% EA 1, Homework program assignment 3
%
% Name: Dhileepan, Vishal
% Section: 21
% Date: 10/18/2018

%Task 1
%Prompt the user for an input
steps = input('How many steps would you like to take? ');
%Creates matrix of possible random movements
possible_points = randi([1,4],steps,1);
figure; %creates a new figure for a plot
h= animatedline(0,0); %initializes an animation of the random walk at the origin
x=0;
y=0;
%Iterates the loop for all steps
for i=1:steps
    if possible_points(i) == 1
        x = x + 1;
    elseif possible_points(i) == 2
        x = x - 1;
    elseif possible_points(i) == 3
        y = y + 1;
    elseif possible_points(i) == 4
        y = y - 1;
    end

    addpoints(h,x,y); %adds a line to point (x,y)
    drawnow %displays the current plot where x and y are the coordinates of the new position

end

%Task 2
%Prompt the user for inputs
steps = input('How many steps would you like to take? ');
trials = input('How many trials would you like? ');
trial = 1;
trial_vector = zeros(1,trials);
x
y
figure;

%Iterates the loop for the number of trials
while trial<=trials
    possible_points = randi([1,4],steps,1);
    x=0;
    y=0;
    %Iterates the loop for all steps
    for i=1:steps
        if possible_points(i) == 1
            x = x + 1;
        elseif possible_points(i) == 2
            x = x - 1;
        elseif possible_points(i) == 3
            y = y + 1;
        elseif possible_points(i) == 4
            y = y - 1;
        end
        final_distance = sqrt(x^2+y^2);
    end
    trial_vector(trial) = final_distance;
    trial = trial+1;
end
trial_vector
average_distance = sum(trial_vector)/trials
histogram(trial_vector)
xlabel('Distance')
ylabel('Number of instances')

%Task 3
%Prompt the user for inputs
steps = input('How many steps would you like to take? ');
trials = input('How many trials would you like? ');
distance_threshold = input('Enter a distance threshold array: ');
steps_array = [1:length(distance_threshold)];
trial=1;
figure;

%Iterates the loop for all values of the distance threshold
for j = 1:length(distance_threshold)
    %Iterates the loop for all trials
    while trial <= trials
        if mod(trial, 400) == 0
            fprintf("distance_threshold= %6.2f, trial= %6.2f\n", distance_threshold(j), trial);
        end
        step = 1;
        x=0;
        y=0;
        %Iterates the loop for all steps
        while step <= steps
            possible_points = randi([1,4],steps,1);
            distance = sqrt(x^2 + y^2);
            if distance >= distance_threshold(j)
                steps_array(j) = steps_array(j) + step;
                break
            end
            if possible_points(i) == 1
                x = x + 1;
            elseif possible_points(i) == 2
                x = x - 1;
            elseif possible_points(i) == 3
                y = y + 1;
            elseif possible_points(i) == 4
                y = y - 1;
            step = step+1;
            end
            if step > steps
                fprintf("Maximum number of steps exceeded!\n");
                break
            end
        end
        trial = trial+1;
    end
    trial = 1;
end

%Calculating and printing average number of steps
fprintf("(distance, average number of steps)\n");
hold on;
for j = 1:length(distance_threshold)
    fprintf("(%6.2f, %6.2f)\n", distance_threshold(j), steps_array(j)/trials);
end
plot(distance_threshold, steps_array/steps);
xlabel("Distance threshold");
ylabel("Average step count");

%%Outputs
%Task 1:
%The final position is (0,-10)
%The distance from the origin is 10

%Task 2
%The average distance was 39.5620

%Task 3
%distance_threshold=   5.00, trial= 400.00
% distance_threshold=   5.00, trial= 800.00
% distance_threshold=   5.00, trial= 1200.00
% distance_threshold=   5.00, trial= 1600.00
% distance_threshold=   5.00, trial= 2000.00
% distance_threshold=  10.00, trial= 400.00
% distance_threshold=  10.00, trial= 800.00
% distance_threshold=  10.00, trial= 1200.00
% distance_threshold=  10.00, trial= 1600.00
% distance_threshold=  10.00, trial= 2000.00
% distance_threshold=  15.00, trial= 400.00
% distance_threshold=  15.00, trial= 800.00
% distance_threshold=  15.00, trial= 1200.00
% distance_threshold=  15.00, trial= 1600.00
% distance_threshold=  15.00, trial= 2000.00
% distance_threshold=  20.00, trial= 400.00
% distance_threshold=  20.00, trial= 800.00
% distance_threshold=  20.00, trial= 1200.00
% distance_threshold=  20.00, trial= 1600.00
% distance_threshold=  20.00, trial= 2000.00
% distance_threshold=  25.00, trial= 400.00
% distance_threshold=  25.00, trial= 800.00
% distance_threshold=  25.00, trial= 1200.00
% distance_threshold=  25.00, trial= 1600.00
% distance_threshold=  25.00, trial= 2000.00
% distance_threshold=  30.00, trial= 400.00
% distance_threshold=  30.00, trial= 800.00
% distance_threshold=  30.00, trial= 1200.00
% distance_threshold=  30.00, trial= 1600.00
% distance_threshold=  30.00, trial= 2000.00
% distance_threshold=  35.00, trial= 400.00
% distance_threshold=  35.00, trial= 800.00
% distance_threshold=  35.00, trial= 1200.00
% distance_threshold=  35.00, trial= 1600.00
% distance_threshold=  35.00, trial= 2000.00
% distance_threshold=  40.00, trial= 400.00
% distance_threshold=  40.00, trial= 800.00
% distance_threshold=  40.00, trial= 1200.00
% distance_threshold=  40.00, trial= 1600.00
% distance_threshold=  40.00, trial= 2000.00
% distance_threshold=  45.00, trial= 400.00
% distance_threshold=  45.00, trial= 800.00
% distance_threshold=  45.00, trial= 1200.00
% distance_threshold=  45.00, trial= 1600.00
% distance_threshold=  45.00, trial= 2000.00
% distance_threshold=  50.00, trial= 400.00
% distance_threshold=  50.00, trial= 800.00
% distance_threshold=  50.00, trial= 1200.00
% distance_threshold=  50.00, trial= 1600.00
% distance_threshold=  50.00, trial= 2000.00
% (distance, average number of steps)
% (  5.00,   7.41)
% ( 10.00,  26.77)
% ( 15.00,  60.50)
% ( 20.00, 101.89)
% ( 25.00, 158.06)
% ( 30.00, 233.35)
% ( 35.00, 315.02)
% ( 40.00, 413.74)
% ( 45.00, 507.54)
% ( 50.00, 638.38)
%The specific function that approximates this is line 124, where the steps
%array divides the number of trials that is chosen by the user