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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
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function path = grFindMaximalLengthPath(nodes, edges, edgeWeights)
%GRFINDMAXIMALLENGTHPATH Find a path that maximizes sum of edge weights.
%
% PATH = grFindMaximalLengthPath(NODES, EDGES, EDGE_WEIGHTS);
% Finds a greatest geodesic path in the graph. A path between two nodes
% is a succession of adjacent edges that link the first and last nodes.
% the length of the path is the sum of weights of edges that constitute
% the path.
% A geodesic path is a path that minimizes the length of the path among
% the set of paths between the nodes.
% A maximal length path maximizes the length of the geodesic path between
% couples of nodes in the graph
%
% The result PATH is the list of edge indices that constitutes the path.
%
% PATH = grFindMaximalLengthPath(NODES, EDGES);
% Assumes each edge has a weight equal to 1.
%
% See also
% grFindGeodesicPath
% ------
% Author: David Legland
% E-mail: david.legland@inrae.fr
% Created: 2011-05-22, using Matlab 7.9.0.529 (R2009b)
% Copyright 2011-2023 INRA - Cepia Software Platform
% ensure weights are defined
if ~exist('edgeWeights', 'var')
edgeWeights = ones(size(edges, 1), 1);
end
% find an extremity vertex
inds = graphPeripheralVertices(nodes, edges, edgeWeights);
ind0 = inds(end);
% find a vertex opposite to the first extremity
dists = grPropagateDistance(nodes, edges, ind0, edgeWeights);
ind1 = find(dists == max(dists), 1, 'first');
% iterate on neighbors of current node: choose next neighbor with smallest
% cumulated weight, until we are back on source node
path = [];
while true
% find neighbor with lowest cumulated distance
neighs = grAdjacentNodes(edges, ind1);
neighDists = dists(neighs);
indN = find(neighDists == min(neighDists), 1);
ind2 = neighs(indN);
% add edge index to the path
indE = find(sum(ismember(edges, [ind1 ind2]), 2) == 2, 1);
path = [path indE]; %#ok<AGROW>
% test if path is finished or not
if ind2 == ind0
break;
end
ind1 = ind2;
end
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