Use code kruskal but result incorrect

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Boonanan Lechayakittikorn
Boonanan Lechayakittikorn 2015 年 10 月 25 日
コメント済み: Josh Meyer 2015 年 11 月 5 日
i use this code http://www.mathworks.com/matlabcentral/fileexchange/41963-kruskal-s-algorithm/content/kruskal.m run with my data. But the result incorrect because I use this code "kruskal" run with my day X and w. X is matrix size 50*50. w is matrix size 50*50. So it has 50 vertices and it must has 49 edges but i use your code run i got 48 edges. Pleases help me thank you so much
The code
function [w_st, ST, X_st] = kruskal(X, w)
% function [w_st, ST, X_st] = kruskal(X, w)
%
% This function finds the minimum spanning tree of the graph where each
% edge has a specified weight using the Kruskal's algorithm.
%
% Assumptions
% -----------
% N: 1x1 scalar - Number of nodes (vertices) of the graph
% Ne: 1x1 scalar - Number of edges of the graph
% Nst: 1x1 scalar - Number of edges of the minimum spanning tree
%
% We further assume that the graph is labeled consecutively. That is, if
% there are N nodes, then nodes will be labeled from 1 to N.
%
% INPUT
%
% X: NxN logical - Adjacency matrix
% matrix If X(i,j)=1, this means there is directed edge
% starting from node i and ending in node j.
% Each element takes values 0 or 1.
% If X symmetric, graph is undirected.
%
% or Nex2 double - Neighbors' matrix
% matrix Each row represents an edge.
% Column 1 indicates the source node, while
% column 2 the target node.
%
% w: NxN double - Weight matrix in adjacency form
% matrix If X symmetric (undirected graph), w has to
% be symmetric.
%
% or Nex1 double - Weight matrix in neighbors' form
% matrix Each element represents the weight of that
% edge.
%
%
% OUTPUT
%
% w_st: 1x1 scalar - Total weight of minimum spanning tree
% ST: Nstx2 double - Neighbors' matrix of minimum spanning tree
% matrix
% X_st: NstxNst logical - Adjacency matrix of minimum spanning tree
% matrix If X_st symmetric, tree is undirected.
%
% EXAMPLES
%
% Undirected graph
% ----------------
% Assume the undirected graph with adjacency matrix X and weights w:
%
% 1
% / \
% 2 3
% / \
% 4 - 5
%
% X = [0 1 1 0 0;
% 1 0 0 1 1;
% 1 0 0 0 0;
% 0 1 0 0 1;
% 0 1 0 1 0];
%
% w = [0 1 2 0 0;
% 1 0 0 2 1;
% 2 0 0 0 0;
% 0 2 0 0 3;
% 0 1 0 3 0];
%
% [w_st, ST, X_st] = kruskal(X, w);
% The above function gives us the minimum spanning tree.
%
%
% Directed graph
% ----------------
% Assume the directed graph with adjacency matrix X and weights w:
%
% 1
% / ^ \
% / / \
% v v
% 2 ---> 3
%
% X = [0 1 1
% 1 0 1
% 0 0 0];
%
% w = [0 1 4;
% 2 0 1;
% 0 0 0];
%
% [w_st, ST, X_st] = kruskal(X, w);
% The above function gives us the minimum directed spanning tree.
%
%
% Author: Georgios Papachristoudis
% Copyright 2013 Georgios Papachristoudis
% Date: 2013/05/26 12:25:18
isUndirGraph = 1;
% Convert logical adjacent matrix to neighbors' matrix
if size(X,1)==size(X,2) && sum(X(:)==0)+sum(X(:)==1)==numel(X)
if any(any(X-X'))
isUndirGraph = 0;
end
ne = cnvrtX2ne(X,isUndirGraph);
else
if size(unique(sort(X,2),'rows'),1)~=size(X,1)
isUndirGraph = 0;
end
ne = X;
end
% Convert weight matrix from adjacent to neighbors' form
if numel(w)~=length(w)
if isUndirGraph && any(any(w-w'))
error('If it is an undirected graph, weight matrix has to be symmetric.');
end
w = cnvrtw2ne(w,ne);
end
N = max(ne(:)); % number of vertices
Ne = size(ne,1); % number of edges
lidx = zeros(Ne,1); % logical edge index; 1 for the edges that will be
% in the minimum spanning tree
% Sort edges w.r.t. weight
[w,idx] = sort(w);
ne = ne(idx,:);
% Initialize: assign each node to itself
[repr, rnk] = makeset(N);
% Run Kruskal's algorithm
for k = 1:Ne
i = ne(k,1);
j = ne(k,2);
if fnd(i,repr) ~= fnd(j,repr)
lidx(k) = 1;
[repr, rnk] = union(i, j, repr, rnk);
end
end
% Form the minimum spanning tree
treeidx = find(lidx);
ST = ne(treeidx,:);
% Generate adjacency matrix of the minimum spanning tree
X_st = zeros(N);
for k = 1:size(ST,1)
X_st(ST(k,1),ST(k,2)) = 1;
if isUndirGraph, X_st(ST(k,2),ST(k,1)) = 1; end
end
% Evaluate the total weight of the minimum spanning tree
w_st = sum(w(treeidx));
end
function ne = cnvrtX2ne(X, isUndirGraph)
if isUndirGraph
ne = zeros(sum(sum(X.*triu(ones(size(X))))),2);
else
ne = zeros(sum(X(:)),2);
end
cnt = 1;
for i = 1:size(X,1)
v = find(X(i,:));
if isUndirGraph
v(v<=i) = [];
end
u = repmat(i, size(v));
edges = [u; v]';
ne(cnt:cnt+size(edges,1)-1,:) = edges;
cnt = cnt + size(edges,1);
end
end
function w = cnvrtw2ne(w,ne)
tmp = zeros(size(ne,1),1);
cnt = 1;
for k = 1:size(ne,1)
tmp(cnt) = w(ne(k,1),ne(k,2));
cnt = cnt + 1;
end
w = tmp;
end
function [repr, rnk] = makeset(N)
repr = (1:N);
rnk = zeros(1,N);
end
function o = fnd(i,repr)
while i ~= repr(i)
i = repr(i);
end
o = i;
end
function [repr, rnk] = union(i, j, repr, rnk)
r_i = fnd(i,repr);
r_j = fnd(j,repr);
if rnk(r_i) > rnk(r_j)
repr(r_j) = r_i;
else
repr(r_i) = r_j;
if rnk(r_i) == rnk(r_j)
rnk(r_j) = rnk(r_j) + 1;
end
end
end
My data for run
X = [0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1;
1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1;
1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1;
1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1;
1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1;
1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1;
1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1;
1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1;
1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1;
1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1;
1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1;
1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1;
1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1;
1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1;
1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1;
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1;
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1;
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1;
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1;
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1;
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1;
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1;
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1;
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1;
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1;
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1;
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1;
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1;
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1;
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1;
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1;
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1;
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1;
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1;
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1;
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1;
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1;
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1;
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1;
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1;
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1;
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1;
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1;
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1;
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1;
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1;
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1;
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1;
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1;
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0];
w = [0 1.137285192 1.219160473 1.273013503 1.369665567 1.159351937 1.189781199 1.135800111 1.210748814 1.206382985 1.288433169 1.281374833 1.020221618 1.127683682 1.27210717 1.332510638 1.196580777 1.248810574 1.048901295 1.297530845 1.239533279 1.403170203 1.121570967 0.867099904 1.197819338 1.262146435 1.323592608 1.236247334 1.236913586 1.366718376 1.221758653 1.221505033 1.071915378 1.255900706 1.175653003 1.231854105 1.201615771 1.463277969 1.228424717 1.267130556 1.276339753 1.288150136 1.285021905 1.377282113 1.279194595 1.191684292 1.179544905 1.227783605 1.35400961 1.234613476;
1.137285192 0 1.231515342 1.142698473 1.203466614 1.13668129 1.243140584 1.082310006 1.114044402 1.227587994 1.168925663 1.081672186 0.930991068 0.912872357 1.134522763 1.249613443 1.053861619 1.297323865 1.136192206 1.223963532 1.275323348 1.36449208 1.104006315 1.116611984 1.019274607 1.155736149 1.148656585 1.148092329 1.028558598 1.265931536 1.132907734 1.15724022 0.987149334 1.052314459 1.042004802 1.129721933 1.036971286 1.208056375 1.043646041 1.092410366 1.14559837 1.078671449 1.108343498 1.156622079 1.144680731 1.032556632 1.153661864 1.171003249 1.395287193 1.254711878;
1.219160473 1.231515342 0 1.128845395 1.26550426 1.10413976 1.343432395 1.154652311 1.279384127 1.312969588 1.222927943 1.212171376 1.242010439 1.14338166 1.314898073 1.239229765 1.186108783 1.394971023 1.295178436 1.236449821 1.319886119 1.438304862 1.190800772 1.042907661 1.089534121 1.229568098 1.38439984 1.141609528 1.23456473 1.340753051 1.151022915 1.14991167 1.297975342 1.287727781 1.004510354 1.112528545 1.221217757 1.323240664 1.199541659 1.128832966 1.120922293 1.143445108 1.267406653 1.249206582 1.169545824 1.197305401 1.090842034 1.215240038 1.360966717 1.126837005;
1.273013503 1.142698473 1.128845395 0 1.164937154 1.158740778 1.31166906 1.212924279 1.327573893 1.055131428 1.131300384 1.152127171 1.221154304 1.155815526 1.144386929 1.149000809 1.138171716 1.331707204 1.240137108 1.277778899 1.302309412 1.346466048 0.973364375 1.217857973 1.003221513 1.04841204 1.34421716 1.034923405 1.086143267 1.156675064 1.177741779 1.237325671 1.181810038 1.174665352 1.132457465 1.014290712 1.218103927 1.247025063 1.173666986 0.959823342 1.163532233 1.100939301 1.057858151 1.136259176 1.081904094 1.065828424 1.092822424 1.29592741 1.356542268 1.276797091;
1.369665567 1.203466614 1.26550426 1.164937154 0 1.176637052 1.175442734 1.242776866 1.418299271 1.256499677 1.320318179 1.229840646 1.211806572 1.213546487 1.266349903 1.16929734 1.170505749 1.31518822 1.309104105 1.268224854 1.326184385 1.457868072 1.204287264 1.156633339 1.159766278 1.109777783 1.362256074 0.915097452 1.044043433 1.313527315 1.095605371 1.352973255 1.354366323 1.242073161 1.143531595 1.15020099 1.219966142 1.40636414 1.233887489 0.872905551 1.312159998 1.238595936 1.159317032 1.285711648 1.047206799 1.062261329 1.206929357 1.315028505 1.238273461 1.220731661;
1.159351937 1.13668129 1.10413976 1.158740778 1.176637052 0 1.102983005 1.150714398 1.121415518 1.091926059 1.251593903 1.235272477 1.190803753 1.084807158 1.132227262 1.139720272 1.221553119 1.23812885 1.141514617 1.296950645 1.013910951 1.385788675 0.966498561 1.042528682 0.895658345 0.951534413 1.318155621 1.139148814 1.080286798 1.35915299 1.102634282 1.07312686 1.171971942 1.043153228 0.983575766 0.973019934 0.860623848 1.258588229 1.057645319 1.046967511 1.070859721 1.157359582 1.131499159 1.247765989 1.284198224 0.865967615 1.073208676 1.110492871 1.227708527 1.187746423;
1.189781199 1.243140584 1.343432395 1.31166906 1.175442734 1.102983005 0 1.270223749 1.262830988 1.24115589 1.322492206 1.223104393 1.154222823 1.25917622 1.113718301 1.323482355 1.202656559 1.151373417 1.244000074 1.331340854 1.080584857 1.430924877 1.271330729 1.183907121 1.176560456 1.175103839 1.171020087 1.20015891 1.195448399 1.385496697 1.21999721 1.343342351 1.246597366 1.18406877 1.123242314 1.208630783 1.075731631 1.371149262 1.243902008 1.162285585 1.351553465 1.292029937 1.272724075 1.345305454 1.21626509 1.166454667 1.266889148 1.258576874 1.343806541 1.114307872;
1.135800111 1.082310006 1.154652311 1.212924279 1.242776866 1.150714398 1.270223749 0 1.091376753 1.192151921 1.323999753 1.218227092 1.172713101 1.125234875 1.169018775 1.186744483 1.025157835 1.334307488 1.123450203 1.141080708 1.281949706 1.460674063 1.109583157 1.092101672 1.088697522 1.233071379 1.265109986 1.155251925 1.173798235 1.367046336 1.167156358 1.12578097 1.150960315 1.128539572 1.046522657 1.054725787 1.081160636 1.330413046 1.010403102 1.163338246 1.064155909 1.165032148 1.069926635 1.295048731 1.154819405 1.11929097 1.141633511 1.257047 1.321100816 1.130158793;
1.210748814 1.114044402 1.279384127 1.327573893 1.418299271 1.121415518 1.262830988 1.091376753 0 1.279707702 1.338153842 1.386233367 1.245405143 1.123292517 1.148530638 1.297917017 1.250838337 1.308060641 1.210081239 1.407150527 1.236096316 1.41971593 1.111394012 1.133187953 1.251437098 1.328370708 1.391004752 1.216034547 1.074670651 1.466445125 1.215394295 1.195961192 1.122067354 1.178237225 1.22113051 1.314960554 1.160110778 1.271334086 1.130991629 1.210861256 1.14768009 1.33019872 1.307404644 1.340970098 1.257968599 1.298979507 1.251227744 1.325049683 1.35820867 1.318731559;
1.206382985 1.227587994 1.312969588 1.055131428 1.256499677 1.091926059 1.24115589 1.192151921 1.279707702 0 1.178196038 1.282814386 1.337193535 1.142970181 1.076674863 1.216980966 1.260291811 1.254009957 1.213568491 1.257024097 1.218525166 1.293291344 1.056488595 1.221199129 1.090498669 1.171005266 1.274789211 1.099379463 1.171288952 1.15806525 1.208875317 1.124898373 1.271803528 1.243601262 1.21323005 1.144579283 1.183888682 1.339875394 1.169218103 1.216879012 1.136054721 1.134871875 1.083000961 1.178517034 1.120225447 1.081635593 1.187592076 1.366055296 1.330767957 1.191102569;
1.288433169 1.168925663 1.222927943 1.131300384 1.320318179 1.251593903 1.322492206 1.323999753 1.338153842 1.178196038 0 1.202541679 1.242580297 1.238810783 1.393153556 1.353916014 1.279474692 1.364310715 1.356225136 1.356758014 1.314787566 1.372767712 1.191251378 1.223927457 1.214062643 1.312488819 1.317225883 1.26054583 1.231349464 1.043896915 1.211595601 1.222949527 1.280203318 1.224307984 1.29965171 1.282857777 1.339940468 1.332244336 1.347512152 1.291438562 1.374269001 1.235841423 1.242741344 1.273643374 1.314131466 1.192878188 1.052284419 1.319940856 1.39272818 1.330580832;
1.281374833 1.081672186 1.212171376 1.152127171 1.229840646 1.235272477 1.223104393 1.218227092 1.386233367 1.282814386 1.202541679 0 1.188548319 1.115589502 1.199371249 1.279287415 1.215524047 1.206968173 1.261973067 1.215012833 1.095192313 1.418171272 1.121676381 1.213717918 1.144535627 1.230639203 1.184819346 1.180039007 1.263757104 1.261296836 1.278061899 1.210337852 1.185758879 1.170940011 1.173333071 1.17140959 1.152876546 1.195337591 1.167977586 1.151254355 1.192723948 1.164327487 1.131868588 1.116706987 1.066758708 1.164333935 1.083668976 1.347090059 1.338949046 1.153653337;
1.020221618 0.930991068 1.242010439 1.221154304 1.211806572 1.190803753 1.154222823 1.172713101 1.245405143 1.337193535 1.242580297 1.188548319 0 1.15302174 1.182811523 1.265935177 1.073747943 1.279279719 1.15103309 1.364481814 1.294695314 1.362302527 1.230522898 1.027582417 1.153461229 1.234955056 1.252289661 1.178994746 1.163119228 1.325884258 1.190617029 1.203364535 0.915382703 1.031020247 1.095225845 1.279431603 1.203272619 1.37404818 1.089246991 1.143494487 1.277427587 1.29540012 1.218262896 1.37676412 1.254498648 1.075932159 1.131441641 1.246719684 1.428229663 1.228276994;
1.127683682 0.912872357 1.14338166 1.155815526 1.213546487 1.084807158 1.25917622 1.125234875 1.123292517 1.142970181 1.238810783 1.115589502 1.15302174 0 1.12557778 1.142965372 1.214058609 1.232713623 1.132957249 1.202462531 1.135602934 1.325713431 1.006141933 1.051898331 1.008211258 1.206932595 1.174689379 1.026914241 1.080049725 1.32269052 1.097110285 1.125499172 1.157552641 1.095963234 1.09083247 1.189781456 1.050058726 1.281666353 1.113336731 1.130699138 1.160763816 1.155543255 1.132461175 1.11802824 1.091237578 0.959331635 0.990974267 1.278656758 1.378120295 1.234087372;
1.27210717 1.134522763 1.314898073 1.144386929 1.266349903 1.132227262 1.113718301 1.169018775 1.148530638 1.076674863 1.393153556 1.199371249 1.182811523 1.12557778 0 1.091804566 1.064310415 1.151081387 1.197408172 1.260957452 1.063002042 1.222875908 1.118017627 1.202886488 1.119233546 1.096498418 1.228851042 1.206874395 1.175132861 1.344164523 1.172578954 1.197674583 1.243137709 1.199126565 1.086587356 1.043131773 1.045983968 1.142890292 1.143201738 1.094217198 1.072270606 1.247649747 1.157003559 1.264572139 1.160691893 1.188833303 1.221795896 1.277096554 1.330254779 1.211471932;
1.332510638 1.249613443 1.239229765 1.149000809 1.16929734 1.139720272 1.323482355 1.186744483 1.297917017 1.216980966 1.353916014 1.279287415 1.265935177 1.142965372 1.091804566 0 1.263706089 1.405619279 1.186768972 1.252561028 1.303312815 1.326890864 1.111431879 1.216946248 1.069344617 1.168139535 1.413662067 1.135192693 1.259430708 1.298065371 1.292613869 1.16037268 1.307045145 1.200868144 1.106642098 1.109900265 1.207814917 1.338315961 1.344771544 1.121527286 1.192281572 1.173472725 1.053079044 1.18403462 1.144798867 1.103900204 1.151121399 1.238665774 1.260160489 1.191078857;
1.196580777 1.053861619 1.186108783 1.138171716 1.170505749 1.221553119 1.202656559 1.025157835 1.250838337 1.260291811 1.279474692 1.215524047 1.073747943 1.214058609 1.064310415 1.263706089 0 1.293572771 1.225404353 1.28471718 1.328928845 1.36464545 1.127147661 1.209330308 1.166027086 1.208539606 1.245695919 1.249311393 1.180445006 1.355096871 1.16725873 1.306050047 1.053877751 1.222599322 1.077056231 1.140880537 1.201133494 1.273506328 1.009246486 1.089005296 1.159619465 1.184674725 1.205989256 1.33733536 1.150739551 1.18423485 1.128928492 1.287416316 1.381425168 1.180160554;
1.248810574 1.297323865 1.394971023 1.331707204 1.31518822 1.23812885 1.151373417 1.334307488 1.308060641 1.254009957 1.364310715 1.206968173 1.279279719 1.232713623 1.151081387 1.405619279 1.293572771 0 1.22008409 1.307147544 1.030230988 1.350356312 1.258385452 1.289487322 1.309281781 1.162076162 1.218175081 1.229389571 1.309368207 1.391651813 1.197505426 1.379875572 1.29556301 1.241611221 1.28221594 1.260803428 1.196222761 1.270198012 1.282390061 1.237653579 1.273927818 1.267039496 1.191507701 1.295880256 1.250119638 1.25235718 1.229576393 1.277240654 1.383058139 1.246536507;
1.048901295 1.136192206 1.295178436 1.240137108 1.309104105 1.141514617 1.244000074 1.123450203 1.210081239 1.213568491 1.356225136 1.261973067 1.15103309 1.132957249 1.197408172 1.186768972 1.225404353 1.22008409 0 1.248487674 1.36384511 1.355250627 1.241223002 1.070353503 1.235256132 1.233321278 1.240480754 1.138141492 1.242449455 1.349010922 1.139348769 1.280224331 1.156916271 1.129106841 1.150128946 1.117772286 1.122845672 1.391944478 1.118194404 1.250172739 1.194824911 1.156585706 1.201619714 1.315497715 1.186466819 1.066395385 1.175461216 1.222974661 1.194074042 1.137905076;
1.297530845 1.223963532 1.236449821 1.277778899 1.268224854 1.296950645 1.331340854 1.141080708 1.407150527 1.257024097 1.356758014 1.215012833 1.364481814 1.202462531 1.260957452 1.252561028 1.28471718 1.307147544 1.248487674 0 1.213464723 1.337630555 1.198918385 1.350291506 1.240244718 1.306927581 1.361844537 1.271820767 1.268395907 1.304752331 1.34306716 1.191578201 1.388819211 1.256595435 1.295291394 1.222398193 1.224623889 1.239496489 1.23717311 1.300223816 1.367430863 1.258591708 1.189979465 1.301538152 1.272738583 1.207759787 1.190204249 1.195810127 1.377975814 1.349262693;
1.239533279 1.275323348 1.319886119 1.302309412 1.326184385 1.013910951 1.080584857 1.281949706 1.236096316 1.218525166 1.314787566 1.095192313 1.294695314 1.135602934 1.063002042 1.303312815 1.328928845 1.030230988 1.36384511 1.213464723 0 1.439808442 1.069133323 1.258450715 1.174381286 1.151949115 1.288496775 1.256387955 1.175422514 1.459545971 1.168647067 1.145093695 1.306302184 1.172186701 1.242622293 1.192694105 1.07710358 1.196356469 1.27077919 1.136153317 1.222624416 1.346152577 1.265654658 1.359219411 1.342171731 1.192200423 1.198721616 1.206637728 1.343535543 1.300974122;
1.403170203 1.36449208 1.438304862 1.346466048 1.457868072 1.385788675 1.430924877 1.460674063 1.41971593 1.293291344 1.372767712 1.418171272 1.362302527 1.325713431 1.222875908 1.326890864 1.36464545 1.350356312 1.355250627 1.337630555 1.439808442 0 1.364283117 1.404272585 1.371230162 1.319578078 1.361817996 1.376373407 1.390703135 1.345577427 1.40301391 1.374243677 1.425270503 1.422515075 1.3313757 1.337113317 1.415507847 1.458733383 1.328503535 1.428196106 1.386475761 1.337281149 1.334080508 1.431699993 1.3332525 1.38837018 1.308056037 1.426023747 1.452743355 1.412649534;
1.121570967 1.104006315 1.190800772 0.973364375 1.204287264 0.966498561 1.271330729 1.109583157 1.111394012 1.056488595 1.191251378 1.121676381 1.230522898 1.006141933 1.118017627 1.111431879 1.127147661 1.258385452 1.241223002 1.198918385 1.069133323 1.364283117 0 1.196947797 1.002211828 1.113253783 1.318670725 1.051322101 1.029828444 1.257335418 1.096206873 1.151119184 1.125776359 1.063224928 1.132006297 1.051365045 1.024749217 1.175490381 1.165663854 1.037861073 1.144692056 1.16310093 1.039176064 1.244424492 1.118788571 1.004216418 1.036982593 1.303872426 1.171161798 1.268728539;
0.867099904 1.116611984 1.042907661 1.217857973 1.156633339 1.042528682 1.183907121 1.092101672 1.133187953 1.221199129 1.223927457 1.213717918 1.027582417 1.051898331 1.202886488 1.216946248 1.209330308 1.289487322 1.070353503 1.350291506 1.258450715 1.404272585 1.196947797 0 1.029336372 1.133507483 1.31333441 1.100750925 1.087952569 1.306658858 1.146153127 1.180413238 1.169398227 1.141037536 0.999014115 1.127754619 1.102424436 1.450078659 1.166877179 1.11103974 1.08277457 1.128962108 1.183262684 1.375120649 1.163787478 1.050183545 1.107612085 1.191630754 1.352065632 1.208972625;
1.197819338 1.019274607 1.089534121 1.003221513 1.159766278 0.895658345 1.176560456 1.088697522 1.251437098 1.090498669 1.214062643 1.144535627 1.153461229 1.008211258 1.119233546 1.069344617 1.166027086 1.309281781 1.235256132 1.240244718 1.174381286 1.371230162 1.002211828 1.029336372 0 0.905852103 1.234358505 1.046915156 1.045583607 1.2689564 1.177370454 1.042495378 1.153440129 1.066260161 0.971087509 1.011840837 0.852940041 1.216702084 1.082660474 1.011560444 1.073462562 1.066659143 0.959053489 1.177606532 1.104750325 0.771179849 1.099319188 1.002981697 1.29670977 1.261195415;
1.262146435 1.155736149 1.229568098 1.04841204 1.109777783 0.951534413 1.175103839 1.233071379 1.328370708 1.171005266 1.312488819 1.230639203 1.234955056 1.206932595 1.096498418 1.168139535 1.208539606 1.162076162 1.233321278 1.306927581 1.151949115 1.319578078 1.113253783 1.133507483 0.905852103 0 1.251490487 1.156467446 1.157659619 1.276526179 1.139636127 1.211667542 1.279153821 1.161921416 1.031919615 0.919857226 0.853252771 1.304312488 1.084932242 1.063885746 1.068900689 1.090299754 1.007256593 1.232674989 1.188546732 1.045984484 1.187785084 1.07768074 1.305479107 1.216372863;
1.323592608 1.148656585 1.38439984 1.34421716 1.362256074 1.318155621 1.171020087 1.265109986 1.391004752 1.274789211 1.317225883 1.184819346 1.252289661 1.174689379 1.228851042 1.413662067 1.245695919 1.218175081 1.240480754 1.361844537 1.288496775 1.361817996 1.318670725 1.31333441 1.234358505 1.251490487 0 1.318716863 1.309197713 1.263613901 1.225152653 1.335294359 1.31144646 1.140006083 1.349539012 1.317163666 1.249818476 1.374783778 1.253958971 1.344662952 1.355064188 1.330687408 1.119331823 1.31058688 1.269182385 1.277337843 1.234788728 1.285968229 1.449532207 1.292221007;
1.236247334 1.148092329 1.141609528 1.034923405 0.915097452 1.139148814 1.20015891 1.155251925 1.216034547 1.099379463 1.26054583 1.180039007 1.178994746 1.026914241 1.206874395 1.135192693 1.249311393 1.229389571 1.138141492 1.271820767 1.256387955 1.376373407 1.051322101 1.100750925 1.046915156 1.156467446 1.318716863 0 0.865117376 1.296310961 1.043083229 1.206534769 1.172303133 1.053302829 1.04388229 1.152697906 1.123023933 1.348699345 1.163788469 0.741101209 1.188695722 1.189075426 1.039678446 1.093364238 0.87262157 1.057890653 1.022243355 1.254409658 1.259618548 1.13615283;
1.236913586 1.028558598 1.23456473 1.086143267 1.044043433 1.080286798 1.195448399 1.173798235 1.074670651 1.171288952 1.231349464 1.263757104 1.163119228 1.080049725 1.175132861 1.259430708 1.180445006 1.309368207 1.242449455 1.268395907 1.175422514 1.390703135 1.029828444 1.087952569 1.045583607 1.157659619 1.309197713 0.865117376 0 1.230065302 1.125490605 1.183692439 1.142330311 1.098737993 1.155123614 1.157496498 1.103504425 1.260757488 1.08718419 0.774626683 1.128587289 1.286645825 1.120574474 1.21486109 1.017536204 1.0608755 1.09657529 1.204634541 1.229733702 1.232677909;
1.366718376 1.265931536 1.340753051 1.156675064 1.313527315 1.35915299 1.385496697 1.367046336 1.466445125 1.15806525 1.043896915 1.261296836 1.325884258 1.32269052 1.344164523 1.298065371 1.355096871 1.391651813 1.349010922 1.304752331 1.459545971 1.345577427 1.257335418 1.306658858 1.2689564 1.276526179 1.263613901 1.296310961 1.230065302 0 1.268245629 1.258241529 1.37324269 1.296796687 1.377984959 1.323368864 1.322283568 1.254148031 1.394123032 1.320125187 1.273602192 1.233497547 1.336925181 1.28569385 1.20516017 1.247742085 1.176387239 1.322038159 1.290530297 1.360701537;
1.221758653 1.132907734 1.151022915 1.177741779 1.095605371 1.102634282 1.21999721 1.167156358 1.215394295 1.208875317 1.211595601 1.278061899 1.190617029 1.097110285 1.172578954 1.292613869 1.16725873 1.197505426 1.139348769 1.34306716 1.168647067 1.40301391 1.096206873 1.146153127 1.177370454 1.139636127 1.225152653 1.043083229 1.125490605 1.268245629 0 1.24592034 1.27673255 1.058688699 1.130210889 1.077088541 1.101377775 1.224990894 1.156354272 1.015576342 1.156414084 1.083641965 1.159232567 1.300542095 1.12644699 1.125680045 1.08397823 1.226501972 1.235670363 1.208710038;
1.221505033 1.15724022 1.14991167 1.237325671 1.352973255 1.07312686 1.343342351 1.12578097 1.195961192 1.124898373 1.222949527 1.210337852 1.203364535 1.125499172 1.197674583 1.16037268 1.306050047 1.379875572 1.280224331 1.191578201 1.145093695 1.374243677 1.151119184 1.180413238 1.042495378 1.211667542 1.335294359 1.206534769 1.183692439 1.258241529 1.24592034 0 1.291060856 1.251875536 1.148663699 1.214281746 1.190532901 1.154079442 1.152625617 1.280405634 1.171461003 1.240365767 1.216471705 1.336815403 1.290194276 1.151490897 1.117592434 1.128192987 1.435224313 1.261173862;
1.071915378 0.987149334 1.297975342 1.181810038 1.354366323 1.171971942 1.246597366 1.150960315 1.122067354 1.271803528 1.280203318 1.185758879 0.915382703 1.157552641 1.243137709 1.307045145 1.053877751 1.29556301 1.156916271 1.388819211 1.306302184 1.425270503 1.125776359 1.169398227 1.153440129 1.279153821 1.31144646 1.172303133 1.142330311 1.37324269 1.27673255 1.291060856 0 1.061662757 1.201529086 1.299625491 1.185674913 1.361921979 1.060349513 1.128015962 1.228230757 1.313764899 1.208935881 1.346987311 1.276720806 1.185735219 1.164890032 1.358212533 1.349217883 1.368267128;
1.255900706 1.052314459 1.287727781 1.174665352 1.242073161 1.043153228 1.18406877 1.128539572 1.178237225 1.243601262 1.224307984 1.170940011 1.031020247 1.095963234 1.199126565 1.200868144 1.222599322 1.241611221 1.129106841 1.256595435 1.172186701 1.422515075 1.063224928 1.141037536 1.066260161 1.161921416 1.140006083 1.053302829 1.098737993 1.296796687 1.058688699 1.251875536 1.061662757 0 1.113462988 1.143652683 1.066170758 1.364671554 1.153052636 1.02321418 1.157394802 1.145462522 0.98263084 1.28902935 1.190618261 1.01821171 1.153951472 1.183142714 1.280431374 1.344839796;
1.175653003 1.042004802 1.004510354 1.132457465 1.143531595 0.983575766 1.123242314 1.046522657 1.22113051 1.21323005 1.29965171 1.173333071 1.095225845 1.09083247 1.086587356 1.106642098 1.077056231 1.28221594 1.150128946 1.295291394 1.242622293 1.3313757 1.132006297 0.999014115 0.971087509 1.031919615 1.349539012 1.04388229 1.155123614 1.377984959 1.130210889 1.148663699 1.201529086 1.113462988 0 0.797753135 0.968702068 1.305579053 1.045116543 1.019637494 0.993201144 1.106442744 1.166370678 1.262654089 1.048927777 1.05416778 1.127247904 1.224776663 1.297622724 1.090800168;
1.231854105 1.129721933 1.112528545 1.014290712 1.15020099 0.973019934 1.208630783 1.054725787 1.314960554 1.144579283 1.282857777 1.17140959 1.279431603 1.189781456 1.043131773 1.109900265 1.140880537 1.260803428 1.117772286 1.222398193 1.192694105 1.337113317 1.051365045 1.127754619 1.011840837 0.919857226 1.317163666 1.152697906 1.157496498 1.323368864 1.077088541 1.214281746 1.299625491 1.143652683 0.797753135 0 0.943794183 1.263749696 1.047597806 1.015210429 1.037159118 1.06194513 1.08994159 1.251385992 1.063629882 1.06477634 1.212314844 1.154975681 1.229569836 1.147486695;
1.201615771 1.036971286 1.221217757 1.218103927 1.219966142 0.860623848 1.075731631 1.081160636 1.160110778 1.183888682 1.339940468 1.152876546 1.203272619 1.050058726 1.045983968 1.207814917 1.201133494 1.196222761 1.122845672 1.224623889 1.07710358 1.415507847 1.024749217 1.102424436 0.852940041 0.853252771 1.249818476 1.123023933 1.103504425 1.322283568 1.101377775 1.190532901 1.185674913 1.066170758 0.968702068 0.943794183 0 1.287233013 0.986214926 1.065424187 1.013973477 1.1273923 1.125848344 1.23737463 1.178684893 0.907372592 1.200501595 1.148708356 1.208158111 1.223342006;
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[w_st, ST, X_st] = kruskal(X, w)
My email: tb_ks@hotmail.com
  1 件のコメント
Josh Meyer
Josh Meyer 2015 年 11 月 5 日
I suggest you use the new graph and digraph objects introduced to MATLAB in R2015b. Once you create your graph(s), you can use the minspantree function with the 'sparse' algorithm method, which is Kruskal's algorithm.

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