Binary Search Tree Reflection (Video by mycodeschool)

Ma. Nikkie Evalla

Mr. Ezra Anglo

BSIT2-6

Data Structure

Reflection Paper on Data structures: Binary Search Tree

In the the foll follow owin ingg ae aerr I will will !i"c !i"cu" u""" what what I have have lear learne ne!! fro# fro# watc watchi hing ng an info infor# r#at ativ ivee vi!e vi!eoo $% mycodeschool  entitle!  entitle! Data structures: Binary Search Tree. Tree . The uro"e of thi" reflection aer an! of the "ource vi!eo a" to how I "ee" it i" to e&lain the Binar% Search Tree. I !eci!e! to inclu!e a co#ari"on of an arra%' linke! li"t an! $inar% "earch tree running ti#e for certain oeration" which i" of cour"e I al"o learnt fro# the "ai! vi!eo to further e&lain the toic. A" "tate! fro# our "ource' Binar% "earch tree i" a special kind of binary tree that organizes data for quick  search and update. update. Thi" i" (u"t an intro!uction intro!uction #uch like giving #eaning to our #ain toic. Thi" Thi" i" followe! followe! $% the overview of two well-known !ata "tructure u"e! for "toring #o!ifia$le collection na#el%) an arra% an! linke! li"t. *"e an arra% or linke! li"t a" a #o!ifia$le collection to $e a$le to "earch' in"ert an! re#ove an ele#ent Before an%thing el"e the "ource ha! a co#ari"on a#ong"t the two well-known !ata "tructure together with the $inar% "earch tree. +e will co#ute the running ti#e for the"e oeration") "earching' in"erting' an! re#oval of recor!" of the two. Starting off with the arra%' how integer" will $e "tore! in it i" "hown. Thi" i" !one $% creating a large enough arra% to "tore the recor!" marking the end of the list  to  to !eter#ine if an in!e& "till contain" a recor! an! "o a" to "a% that tho"e after the #ark are availa$le "ace or e#t% in!e&e". ,or e&a#le' if we have in!e&  #arke! a" the en! then that #ean" we have / recor!" 0of cour"e 1 i" inclu!e!. To "earch let "a% varia$le 3 x   x 4 in the recor!" we have to "can the arra% fro# in!e& 1 u to the #arke! en!' if what we are "earching for unfortunatel% i" in the en! a" to what I un!er"too! fro# the vi!eo i" that we nee! to look through all the ele#ent" in the arra%. So let 3 n4 $e the nu#$er of ele#ent" we have in our arra% therefore the running ti#e of an arra% for the oeration of "earching will $e roortional to the nu#$er of ele#ent" 3n 3 n4 in it. The larger the arra% the higher the ti#e it will con"u#e to "earch for a given x  given x . The "ource !enote! thi" a" Search(ŋ)= o(ŋ) 5ur reviou"l% reviou"l% !one #arker en! will $e ver% vital in the roce"" of in"erting in"erting a new recor! to the arra%) a" "tate! a$ove tho"e in!e& that follow" the #aker en! are all availa$le "ace. Thi" i" where we will $e a!!ing the new recor!' thi" i" !one $% incre#enting the #arker en!. After incre#enting we can now a!! the new recor! which i" an integer in the ca"e "hown in the "ource vi!eo. ,or thi" oeration 0which i" in"erting ti#e taken will not !een! on the nu#$er of ele#ent" in"tea! it i" con"tant. It can $e !enote! a" Insert(ŋ)= Insert(ŋ)= o(1)

The ne&t oeration !eleting i" uite a crucial one. Sa% for e&a#le we want to re#ove the recor! in in!e& 7' in or!er to !o that we4ll have to "hift all recor!" to the right of in!e& 7 one in!e& to the left. 8a"tl% we will !ecre#ent our #arker en! thu" re"ulting to a running oeration of Remove(ŋ)= o(ŋ). Moving forwar! to linke! li"t thi" !ata "tructure runs almost the same as an array  therefore the running ti#e of the oeration "earch i" al"o Search(ŋ)= o(ŋ) $ut in thi" ca"e we are ertaining to nu#$er of no!e" in the linke! li"t. In or!er to "earch we will have to traver"e all the recor!" of the whole li"t "a#e a" to an arra% we #a% nee! to look through all the no!e" in the linke! li"t. +hile the co"t of in"ertion in a linke! li"t ha" two roce"" either Insertion(ŋ)= o(1) if it4" at the hea! or Insertion(ŋ)= o(ŋ) at the tail. It i" a!vi"e! to in"ert at the hea! to kee the running co"t low an! con"tant. In the roce"" of re#oval we #a% have to traver"e the linke! li"t an! "earch the recor! checking at all the no!e" Remove(ŋ)= o(ŋ). +e #a% think of the"e two a" a "uita$le !ata "tructure for "earching' in"erting an! re#oving. Even #e I  woul! think of u"ing it $ut after watching the fir"t 9 #inute" of the "ource vi!eo I !ou$t if %ou "till have %our initial oinion regar!ing thi". It ha" $een clearl% "tate! that in realit% any of the two is not a practical method to use although in"ertion $etween the# i" fa"t. 5ne oint that we #a% not have notice! i" that the"e #a% con"u#e a relativel% large a#ount of ti#e if we have large collection of recor!". :ow a$out a recor! for a $aranga% with 111 fa#ilie" #o"t of the# con"i"ting of 7 #e#$er" gaining a total of 7111 in!ivi!ual recor!"; If we will go for an e"ti#ate!  "econ! er "earch then we will en! u con"u#ing 7111 "econ!" "earching for that certain x .
three oeration" in lowe"t value o""i$le that i" o(logŋ) for average ca"e" an! will hit a" low a" o(ŋ) for it" wor"t ca"e". 5f cour"e we can a" #uch a" o""i$le avoi! wor"t ca"e "cenario" $% #aking "ure that the tree i" alwa%" $alance!. Moving on let4" tackle fir"t how co"t of $inar% "earch tree oeration" are #ini#ize!. B% !efinition' $inar% "earch tree i" a $inar% tree in which for each no!e' value of all the no!e" in left "u$ tree i" le""er or eual 0to han!le !ulicate" an! value of all the no!e" in right "u$ tree i" greater. In $inar% tree each no!e can have at #o"t two chil!ren. The "ource vi!eo illu"trate! $inar% "earch tree a" a circle on to $ranching out to two #ore circle" 0one on the left an! one on the right which in return al"o $ranche" out into two #ore circle". The illu"tration ha" the !ata t%e of integer with nu#$er 9 lace! on the to#o"t circle. To check if the illu"tration i" correct we !ivi!e the tree into two) left an! right after that we check if all the value" of the circle on the left "i!e i" lower or eual" the value on the to#o"t of the tree 0in our ca"e it4" 9. The value" on the right "i!e i" a" follow") 1'  an! 2 the"e are le"" than 9 "o the left "i!e of the tree i" correct. Ne&t i" the "a#e a" the left "i!e $ut thi" ti#e we have to #ake "ure that the value" in right "i!e are alwa%" greater than 9. The illu"tration contain" 21' = an! 29 o$viou"l% the"e are greater than 9 "o the right "i!e of the tree i" al"o correct. B% the wa% the "ource vi!eo "tate" that the to#o"t value 09 in our illu"tration i" calle! the root. :ow i" it reall% o""i$le for $inar% "earch tree to have a co"t of running a" o(logŋ) for "earching' in"erting an! !eleting; ,ir"t let4" !i"cu"" "earch' thi" oerate" $% co#aring what %ou are "earching for with the root. 8et4" u"e the reviou" illu"tration for thi". I woul! like for u" to tr% an! "earch for 2 "o co#aring 2 to 9 it i" le""er in thi" ca"e we will continue "earching for 2 on the left "u$ tree "ince we4ve known that left "u$ tree contain value" le""er than the root. The a!vantage of thi" i" that we can re!uce the ele#ent" we nee! to "earch through a" we are #oving to the ne&t "te" #aking it a lot fa"ter. The ne&t root i" 1 "o !o the "a#e "te" again' 2 i" greater than 1 rocee! the "earch to right "u$ tree we have root 2 in there an! it" eual to what we are "earching for "o the "earch en!". +e can e&erience the wor"t ca"e if the tree i" un$alance! hence re!ucing onl% one ele#ent" fro# the "earch "ace. It onl% work" a" if it i" "o#ewhat a linke! li"t "o we e&erience #uch "lower "earching. The "a#e goe" for in"erting a new recor! to the $inar% tree' we "tart off co#aring the root to the value we will a!!. If it i" greater then rocee! to right el"e rocee! to left "u$ tree. If there i" "till a chil! continue co#aring until %ou reache! where it "houl! $e a!!e! lace it a" a chil! either to the left or to the right. 8a"tl% for the !eletion it i" #uch like "earching with  (u"t a little $it of a!(u"t#ent of no!e" or link". !ata "tructure" that can $e u"e! for "earching' in"erting an! !eleting recor!") an arra%' linke! li"t an! $inar% "earch tree. It i" a!vi"a$le to u"e $inar% "earch tree a#ong the# $ecau"e it ha" lower co"t of running oeration". Binar% "earch tree encounter" wor"t ca"e wherein the co"t of running oeration" ro"e to a higher level an! to avoi! thi" we "houl! make sure that the tree is always

balanced . In"erting an! !eleting recor!" cau"e" $inar% "earch tree to $e un$alance! all we have to !o i" to restore the balancing.