Disjoint-Set (union-find) data structure in MATLAB

Question

Are there any implementations of the union-find algorithm in MATLAB?

If not, is it possible to implement it using a classdef or any other method?

I looked online a lot and couldn't find any implementations for MATLAB! This was the last place I could ask, a hand would be awesome!

Thanks in advance

According to [Steve Eddins](https://blogs.mathworks.com/steve/2007/05/25/connected-component-labeling-part-6/) (look at the very end of the article), there *is* an implementation in MATLAB that's used in [`bwlabeln`](https://www.mathworks.com/help/images/ref/bwlabeln.html#f1-303225). It's located in `toolbox\images\images\private`. I don't know of any other implementation that's available. — beaker, Dec 19 '19 at 21:32
All you need is a vector to represent the set of trees. This is really simple to implement. — Cris Luengo, Dec 19 '19 at 21:39
Wikipedia links to this copyright-free implementation: https://github.com/USNavalResearchLaboratory/TrackerComponentLibrary/blob/master/Container%20Classes/DisjointSet.m — Cris Luengo, Dec 20 '19 at 04:59

9mat · Accepted Answer · 2019-12-20T10:46:42.103

A disjoint set can be implemented by just using vector. a[u] = ancestor of node u.

My implementation, using path halving and union by size to limit the height of the tree (not very well tested):

classdef DJSet < handle
    properties
        N; root;size;
    end

    methods
        function obj=DJSet(n)
            obj.N = n;
            obj.root = 1:n;
            obj.size = ones(1,n);
        end

        function root = find(obj, u)
            while obj.root(u) ~= u
                obj.root(u) = obj.root(obj.root(u));
                u = obj.root(u);
            end
            root = u;
        end

        function union(obj, u, v)
            root_u = obj.find(u);
            root_v = obj.find(v);
            if root_u == root_v
                return;
            end
            if obj.size(root_u) < obj.size(root_v)
                obj.root(root_u) = root_v;
                obj.size(root_v) = obj.size(root_v) + obj.size(root_u);
            else
                obj.root(root_v) = root_u;
                obj.size(root_u) = obj.size(root_u) + obj.size(root_v);
            end
        end

        function res = is_connected(obj, u, v)
            root_u = obj.find(u);
            root_v = obj.find(v);
            res = root_u == root_v;
        end
    end
end

Test cases:

dj=DJSet(10);
edges = [1 2; 3 4; 5 6; 7 8; 2 3; 1 3; 6 7];

for i = 1:size(edges,1)
    dj.union(edges(i,1), edges(i,2));
end

for j = 2:10
    fprintf('%d and %d connection is %d\n', 1, j, dj.is_connected(1, j));
end

dj.union(3,6);

fprintf('#####\nAfter connecting 3 and 6\n')
for j = 2:10
    fprintf('%d and %d connection is %d\n', 1, j, dj.is_connected(1, j));
end

>> test
1 and 2 connection is 1
1 and 3 connection is 1
1 and 4 connection is 1
1 and 5 connection is 0
1 and 6 connection is 0
1 and 7 connection is 0
1 and 8 connection is 0
1 and 9 connection is 0
1 and 10 connection is 0
#####
After connecting 3 and 6
1 and 2 connection is 1
1 and 3 connection is 1
1 and 4 connection is 1
1 and 5 connection is 1
1 and 6 connection is 1
1 and 7 connection is 1
1 and 8 connection is 1
1 and 9 connection is 0
1 and 10 connection is 0

Disjoint-Set (union-find) data structure in MATLAB

1 Answers1