%% Monte carlo project 2
N = 5;
d = 2;
n=10000;
test = zeros(N+1, 2*n);
%%

for j=1:N
r = rand(1,n);
test(j+1, :) = test(j, :) + draw(r);
end
%%


saw = 0;
for j = 1:n
if(size(unique(test(:, j*2-1:j*2), 'rows')) == size(test(:, j*2-1:j*2)))
    saw=saw+1;

end
end
(saw/n)*(2*d)^N

%%
r = linspace(0,N,n);
gdist = @(x, n) 2*x.*exp(-x.^2/n)/n; %x equals radius, which represents which is max n in our case;

plot(r, gdist(r, 6))
%%
subplot(211)

histogram(radius)
subplot(212)
plot(r, gdist(r, 10))

%%

for j=1:N
r = rand(1,n);
test(j+1, :) = test(j, :) + draw(r);
end
%%

temp = zeros(N, 2);
weights = zeros(N,1);
weights(1, :) = 1;
check = zeros(N,1);
for j=1:n
    for i = 2:N
   temp(i, :) = drawSaw(temp,i-1);
    if(temp(i, :) == temp(i-1, :))
    weights(i, 1) = 0;
    else
    weights(i,1) = 1;
    end
    end
check = check+weights;
temp = zeros(N, 2);
weights = zeros(N,1);
weights(1, :) = 1;
end



%%
x=temp(:,1);
y=temp(:,2);
plot(x,y)
axis([-10 10 -10 10])