% 
% Written by:
% -- 
% John L. Weatherwax                2006-12-31
% 
% email: wax@alum.mit.edu
% 
% Please send comments and especially bug reports to the
% above email address.
% 
%-----

close all; clc; clear;

n = 1000; 

[probs,mi,mv] = eval_prob_best_selection(n);

figure; plot( 1:(n-1), probs, '-o' ); 
xlabel('number of prescreening interviews'); ylabel('probability of picking the optimal secretary');

addpath('~/Matlab');
ms = 1:(n-1);
vline( ms(mi) );
text( ms(mi)*(1+.1), mv*(1-0.5), ['optimal m=',num2str(ms(mi)),'; n=',num2str(n)] );

saveas(gcf,'../WriteUp/Graphics/example_prob_best_calc.eps', 'epsc');


% Plot what the optimal fraction of the candidates to interview is each value of n
%
ns = 10:1000;
opt_fraction_of_candidates_to_interview = zeros(1,length(ns));
for ni = 1:length(ns),
  [probs,mi,mv] = eval_prob_best_selection(ns(ni));
  opt_fraction_of_candidates_to_interview(ni) = mi/ns(ni);
end

figure; plot( ns, opt_fraction_of_candidates_to_interview, '-o' );
xlabel('number of total candidates (n)'); ylabel('optimal fraction of candidates to interview');
saveas(gcf,'../WriteUp/Graphics/opt_fraction_to_interview.eps', 'epsc');