18 21
2 19 3 19
18 5 19 5
28 0 27 0
19 22 18 22
10 22 10 21
29 5 29 4
2 20 2 19
2 21 2 20
23 12 24 12
24 16 24 15
9 0 10 0
18 6 17 6
22 0 22 1
27 10 27 11
15 25 14 25
21 22 21 21
1 16 1 15
25 8 25 7
14 29 14 28
2 22 2 21
3 22 2 22
15 1 15 2
15 26 15 25
20 22 19 22
4 1 4 2
14 19 14 18
23 19 22 19
3 4 4 4
25 17 25 16
9 14 10 14
3 2 4 2
12 1 11 1
18 19 17 19
22 22 22 21
0 16 1 16
26 16 25 16
26 17 26 16
6 24 7 24
0 11 0 12
16 25 16 24
8 14 7 14
12 5 11 5
9 13 8 13
21 23 21 22
26 7 26 6
7 26 7 27
24 20 23 20
19 18 19 17
6 8 7 8
4 20 3 20
6 26 7 26
21 19 21 20
2 23 2 22
4 8 4 9
21 16 20 16
24 21 24 20
1 21 2 21
19 23 18 23
22 14 21 14
26 18 26 17
13 5 12 5
5 4 4 4
3 1 3 2
15 17 14 17
16 26 15 26
27 17 26 17
25 3 24 3
2 1 3 1
23 16 24 16
10 19 11 19
22 23 22 22
28 17 27 17
26 9 25 9
13 29 13 28
5 5 6 5
23 22 22 22
8 29 8 28
18 7 17 7
7 28 7 27
20 23 19 23
6 27 6 26
19 8 18 8
3 0 4 0
26 15 26 14
2 4 3 4
5 26 6 26
28 18 28 17
26 2 25 2
2 24 2 23
13 12 13 11
27 16 27 17
7 21 7 20
6 25 7 25
16 5 17 5
24 22 24 21
4 26 5 26
24 7 25 7
25 22 24 22
11 17 10 17
29 0 28 0
24 23 24 22
23 13 23 12
5 15 4 15
3 10 3 9
15 27 14 27
24 24 24 23
20 21 20 22
26 4 26 5
7 29 8 29
29 18 28 18
4 16 3 16
22 18 22 19
25 23 24 23
7 22 7 21
4 19 4 20
17 11 18 11
21 24 21 23
25 4 24 4
23 18 23 19
21 25 21 24
6 7 6 8
12 14 12 15
24 25 24 24
6 29 7 29
1 4 2 4
16 27 16 26
25 24 25 23
20 25 21 25
3 21 3 22
0 10 0 11
0 4 1 4
20 26 20 25
24 14 24 15
21 26 21 25
16 19 16 18
26 3 26 4
24 17 24 16
0 3 0 4
26 23 25 23
21 9 21 10
2 13 1 13
4 7 4 8
1 17 1 16
21 7 20 7
29 11 29 12
19 24 19 23
5 25 6 25
15 28 14 28
12 27 12 26
5 6 6 6
17 25 16 25
14 13 14 14
0 5 0 4
1 9 1 10
12 29 13 29
1 1 2 1
2 2 2 1
16 28 15 28
6 19 5 19
14 10 13 10
23 23 23 22
12 12 12 13
0 15 1 15
0 9 0 10
27 15 27 14
19 25 19 24
21 6 20 6
24 26 24 25
0 2 0 3
26 19 26 18
3 8 4 8
4 10 4 11
15 29 14 29
16 29 16 28
26 22 26 23
2 0 2 1
3 26 4 26
9 25 9 26
3 27 3 26
14 12 15 12
22 17 22 18
1 5 0 5
24 19 24 20
15 0 15 1
18 24 17 24
0 21 1 21
2 5 2 4
16 1 17 1
14 26 15 26
14 5 13 5
10 18 11 18
26 20 26 19
28 14 27 14
2 17 3 17
24 27 24 26
25 25 24 25
8 10 9 10
1 24 2 24
27 9 27 10
5 24 6 24
2 6 2 5
27 22 26 22
29 19 29 18
3 7 4 7
17 13 18 13
7 19 6 19
26 21 26 20
5 11 4 11
3 28 3 27
29 1 28 1
22 24 21 24
0 20 0 21
27 8 27 9
0 8 0 9
23 9 24 9
25 20 24 20
28 10 27 10
23 27 24 27
5 16 6 16
3 13 2 13
28 9 27 9
2 14 2 13
9 21 10 21
16 4 16 5
24 13 25 13
12 0 12 1
23 0 24 0
26 25 25 25
6 11 5 11
16 20 16 21
22 25 22 24
15 13 15 14
15 19 14 19
1 2 2 2
16 6 16 5
4 27 3 27
2 28 3 28
28 13 28 12
24 18 24 17
14 23 13 23
4 21 3 21
25 18 26 18
14 1 14 2
22 3 21 3
29 8 28 8
23 15 24 15
22 12 23 12
1 28 2 28
1 25 1 24
1 8 0 8
17 28 16 28
4 5 5 5
18 15 17 15
23 24 22 24
5 23 5 24
6 23 6 24
26 26 26 25
29 20 29 19
20 14 21 14
7 7 6 7
16 13 16 12
18 28 17 28
13 0 12 0
0 17 0 16
1 3 1 2
26 24 26 25
7 23 7 22
1 22 2 22
0 13 1 13
20 0 20 1
25 0 24 0
27 25 26 25
28 25 27 25
4 24 5 24
29 14 29 13
14 0 14 1
8 15 7 15
21 27 21 26
27 26 27 25
28 26 28 25
4 28 3 28
17 27 17 28
23 17 24 17
0 1 1 1
25 21 24 21
25 27 24 27
0 24 1 24
0 19 0 20
5 27 5 26
20 12 20 11
12 9 12 8
3 3 3 4
28 15 28 14
18 27 18 28
21 18 20 18
7 18 6 18
23 26 23 27
15 6 16 6
16 7 16 6
8 9 7 9
17 29 17 28
10 23 10 22
23 21 24 21
18 25 19 25
8 24 7 24
9 22 9 21
24 28 24 27
1 23 1 22
29 26 28 26
28 19 29 19
29 3 29 4
4 17 4 16
28 27 28 26
27 21 26 21
0 14 0 13
0 7 0 8
22 13 23 13
2 3 3 3
29 27 28 27
12 28 12 27
1 0 2 0
18 17 18 18
20 27 20 26
27 19 26 19
27 18 27 19
0 22 0 21
8 18 7 18
6 20 7 20
0 25 0 24
14 24 14 25
29 28 29 27
0 18 0 19
28 11 27 11
27 20 27 19
5 10 4 10
5 7 5 6
22 26 23 26
26 8 25 8
13 6 13 7
6 22 6 23
9 24 8 24
28 3 29 3
18 0 18 1
8 23 7 23
21 28 21 27
2 10 3 10
14 7 13 7
4 18 4 19
26 27 25 27
19 12 18 12
16 17 15 17
2 26 3 26
19 0 18 0
11 29 12 29
28 21 27 21
4 23 4 24
29 6 29 5
5 29 6 29
22 27 23 27
3 6 2 6
14 8 14 7
15 24 16 24
21 12 20 12
8 5 7 5
1 20 1 21
24 29 24 28
6 21 7 21
21 11 20 11
29 10 29 11
28 22 28 21
27 27 27 26
0 0 0 1
6 28 7 28
4 22 4 23
23 28 24 28
27 2 26 2
19 9 18 9
28 23 28 22
5 28 5 29
16 0 16 1
2 7 3 7
8 21 9 21
23 14 23 15
25 28 24 28
21 29 21 28
10 29 11 29
0 28 1 28
20 29 21 29
3 25 3 26
15 23 15 22
0 26 0 25
18 26 18 25
1 7 2 7
3 29 3 28
3 11 3 12
29 25 29 26
18 29 18 28
5 21 6 21
28 24 28 25
19 29 18 29
14 6 14 5
23 25 23 24
26 0 26 1
1 29 1 28
0 23 0 22
26 10 26 9
4 6 4 5
19 10 19 9
25 29 25 28
29 15 28 15
1 26 2 26
1 14 1 15
27 28 27 27
6 15 6 14
1 6 1 5
29 7 29 6
3 23 2 23
8 19 8 20
27 24 27 25
9 28 8 28
29 17 29 18
13 1 12 1
11 23 11 24
6 10 6 9
2 25 3 25
8 11 8 10
5 17 4 17
15 5 16 5
20 24 20 25
22 16 23 16
25 26 26 26
28 28 28 27
19 28 18 28
1 27 1 28
1 18 0 18
29 16 29 15
9 23 9 24
2 16 1 16
28 16 28 17
11 28 11 27
17 0 18 0
17 26 17 27
3 5 3 6
5 8 5 9
27 23 26 23
27 3 28 3
28 2 27 2
28 20 27 20
19 11 20 11
23 29 23 28
29 22 28 22
15 20 16 20
26 29 25 29
5 22 5 21
20 13 20 12
22 29 23 29
25 19 25 20
22 28 21 28
9 27 9 26
21 13 22 13
19 26 19 25
11 0 12 0
2 27 1 27
19 13 20 13
0 29 0 28
2 29 2 28
12 6 12 7
29 23 28 23
28 29 28 28
8 17 7 17
11 10 12 10
0 27 0 28
6 4 6 3
29 29 28 29
4 25 3 25
4 29 5 29
29 21 28 21
17 2 16 2
19 27 20 27
15 7 14 7
20 28 20 29
27 29 27 28
5 20 6 20
22 11 21 11
9 29 10 29
11 9 12 9
10 24 10 23
2 8 1 8
1 19 0 19
29 9 29 8
29 24 29 23
29 2 29 3
0 6 0 5
3 24 4 24
26 28 26 27
8 22 9 22
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