function [plain,ssd] = condorcet(election)
% [plain,ssd] = condorcet(election): Plain and SSD Condorcet winners
%     $election$: matrix or name of file containing pairwise matrix or ballots
%                 -- same conventions as $tallies$, below
%     $plain$:   winners from Plain Condorcet voting
%     $ssd$:     winners from SSD Condorcet voting (BONUS)
%     note: when there are ties, *all* possible answers are returned

    % ----- << your code for condorcet goes here >> -----
  
function [i,j,v] = alldefeats(pwm)
% [i,j,v] = alldefeats(pwm): defeats in ascending order in pairwise matrix 
%     $pwm$:   pairwise matrix
%     $i,j,v$: $k$-th defeat is $i(k)$ over $j(k)$ with magnitude $v(k)$;
%              $v$ is sorted in ascending order

    % ----- << your code for alldefeats goes here >> -----

function  t = issubset(a,b)
% t = issubset(a,b): "$a$ is a subset of $b$?"

    % ----- << your code for issubset goes here >> -----

% function pwm = tallies(election)
% pwm = tallies(election): pairwise matrix specified by election$
%     $election$: matrix or name of file containing pairwise matrix or ballots
%     + if $election$ is an array of numbers, it is a pairwise matrix
%     + if $election$ is a string vector, has length $>2$, and has second
%       character neither $'>'$ nor $'='$, it is the name of a file:
%        + if the file contains numbers, it holds a pairwise matrix
%        + otherwise, the $i$-th line holds the ballot of the $i$-th voter
%     + otherwise, $election$ is a 2-D string matrix where 
%       the $i$-th row is the ballot of the $i$-th voter
%
%     the format of a single ballot is the same as for $tally$, below;
%     each ballot is assumed to have the same number of candidates

    % ----- << your code for tallies goes here >> -----

function pwm = tally(ballot): pairwise matrix for single ballot $ballot$
% pwm = tally(ballot): pairwise matrix for single ballot $ballot$
%     $ballot$: a string vector of holding an ordered sequence of candidates
%     + candidates are represented by consecutive letters of the alphabet,
%       starting at $'a'$, and ignoring case ($'a'$ and $'A'$ are the same)
%     + $ballot(1:2:end)$ is the list of candidates
%     $ $ballot(2:2:end)$ holds comparisons $'>'$ and/or $'='$
%
%     example: $tally('d>c=e=b>a')$

    % ----- << your code for tally goes here >> -----

function top = topmost(pwm)
% top = topmost(pwm): innermost unbeaten sets for pairwise matrix $pwm$

    % ----- << BONUS: your code for topmost goes here >> -----

function list = unbeaten(pwm,list): smallest unbeaten set containing $list$
% list = unbeaten(pwm,list): smallest unbeaten set containing $list$
%     $pwm$: pairwise matrix
%     note: $list$ is both a return variable and a parameter

    % ----- << BONUS: your code for unbeaten goes here >> -----