%% Monte carlo project 2
N = 2;
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
%%
N = 8;
n = 100;
temp = zeros(N, 2);
weights = zeros(n,1);
weight_temp = 1;


for j=1:n
    for i = 2:N+1

    [move, w] = drawSaw(temp, i-1);

    temp(i, :) = move;
    if(temp(i, :) == temp(i-1, :))
    weight_temp = 0;
    else
    weight_temp = w.*weight_temp;
    end
    end

temp = zeros(N, 2);
weights(j,1) = weight_temp;
weight_temp=1;
end
mean(weights)

%%