Trees. Trees are everywhere. One of these is not a tree. Binary trees. Recursive data structures

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1 Trees Trees are everywhere Recursive data structures CS112 Scientific Cmputatin Department f Cmputer Science Wellesley Cllege Trees 21-2 One f these is nt a tree Binary A binary tree has at mst tw branches at each nde tp nde f a binary tree is the rt nde ndes with n branches are leaves sub belw a nde are the left and right sub ndes stre values We will represent a binary tree using a cell array f 3 elements: {value {left subtree} {right subtree} } Trees 21-3 Trees

2 A binary frest >> seed = {'ne' {} {}}; >> twig = {'ne' {'tw' {} {}} {'three' {} {}}}; tw ne ne three >> = {'ne' {'tw' {} {'fur' {} {}}} {'three' {'five' {} {}} {}}}; Phylgenic tree f phyl = {'' {'deciduus' {'' {} {}}... {'' {'' {} {}}... {'' {} {}}}}... {'' {'' {} {}}... {'' {'' {} {}}... {'suthern yellw' {} {}}}}}; deciduus suthern yellw Trees 21-5 Trees 21-6 Prcessing Trees are defined recursively s we will prcess them recursively T slve a prblem recursively: If it is simple enugh then slve it express slutin in terms f smaller, similar prblem(s) Print the cntents f a tree phyl = {'' {'deciduus' {'' {} {}}... {'' {'' {} {}}... {'' {} {}}}}... {'' {'' {} {}}... {'' {'' {} {}}... {'suthern yellw' {} {}}}}}; deciduus suthern yellw Trees 21-7 Trees

3 Think recursively! d nthing print the string in the rt nde print the cntents f the left subtree print the cntents f the right subtree deciduus Let s write the cde d nthing print the string in the rt nde print the cntents f the left subtree print the cntents f the right subtree functin printtree (tree) % prints all f the strings cntained in the input tree suthern yellw Trees 21-9 Trees Let s write the cde If the tree is nt empty print the string in the rt nde print the cntents f the left subtree print the cntents f the right subtree S is it empty? functin answer = isempty (tree) % returns true if the input tree is an empty cell array answer = (length(tree) == 0); functin printtree (tree) % prints all f the strings cntained in the input tree if ~isempty(tree) disp(tree{1}); printtree(tree{2}); printtree(tree{3}); % if tree is nt empty % print string in rt nde % print left subtree % print right subtree Trees Trees

4 Cunt the ndes in a tree return zer cunt ndes in left subtree cunt ndes in right subtree return sum f cunts plus ne Cunt the ndes in a tree return zer cunt ndes in left subtree cunt ndes in right subtree return sum f cunts plus ne functin ndes = cuntndes(tree) if isempty(tree) ndes = 0; ndes = 1 + cuntndes(tree{2}) + cuntndes(tree{3}); Exercise: Mdify cuntndes t cmpute the height f a tree Trees Trees Search fr a string in a tree Let s play twenty questins >> fund = searchtree(phyl, '') suthern yellw fund = 1 >> fund = searchtree(phyl, 'stella') fund = 0 >> Write searchtree deciduus hi suthern yellw >> twentyquests(twenty) fur legs? yes hves? n stripes? yes tiger? yes Ww! I wn! Play again? yes fur legs? n fly? yes feathers? n butterfly? n Oh well, better luck next time Play again? n >> Trees Trees

5 Game tree fr twenty questins twenty = {'fur legs? ' {'hves? ' {'lng neck? ' {'giraffe? ' {} {}}... {'zebra? ' {} {}}}... {'stripes? ' {'tiger? ' {} {}}... {'dg? ' {} {}}}}... {'fly? ' {'feathers? ' {'eagle? ' {} {}}... {'butterfly? ' {} {}}}... {'swim? ' {'penguin? ' {} {}}... {'centipede? ' {} {}}}}}; lngneck? hves? stripes? fur legs? yes feather? n fly? giraffe? zebra? tiger? dg? eagle? butter fly? swim? penguin? centipede? Trees TwentyQuests functin twentyq (questtree) % recursive functin that implements the twenty questins game reply = input(questtree{1}, 's'); % print questin in rt nde and if isleaf(questtree) % input user's reply (yes r n) if strcmp(reply, 'yes') % leaf nde is reached, s disp('ww! I wn!'); % determine utcme f game disp('oh well, better luck next time'); % leaf nde nt yet reached if strcmp(reply, 'yes') % if user replied yes, fllw left subtree twentyq(questtree{2}) % therwise fllw right subtree twentyq(questtree{3}) Trees TwentyQuests functin twentyquests (questtree) % plays the twenty questins game, using a binary tree that % cntains questins in the ndes playagain = 1; while playagain % keeps ging as lng as user answers yes t twentyq(questtree) % Play again? questin playagain = strcmp(input('play again? ', 's'), 'yes'); Trees