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[system]

function D = dijkstra(G, pairs)
% This function takes an adjacency matrix called G
% and a p-by-2 matrix called pairs.
% The pairs matrix will contain pairs of indices.
% This function will determine the shortest distance from
% the first index in the pair to the second index for
% every pair in matrix pairs.
%
% The function will only return a p-by-1 matrix of shortest
% distances. I could use it to also return the shortest path,
% but I don’t need that data, so only shortest distance is
% calculated.

p = size(pairs, 1);  % Number of pairs 
v = size(G, 1); % Number of vertices 
D = []; 

for i = 1:v 
    for j = 1:v 
        if G(i,j) <= esp 
            G(i,j) = inf 
        end 
    end 
end 

for i = 1:p  
    dist = inf(1, v); 
    seen = ones(1, v); 
    not_seen = v; 

    dist(1, pairs(i,1)) = 0; 

    while not_seen > 0 
        [distance index] = min(dist .* seen); 

        if distance == inf 
            break; 
        end 

        if index == pairs(i,2) 
            break; 
        end 

        seen(index) = inf; 
        not_seen = not_seen - 1; 

        for n = 1:v 
            if seen(n) == 1 
                alt = distance + G(index, n); 
                if alt < dist(n) 
                    dist(n) = alt; 
                end 
            end 
        end 
    end 
    D = [D ; dist(pairs(i,2))]; 
end 

end