clc;
clear;

M = 50;
eps = 1e-5;
delta = 1/3;
C = 10.66;

nums = 20:0.1:50;
len = length(nums);
N = zeros(1, len);
upper_bound_C1 = zeros(1, len);
upper_bound_C2 = zeros(1, len);
log_ub_C1 = zeros(1, len);
log_ub_C2 = zeros(1, len);

for i = 1: len
    N(i) = 10^nums(i);
    upper_bound_C1(i) = get_our_ub(1, N(i), C, M, eps);
    log_ub_C1(i) = log(upper_bound_C1(i));
    upper_bound_C2(i) = get_wl_ub(N(i), M, eps);
    log_ub_C2(i) = log(upper_bound_C2(i));
    N(i) = nums(i);
end

semilogy(N, upper_bound_C1, 'r-', N, upper_bound_C2, 'b');
legend("Our result", "Wang's result");
xlabel("log_{10}(N)");
ylabel("Upper bound of K");
title_name = strcat("Prob(\delta_K < ", string(delta), ") >= 1 - ", string(eps));
title(title_name);

[k1, b1] = linefit(N, log_ub_C1);
[k2, b2] = linefit(N, log_ub_C2);
fprintf("Our result gradient: %f\n", k1);
fprintf("Wang's result gradient: %f\n", k2);