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## Copyright (C) 2024 David Legland
## All rights reserved.
##
## Redistribution and use in source and binary forms, with or without
## modification, are permitted provided that the following conditions are met:
##
## 1 Redistributions of source code must retain the above copyright notice,
## this list of conditions and the following disclaimer.
## 2 Redistributions in binary form must reproduce the above copyright
## notice, this list of conditions and the following disclaimer in the
## documentation and/or other materials provided with the distribution.
##
## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS''
## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR
## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
##
## The views and conclusions contained in the software and documentation are
## those of the authors and should not be interpreted as representing official
## policies, either expressed or implied, of the copyright holders.
function varargout = prim_mst(edges, vals)
%PRIM_MST Minimal spanning tree by Prim's algorithm.
%
% EDGES2 = prim_mst(EDGES, WEIGHTS)
% Compute the minimal spanning tree (MST) of the graph with edges given
% by EDGES, and using the specified edge weights.
% The nodes of the resulting tree are the same as the nodes of the
% original graph. Therefore, the function requires only to specify edges.
%
% Example
% pts = load('sedgewick_points.txt');
% [nodes, edges] = delaunayGraph(pts);
% figure; drawGraphEdges(nodes, edges, 'color', 'k');
% axis equal; axis([10 27 10 27]); hold on;
% weights = grEdgeLengths(nodes, edges);
% edges2 = prim_mst(edges, weights);
% drawGraphEdges(nodes, edges2, 'linewidth', 2, 'color', 'b');
%
% See also
% euclideanMST, grEdgeLengths
%
% ------
% Author: David Legland
% E-mail: david.legland@inrae.fr
% Created: 2007-07-27, using Matlab 7.4.0.287 (R2007a)
% Copyright 2007-2023 INRA - BIA PV Nantes - MIAJ Jouy-en-Josas
% isolate vertices index
nodes = unique(edges(:));
N = length(nodes);
% initialize memory
nodes2 = zeros(N, 1);
edges2 = zeros(N-1, 2);
vals2 = zeros(N-1, 1);
% initialize with a first node
nodes2(1) = nodes(1);
nodes = nodes(2:end);
% iterate on edges
for i = 1:N-1
% find all edges from nodes2 to nodes
ind = unique(find(...
(ismember(edges(:,1), nodes2(1:i)) & ismember(edges(:,2), nodes)) | ...
(ismember(edges(:,1), nodes) & ismember(edges(:,2), nodes2(1:i))) ));
% choose edge with lowest value
[tmp, ind2] = min(vals(ind)); %#ok<ASGLU>
ind = ind(ind2(1));
vals2(i) = vals(ind);
% index of other vertex
edge = edges(ind, :);
neigh = edge(~ismember(edge, nodes2));
% add to list of nodes and list of edges
nodes2(i+1) = neigh;
edges2(i,:) = edge;
% remove current node from list of old nodes
nodes = nodes(~ismember(nodes, neigh));
end
% process output arguments
if nargout == 1
varargout{1} = edges2;
elseif nargout==2
varargout{1} = edges2;
varargout{2} = vals2;
end
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