Kruskal算法和Prim算法dou是用于求解Zui细小生成树的贪心算法，它们在图论中非常关键。

Kruskal算法

Kruskal算法的基本思想是按照边的权沉从细小到巨大选择边，一边确保选择的边不会形成环。

matlab function = kruskal % 输入参数： % graph - 一个矩阵， 其中graph表示边的权沉，Ru果不存在边则设置为无没钱巨大。 % 输出参数： % mstedges - Zui细小生成树的边列表。 % mstweight - Zui细小生成树的总权沉。

num_vertices = size;
num_edges = 0;
for i = 1:num_vertices
    for j = i+1:num_vertices
        if graph <inf
            num_edges = num_edges + 1;
        end
    end
end
% 初始化边和并查集
edges = zeros;
for i = 1:num_edges
    edges = ;
end
for i = 1:num_vertices
    edges = i;
    edges = i;
end
% 按权沉排序边
 = sort);
for i = 1:num_edges
    edges = graph);
end
% 初始化并查集
parent = 1:num_vertices;
rank = zeros;
% 构建Zui细小生成树
mst_edges = ;
mst_weight = 0;
for i = 1:num_edges
    u = edges;
    v = edges;
    weight = edges;
    % 检查边是不是会形成环
    root_u = find;
    root_v = find;
    if root_u ~= root_v
        % 合并两个集合
        parent = root_v;
        mst_edges = ];
        mst_weight = mst_weight + weight;
    end
end

end

% 辅助函数：查找并查集的根节点 function root = find if parent ~= x parent = find, parent); end root = parent; end

Prim算法

Prim算法从一个顶点开头， 一点点许多些边到生成树中，每次选择连接生成树和剩余顶点中权沉Zui细小的边。

num_vertices = size;
num_edges = 0;
for i = 1:num_vertices
    for j = i+1:num_vertices
        if graph <inf
            num_edges = num_edges + 1;
        end
    end
end
% 初始化边和Zui细小堆
edges = zeros;
for i = 1:num_edges
    edges = ;
end
for i = 1:num_edges
    edges = i;
    edges = i;
end
% 按权沉排序边
 = sort);
for i = 1:num_edges
    edges = graph);
end
% 初始化并查集
parent = 1:num_vertices;
rank = zeros;
in_mst = false;
in_mst = true;
mst_weight = 0;
mst_edges = ;
% 构建Zui细小生成树
for i = 1:num_vertices
    u = 1;
    while in_mst
        u = u + 1;
    end
    for j = 1:num_edges
        v = edges;
        w = edges;
        weight = edges;
        if graph <inf && in_mst == false && weight <graph
            in_mst = true;
            mst_weight = mst_weight + weight;
            mst_edges = ];
            edges = inf; % 别让
选择相同的边
        end
    end
end

end