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% Solution to Question 1a
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% Student 1: SID = 311178480
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% One paragraph description of how this program works:
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GRID_SIZE  = 100;
N_STEPS    = 1000;
START_LOC  = 0.5 * [GRID_SIZE GRID_SIZE];

grid = zeros(GRID_SIZE);

% r_dir = 0 corresponds to movement in the first dimension, r_dir = 1
% corrresponds to movement in the second dimension
r_dir  = round(rand(N_STEPS, 1));
% r_sign = -1 corresponds to negative movement(left/up), r_sign = 1 correspods
% to positive movement(right/down)
r_sign = 2 * round(rand(N_STEPS, 1)) - 1;
% Combine the directions and signs to find all the movements
v = [r_sign r_sign] .* [r_dir ~r_dir];
% Sum up the movements up to find the locations of the random walk over time
loc = cumsum([START_LOC; v]);
% Open a figure window to output the motion of the walk to screen
fig = figure('Name', 'Single Random Walk', 'NumberTitle', 'off');
for i = 1:N_STEPS
    % At each step, add the locations up to that timestep to the grid
    if all(loc(i,:) > 0 & loc(i,:) <= GRID_SIZE*GRID_SIZE)
        grid(loc(i,1),loc(i,2)) = 1;
    end
    % Show the grid
    imagesc(grid);
    pause(0);
end
% Print the figure out to pdf
print(fig, '-dpdf', 'single_random_walk.pdf');