matlab写出下面代码:对于给定的n个坐标轴上的点A1,A2,……,An,使用Prim算法找出最小生成树MT。 根据Steiner最短树性质,分解MT成为n′棵子树(1≤n′≤n-1)。
时间: 2024-05-24 15:11:48 浏览: 129
贪婪算法_最小生成树Prim算法_matlab
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以下是Matlab代码:
% 输入n个点的坐标
n = input("请输入点的个数:");
points = zeros(n,2);
for i = 1:n
fprintf("请输入第%d个点的坐标:\n",i);
points(i,:) = input("");
end
% 构造邻接矩阵
dist = zeros(n);
for i = 1:n
for j = i+1:n
dist(i,j) = norm(points(i,:)-points(j,:));
dist(j,i) = dist(i,j);
end
end
% Prim算法求最小生成树
visited = zeros(1,n);
visited(1) = 1;
tree = zeros(n-1,2);
for k = 1:n-1
min_dist = Inf;
for i = 1:n
if visited(i)
for j = 1:n
if ~visited(j) && dist(i,j)<min_dist
min_dist = dist(i,j);
u = i;
v = j;
end
end
end
end
visited(v) = 1;
tree(k,:) = [u,v];
end
% 分解成n'棵子树
subtrees = cell(1,n-1);
for i = 1:n-1
subtree = tree;
subtree(i,:) = [];
subtrees{i} = subtree;
end
% 输出结果
disp("最小生成树:");
disp(tree);
fprintf("共分解成%d棵子树:\n",n-1);
for i = 1:n-1
fprintf("第%d棵子树:\n",i);
disp(subtrees{i});
end
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