Question

From the following numbers...

Please follow steps 1-3 for these integers ~ 14,40,26,32 ,12,45,28,9,8,16

remove the numbers below individual which show the fusions and correction of them

~ 26, 9, 16

1. Make a 2-3 Tree so that... (all steps and the removal  

2. You can make a 2-3-4 Tree (all steps and the removal  

3.so finally you can make Red-Black Tree (showing red and black lines for the node that are red/black)(all steps and the removal  

Do Not Use Tree Calculator it should SHOW ALL STEPS FOR ALL OF THEM I will share and upvote, THANKS!

Answer 1

ANSWER m Given numbeu 14 ,40, 26, 32 , 12 , 45, 28, 9, aue 8, 16 Step 1 Make 2-3 Taee intich thee data stnctmu 2-3 Tree M- laf node) has non every nleunal node data element and tusv Childun dA either tuv data element and thuee childen going to mseut the values iuto Inikaly empty , we aue 2-3 Thee. Since es empty neus a to be nuU eu initial Aevf noe goring to be ieated -fe it value w mseit 14 So the first aquirs new node a Insent o :-As 1 hawe a Alot available in thi Leaf node just add it to the nde Tncit 26 Node is fuu , add 26 ond split it oveflas 40 4 26 26 Heue 26 240 K2 14 40

32 Value goes to child as ght Tnest 32 22 26 hue chan auadingly becaur 3 2 L4o Tnent 12 as 2 26 26 3240 14 12 clild sight Trseut 45 So to 2645 26 45je eveflns C.So Split it) 2 2040 45 32 2 4

2S Insut ni ddle child 26|4ロ 2832 214 45 Frseut cua tana left child 26 40 apit it) 28 32 45 aain oiflaro at top node am 28 32 Csplit it) .C 12 293245 4 child eft-eft Pnsest 8 2.6> & 2 > 8 26 2. 45 2&|31

Tngeot 26 So it gees child eft -ight 451 4 6232 final 2-3 Tree 26,9, 16 need to amove Non Le Rigiut subtree gorna jemain same Left Subtree is uftsubtoee Aeplaes 26 Yemove change to Largest value 26 4 5 23 2 14 By Aemovin ' thue wiu no overfhons reimove 'undu flovo 40 45 2832

Right subtre qowna Aeman same 6ft Subtree gmna change laiest ft subtree replie 6 vaine [4 40 2832 45 undeflow No oft Subtree is in 2 and 8 need to 45 2832 wwged leht child and Aovt shonld be Non undeuflors as 14| 40 2832 2 Final Thce ale deletion

Stp 2: 2-3-4 Tre - A 2-node has inteinal data element and h one has tw child nodes A -node hau tuo data eiements , and if Lnteinal has thee chi ld nodes has thiee dat elements ntaunat has -fon child nods and / Tnut 4 14 Tnsent 4 440 Inseut 26 49640 44b26 Twseut 32: 32 26 l426 40 324D

Tneat 12 32 14 Busut 4S 20 45 1214 32 Tnseut 28 24 26 2 3240 5 (ovesfla) 14 40 45 28 121 1니 Ssput 26 32 40145 28 12 14 Inseut 2432 4045 28

2632 41214 28 pweuf low split 26/32 4045 28 12 14 Tnseut 6 92632 401451 28 2 1416 final Tree qamd 26 is Delet 26: ubtree between Choosen becaue left Laugest value ie, it wiu be Subtree 26 ioiheplace 2G 3 2 1214 4045 28

delete deteti (4) hen Maplace undeyflono mallestvalu d iyht Subtree Huis Condsti on ondi tu Aeplaiad y wil be | 6 32. 445 28 oplaced y 14. T underflano Theasfehe Will Le delete 16 16 again leads to ement tu data as it soes the undeufh prdem 124 32 40 4 5 3 2 4 t0 45 28 with dalation final 1-3-4 Tree

Ved -Bla ck Stap Tree /C A node 2 The ot and leaves (NIL) are black node i^^ed -hm i childsen are black 3. Df a a node to descendants it NIL paths form 4 AU black nodeu Contam the Same no black Tnseut 4 Aed 40 nseut 24 40 26 ingle rotato (4D

Pnset 32 3 2 26 E14 3 2 32 net 2 26

Tuset 45 (1D 45 3 2 Tnnt 28 26. 45 28 28 Singe 28 28

push Llack |2 45 28 28 Tnseut l6 26 4 45 14 Rad Black Tree inal

tHighest valu in oplaces Deliti 2 &ubtree 26 40 45 28 Delet and make g as black Deleti 9 28

Delit 16 Replace and 6with lagest valu ic, 14 make 12 4 40 45 22 28 fnal Rad Black Tiee after deletion