MATLAB 中的 Disjoint-Set (union-find) 数据结构

Question

MATLAB 中是否有联合查找算法的任何实现？

如果没有，是否可以使用 classdef 或任何其他方法来实现它？

我在网上看了很多，找不到任何 MATLAB 的实现！ 这是我能问的最后一个地方，一只手会很棒！

提前致谢

Answer 1

一个不相交的集合可以通过使用向量来实现。 a[u] = ancestor of node u 。

我的实现，使用路径减半和大小联合来限制树的高度（没有很好的测试）：

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

测试用例：

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