%%%%%%% % findmin.m % Author: Lance Harden, Davidson College % June 2006 % % Description: A variation of powerflipper, findmin randomly flips an % inputted initial permutation until either (1) the stack has been % reordered into the home permutation in less than or equal to br flips, or % (2) all n trials are run. It accepts the same inputs as powerflipper: % number of spatulas (1 or 2), type of permutation ('s' or 'u', for signed % or unsigned), initial permutation, number of trials, and the number of % random flips per trial, respectively. It stores the flip history for the % last trial in the matrix, flips, and the number of flips it took to reach % the home permutation for each trial in the Results matrix. function [Results,flips] = findmin(s,t,I,n,br) Results = []; if (s ~= 1 & s ~= 2) disp('How many arms do you have!') return end if (t ~= 's' & t ~= 'u') disp('Error: You must enter "s" or "u". Try again by re-running the program.') return 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 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; flips = []; while ( any(G ~= 1:k) || any(G ~= -k:-1) ) count = count + 1; flips(:,count) = G'; 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; flips(:,count + 1) = G'; if (count <= br) time = toc beep return end end else for i = 1:n G = I; count = 0; flips = []; while any(G ~= 1:k) count = count + 1; flips(:,count) = G'; P = G; a = ceil(k*rand); G = [fliplr(P(1:a)) P(a+1:k)]; end Results(i) = count; flips(:,count + 1) = G'; if (count <= br) time = toc beep return end end end else if t == 's' for i = 1:n G = I; count = 0; flips = []; while ( any(G ~= 1:k) || any(G ~= -k:-1) ) count = count + 1; flips(:,count) = G'; 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; flips(:,count + 1) = G'; if (count <= br) time = toc beep return end end else for i = 1:n G = I; count = 0; flips = []; while any(G ~= 1:k) count = count + 1; flips(:,count) = G'; 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; flips(:,count + 1) = G'; if (count <= br) time = toc beep return end end end end time = toc beep