MATLAB 中的 Disjoint-Set (union-find) 數據結構

Question

MATLAB 中是否有聯合查找算法的任何實現？

如果沒有，是否可以使用 classdef 或任何其他方法來實現它？

我在網上看了很多，找不到任何 MATLAB 的實現！ 這是我能問的最后一個地方，一只手會很棒！

提前致謝

Answer 1

一個不相交的集合可以通過使用向量來實現。 a[u] = ancestor of node u 。

我的實現，使用路徑減半和大小聯合來限制樹的高度（沒有很好的測試）：

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

測試用例：

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