52 lines
1.7 KiB
R
52 lines
1.7 KiB
R
|
minimum_spanning_tree <- function(C1, C2) stop("needs translation")
|
||
|
|
# function A = minimum_spanning_tree(C1, C2)
|
||
|
|
# %
|
||
|
|
# % Find the minimum spanning tree using Prim's algorithm.
|
||
|
|
# % C1(i,j) is the primary cost of connecting i to j.
|
||
|
|
# % C2(i,j) is the (optional) secondary cost of connecting i to j, used to break ties.
|
||
|
|
# % We assume that absent edges have 0 cost.
|
||
|
|
# % To find the maximum spanning tree, used -1*C.
|
||
|
|
# % See Aho, Hopcroft & Ullman 1983, "Data structures and algorithms", p 237.
|
||
|
|
|
||
|
|
# % Prim's is O(V^2). Kruskal's algorithm is O(E log E) and hence is more efficient
|
||
|
|
# % for sparse graphs, but is implemented in terms of a priority queue.
|
||
|
|
|
||
|
|
# % We partition the nodes into those in U and those not in U.
|
||
|
|
# % closest(i) is the vertex in U that is closest to i in V-U.
|
||
|
|
# % lowcost(i) is the cost of the edge (i, closest(i)), or infinity is i has been used.
|
||
|
|
# % In Aho, they say C(i,j) should be "some appropriate large value" if the edge is missing.
|
||
|
|
# % We set it to infinity.
|
||
|
|
# % However, since lowcost is initialized from C, we must distinguish absent edges from used nodes.
|
||
|
|
|
||
|
|
# n = length(C1);
|
||
|
|
# if nargin==1, C2 = zeros(n); end
|
||
|
|
# A = zeros(n);
|
||
|
|
|
||
|
|
# closest = ones(1,n);
|
||
|
|
# used = zeros(1,n); % contains the members of U
|
||
|
|
# used(1) = 1; % start with node 1
|
||
|
|
# C1(find(C1==0))=inf;
|
||
|
|
# C2(find(C2==0))=inf;
|
||
|
|
# lowcost1 = C1(1,:);
|
||
|
|
# lowcost2 = C2(1,:);
|
||
|
|
|
||
|
|
# for i=2:n
|
||
|
|
# ks = find(lowcost1==min(lowcost1));
|
||
|
|
# k = ks(argmin(lowcost2(ks)));
|
||
|
|
# A(k, closest(k)) = 1;
|
||
|
|
# A(closest(k), k) = 1;
|
||
|
|
# lowcost1(k) = inf;
|
||
|
|
# lowcost2(k) = inf;
|
||
|
|
# used(k) = 1;
|
||
|
|
# NU = find(used==0);
|
||
|
|
# for ji=1:length(NU)
|
||
|
|
# for j=NU(ji)
|
||
|
|
# if C1(k,j) < lowcost1(j)
|
||
|
|
# lowcost1(j) = C1(k,j);
|
||
|
|
# lowcost2(j) = C2(k,j);
|
||
|
|
# closest(j) = k;
|
||
|
|
# end
|
||
|
|
# end
|
||
|
|
# end
|
||
|
|
# end
|