%%%%%%% % randompancakeflipper.m % Author: Lance Harden, Davidson College % June 2006 % % Description: This original, user-friendly version of the pancake % simulator models all variations of problem, accepting inputs for the % number of spatulas and whether the pancakes are signed. The output is a % histogram that displays the number of random flips it took in each trial % for the stack to be sorted into the home, [1 2 3 4 5], permutation. Results = []; s = input('Number of spatulas: ') if (s ~= 1 & s ~= 2) disp('How many arms do you have!') return end t = input('Signed or unsigned permutation? (Enter s or u): ', 's') if (t ~= 's' & t ~= 'u') disp('Error: You must enter "s" or "u". Try again by re-running the program.') return end if t == 's' I = input('Enter your desired initial permutation as a row vector (you MUST use brackets), e.g. [2 -3 4 -1]: ') elseif t == 'u' I = input('Enter your desired initial permutation as a row vector (you MUST use brackets), e.g. [2 3 4 1]: ') end k = length(I); if k < 2 disp('Error: You must enter your initial permutation as a row vector with at least two entries.') return end B = sort(abs(I)); if (B ~= 1:k & t == 's') disp('Error: Your initial permutation must consist of signed consecutive integers starting at 1, e.g. [3 -2 -4 1] is OK, but [8 3 5 1] and [0 -2 1 -3] are not.') return end if (B ~= 1:k & t == 'u') disp('Error: Your initial permutation must consist of consecutive integers starting at 1, e.g. [3 1 2 4] is OK, but [2 8 0 5] is not.') return end n = input('Number of trials: ') slots = k+1; choices = nchoosek(1:slots,2); choices(:,2) = choices(:,2) - 1; numchoices = length(choices); tic if s == 1 if t == 's' for i = 1:n G = I; count = 0; while ( any(G ~= 1:k) || any(G ~= -k:-1) ) count = count + 1; P = G; a = ceil(k*rand); G = [fliplr(P(1:a)) P(a+1:k)]; for j = 1:a G(j) = -G(j); end end Results(i) = count; end else for i = 1:n G = I; count = 0; while any(G ~= 1:k) count = count + 1; P = G; a = ceil(k*rand); G = [fliplr(P(1:a)) P(a+1:k)]; end Results(i) = count; end end else if t == 's' for i = 1:n G = I; count = 0; while ( any(G ~= 1:k) || any(G ~= -k:-1) ) count = count + 1; P = G; a = ceil(numchoices*rand); G = [P(1:(choices(a,1)-1)) fliplr(P(choices(a,1):choices(a,2))) P((choices(a,2)+1):k)]; for j = choices(a,1):choices(a,2) G(j) = -G(j); end end Results(i) = count; end else for i = 1:n G = I; count = 0; while any(G ~= 1:k) count = count + 1; P = G; a = ceil(numchoices*rand); G = [P(1:(choices(a,1)-1)) fliplr(P(choices(a,1):choices(a,2))) P((choices(a,2)+1):k)]; end Results(i) = count; end end end time = toc beep x = 5:10:max(Results); hist(Results,x); figure(gcf)