Massey_network_ranking.m

% Problem 3 Massey's network method

A = importdata('examscores.dat');

Q = zeros(1,7);


% get the students' point differentials
for i = 1:7
    for j = 1:31
        if A(j,i) >= 3
            Q(1,i) = Q(1,i) + 1;
        else
            Q(1,i) = Q(1,i);
        end
    end
end

c = 1;
X = zeros(21,7);
Y = zeros(21,1);
for a = 1:7
    for b = (a + 1):7
        if Q(a) < Q(b)
            X(c,a) = -1;
            X(c,b) = 1;
            Y(c,1) = Q(b) - Q(a);
            c = c + 1;
        elseif Q(a) > Q(b)
            X(c,b) = -1;
            X(c,a) = 1;
            Y(c,1) = Q(a) - Q(b);
            c = c + 1;
        elseif Q(a) == Q(b)
            X(c,a) = 0;
            X(c,b) = 0;
            Y(c,1) = 0;
            c = c + 1;
        end
    end    
end
% get the Massey Matrix with diagonal is the total games they played
% and the others is the -1* (#question i played against j)
tans_X = X';
M = tans_X * X;
D = tans_X * Y;

r = M \ D;
[sorted_value,ranked] = sort(r,'ascend');
fprintf('\n');

fprintf('The unique solution of question 1 to 7: \n')
disp(r);

fprintf('The difficulty rank of these 7 questions is %d %d %d %d %d %d %d. \n', ranked(1), ranked(2), ranked(3), ranked(4), ranked(5), ranked(6), ranked(7))
fprintf('second question is the most difficult and fifth and sixth question are the easiest.')
fprintf('\n')