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Binary Tree to Binary Search Tree Conversion - GeeksforGeeks

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Rishikesh Agrawani
Rishikesh Agrawani

The document describes a 3-step algorithm to convert a binary tree to a binary search tree while maintaining the original structure of the binary tree. The steps are: 1) Perform an inorder traversal of the binary tree and store the node values in an array. This takes O(n) time. 2) Sort the array. This takes O(nlogn) time using an efficient sorting algorithm like merge sort. 3) Perform another inorder traversal of the binary tree and replace each node's value with the corresponding value from the sorted array. This again takes O(n) time.

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2/29/2016 Binary?Tree?to?Binary?Search?Tree?Conversion???GeeksforGeeks http://www.geeksforgeeks.org/binary?tree?to?binary?search?tree?conversion/ 1/13 CA ?GATE?CS ?Practice ?Suggest ?IDE ?Q&A GeeksQuiz GeeksforGeeks? A?computer?science?portal?for?geeks Binary?Tree?to?Binary?Search?Tree?Conversion Given? a? Binary?Tree,? convert? it? to? a? Binary? Search?Tree.?The? conversion? must? be? done? in? such? a? way? that keeps?the?original?structure?of?Binary?Tree. Examples. Solution
2/29/2016 Binary?Tree?to?Binary?Search?Tree?Conversion???GeeksforGeeks http://www.geeksforgeeks.org/binary?tree?to?binary?search?tree?conversion/ 2/13 Following?is?a?3?step?solution?for?converting?Binary?tree?to?Binary?Search?Tree.? 1)?Create?a?temp?array?arr[]?that?stores?inorder?traversal?of?the?tree.?This?step?takes?O(n)?time.? 2)?Sort?the?temp?array?arr[].?Time?complexity?of?this?step?depends?upon?the?sorting?algorithm.?In?the?following implementation,?Quick?Sort?is?used?which?takes?(n^2)?time.?This?can?be?done?in?O(nLogn)?time?using?Heap?Sort or?Merge?Sort. 3)?Again?do?inorder?traversal?of?tree?and?copy?array?elements?to?tree?nodes?one?by?one.?This?step?takes?O(n) time. Following? is? C? implementation? of? the? above? approach.? The? main? function? to? convert? is? highlighted? in? the following?code. struct int struct struct void struct int int if return int struct if return return int const void const void return int int void int struct int
2/29/2016 Binary?Tree?to?Binary?Search?Tree?Conversion???GeeksforGeeks http://www.geeksforgeeks.org/binary?tree?to?binary?search?tree?conversion/ 3/13 void int struct int if return void struct if return int int new int int qsort sizeof delete struct int struct new struct return void struct if return printf
2/29/2016 Binary?Tree?to?Binary?Search?Tree?Conversion???GeeksforGeeks http://www.geeksforgeeks.org/binary?tree?to?binary?search?tree?conversion/ 4/13 Output: We? will? be? covering? another? method? for? this? problem? which? converts? the? tree? using? O(height? of? tree)? extra space. Please?write?comments?if?you?find?anything?incorrect,?or?you?want?to?share?more?information?about?the?topic discussed?above 42?Comments ?Category:? Binary?Search?Tree Related?Posts: Count?inversions?in?an?array?|?Set?2?(Using?Self?Balancing?BST) Print?Common?Nodes?in?Two?Binary?Search?Trees Construct?all?possible?BSTs?for?keys?1?to?N K¨th?smallest?element?in?BST?using?O(1)?Extra?Space Run?on?IDE int struct printf return
2/29/2016 Binary?Tree?to?Binary?Search?Tree?Conversion???GeeksforGeeks http://www.geeksforgeeks.org/binary?tree?to?binary?search?tree?conversion/ 5/13 Count?BST?subtrees?that?lie?in?given?range Count?BST?nodes?that?lie?in?a?given?range Data?Structure?for?a?single?resource?reservations How?to?handle?duplicates?in?Binary?Search?Tree? (Login?to?Rate?and?Mark) 2.8 ? Average?Difficulty?:?2.8/5.0? Based?on?6?vote(s) ? ? ?Add?to?TODO?List ? ?Mark?as?DONE ? Writing?code?in?comment??Please?use?code.geeksforgeeks.org,?generate?link?and?share?the?link?here. 42?Comments GeeksforGeeks ?Login]1 ?Share? Sort?by?Newest Join?the?discussion´ ? Reply ? He?Man? ? ?6?months?ago One?solution?that?does?not?use?any?extra?space?is?: Perform?standard?preorder?traversal?of?the?given?Binary?Tree.?Instead?of?printing?the?value in?preorder,?just?call?insert()?function?of?binary?search?tree. BT_2_BST(root) if(root!=NULL) 1.)*root_BST?=?insert(root_BST,root?>data)??//http://geeksquiz.com/binary?se... 2.)?preorder(root?>left)? 3.)?preorder(root?>right)? ?＠ ? ? Reply ? holdnet? ? ? ?2?months?ago>?He?Man In?your?solution?original?structure?of?the?tree?will?not?be?maintained. ?＠ ? He?Man? ? ? ?2?months?ago>?holdnet You?are?right...Actually..?I'm?trying?to?convert?the?existing?tree?to?a?BST ?Recommend? Share?? Share?? 3?people?like?this.?Sign?Up?to?see?what?your?friends?like.Like Share
2/29/2016 Binary?Tree?to?Binary?Search?Tree?Conversion???GeeksforGeeks http://www.geeksforgeeks.org/binary?tree?to?binary?search?tree?conversion/ 6/13 ? Reply ? You?are?right...Actually..?I'm?trying?to?convert?the?existing?tree?to?a?BST without?allocating?separate?space?for?resulting?BST. ?＠ ? ? Reply ? Bewkoof_coder? ? ?8?months?ago see?more first?call?the?below?function?with?a=1,where?i?will?gives?the?size?of?array,,which?i?returning by?function,,in?second?clling?its(?i?)?not?of?any?use.? then?sort?array?A then?again?call?the?below?function?with?a=0? int?BT_to_BST(struct?node?*start,int?*A,int?a){ static?int?i=?1? static?int?k=?1? if(start==NULL) return?i? else{ BT_to_BST(start?>left,A,a)? if(a){ ??1 ＠ ? ? Reply ? Dipankar?Bhardwaj? ? ?8?months?ago http://code.geeksforgeeks.org/... ?＠ ? ? Reply ? vergil? ? ?8?months?ago rather?than?using?two?separate?functions?for?storeInorder?and?arrayToBST?we?can?use either?one?only?and?add?a?boolean?flag?to?coditionally?execute?either? inorder[*index_ptr]?=?node?>data?or?node?>data?=?inorder[*index_ptr] respectively ?＠ ? Yaduvir? ? ?8?months?ago SEE?THIS?CODE #include?<iostream> #define?MAX?100000000 Share?? Share?? Share?? Share??
2/29/2016 Binary?Tree?to?Binary?Search?Tree?Conversion???GeeksforGeeks http://www.geeksforgeeks.org/binary?tree?to?binary?search?tree?conversion/ 7/13 ? Reply ? see?more using?namespace?std? int?size? struct?node { int?data? node?*left? node?*right? }? ?＠ ? ? Reply ? Radhika?Bansal`? ? ?9?months?ago According?to?me?the?minimum?time?complexity?for?this?problem?is?O(n)?because?at?least once?we?are?to?traverse?every?node. ?＠ ? ? Reply ? Monica?Shankar? ? ? ?7?months?ago>?Radhika?Bansal` the?minimum?complexity?for?sorting?is?O(nlgn)?which?is?greater?than?O(n) ?＠ ? ? Reply ? Guest? ? ?a?year?ago traverse?the?given?tree?in?postorder,?delete?every?node?&?re?insert?it?into?a?new?BST.?This is?O(n+n*log(n)),?which?is?O(n*log(n)). ?＠ ? ? Reply ? prashant?saxena? ? ? ?a?year?ago>?Guest This?may?not?create?same?spatial?arrangement?of?nodes. ??1 ＠ ? ? Reply ? ffff? ? ?a?year?ago this?algo?doesn't?work?in?java?implementation ?＠ ? ? Reply ? prashant?saxena? ? ? ?a?year?ago>?ffff Then?your?implementation?might?me?wrong.?I?don't?see?any?issue?with?the?algo. May?be?you?might?want?to?share?your?implementation?on?this?forum. ?＠ ? Share?? Share?? Share?? Share?? Share?? Share?? Share??
2/29/2016 Binary?Tree?to?Binary?Search?Tree?Conversion???GeeksforGeeks http://www.geeksforgeeks.org/binary?tree?to?binary?search?tree?conversion/ 8/13 ? Reply ? spm? ? ?a?year?ago see?more My?logic?is?: 1.First?do?inorder?traversal?of?the?given?tree?and?store?the?keys?in?an?array(Yes?this?algo uses?auxilliary?space?:(?). 2.Sort?the?keys?of?the?tree.<used?bubble=""?sort=""?here=""?but=""?that=""?is=""?just="" to=""?verify=""?correctness=""?of=""?algo,should=""?be=""?using=""?quicksort=""> 3.Do?the?inorder?traversal?of?the?given?tree?and?replace?the?node's?data?values?with?the sorted?values,this?ensures?that?its?a?BST?as?well?as?the?fact?that?it?has?the?same?structure as?given?tree. Please?let?me?know?if?this?is?a?good?way. /* Binary?Tree?to?BST?Conversion http://www.geeksforgeeks.org/b... */ #include<stdio.h> #include<stdlib.h> ?＠ ? ? Reply ? spm? ? ? ?a?year?ago>?spm Sorry?for?writing?the?code?there?itself Refer?http://ideone.com/65vj80?for?code ?＠ ? indian.samurai? ? ?2?years?ago Create?a?inorder?array?which?has?another?column?containing?the?number?of?child?for?that index.?In?above?example?it?will?be: inorder?[0][]?=?8?2?4?10?7 inorder?[1][]?=?0?2?0?4?0 Now?sort?the?first?column?without?changing?the?values?for?second,?this?will?become inorder?[0][]?=?2?4?7?8?10 inorder?[1][]?=?0?2?0?4?0 Build?a?tree?using?this.?index?with?maximum?children?count?will?be?root.?Next?Max?on?its?left its?left?child?and?on?right?..?right?child.?Do?this?recursively. 8 /? Share?? Share??
2/29/2016 Binary?Tree?to?Binary?Search?Tree?Conversion???GeeksforGeeks http://www.geeksforgeeks.org/binary?tree?to?binary?search?tree?conversion/ 9/13 ? Reply ? /? 4?10 /? 2?7 ??1 ＠ ? ? Reply ? Rahul? ? ?2?years?ago Following?is?the?constant?space?and?O(n2)?solution http://pastebin.com/FV5hg3H2 ?＠ ? ? Reply ? Jun? ? ?2?years?ago http://ideone.com/3JSsCy ?＠ ? ? Reply ? GS? ? ?2?years?ago Think?If?we?need?to?do?this?without?extra?space?:) I?can?think?of?an?O(n^2)?algo if?some?one?can?think?better?let?us?know ?＠ ? ? Reply ? GS? ? ? ?2?years?ago>?GS convert?to?DLL?then?sort?then?convert?to?bst?nlogn ??4 ＠ ? ? Reply ? DS+Algo? ? ? ?2?years?ago>?GS We?need?to?retain?original?structure,?man ??3 ＠ ? ? Reply ? Palak?Jain? ? ? ?2?years?ago>?GS This?soln?won't?maintain?the?original?structure?of?binary?tree!! ?＠ ? ? Reply ? ganesh? ? ?2?years?ago In?c?we?cant?create?dynamic?array?using?new?operator?right??? ?＠ ? ? Reply ? np? ? ? ?2?years?ago>?ganesh correct!!!?but?if?you?are?using?c++?environment?to?write?c?code?new?operator?will?be supported ??1 ＠ ? RACHIT?SAXENA? ? ?2?years?ago Share?? Share?? Share?? Share?? Share?? Share?? Share?? Share?? Share??
2/29/2016 Binary?Tree?to?Binary?Search?Tree?Conversion???GeeksforGeeks http://www.geeksforgeeks.org/binary?tree?to?binary?search?tree?conversion/ 10/13 ? Reply ? RACHIT?SAXENA? ? ?2?years?ago what?about?O(log?n)?space?compexity?solution ??? ?＠ ? ? Reply ? Vikas?Rajoria? ? ?2?years?ago How?is?quick?sort?having?n^2?complexity,?by?all?practical?needs?it?yields?nlogn?.?n^2?is worst?case?for?quick?sort,?we?hardly?run?into?such?cases. ??3 ＠ ? ? Reply ? Sudarshan?Kj? ? ?2?years?ago what?is?the?use?of?compare?fuction?there? anyone?pls?tell?me ?＠ ? ? Reply ? Harry? ? ? ?2?years?ago>?Sudarshan?Kj It?used?by?the?c?function?"qsort",?refer?to?http://www.cplusplus.com/refer... ?＠ ? ? Reply ? Vivek? ? ?2?years?ago see?more O(n^2)?with?space?O(1) #include<stdio.h> #include<stdlib.h> int ?＠ ? vibhor? ? ? ?2?years?ago>?Vivek Why?do?u?say?its?complexity?is?O(n^2)?it?is?O(n)?only ＠ Share?? Share?? Share?? Share?? Share??
2/29/2016 Binary?Tree?to?Binary?Search?Tree?Conversion???GeeksforGeeks http://www.geeksforgeeks.org/binary?tree?to?binary?search?tree?conversion/ 11/13 ? Reply ??＠ ? ? Reply ? Deepanshu?Arora? ? ? ?2?years?ago>?Vivek It?will?be?really?helpful?if?you?would?add?a?documentation?to?your?solution ?＠ ? ? Reply ? Guest? ? ? ?2?years?ago>?Deepanshu?Arora why?do?u?say?that?its?complexity?is?n^2?it?is?O(n)?only ?＠ ? ? Reply ? Vinodhini? ? ?2?years?ago could?you?guys?post?the?O(height?of?tree)?solution? ?＠ ? ? Reply ? Amit?Bgl? ? ?3?years?ago wow?code?:D ?＠ ? ? Reply ? abhishek08aug? ? ?3?years?ago Intelligent?:D ?＠ ? ? Reply ? prakash_ntk? ? ?3?years?ago see?more //Here?is?a?solution?for?converting?a?Binary?tree?to?BST?without?//using?extra?space.time?comple int return int int ??2 ＠ ? Share?? Share?? Share?? Share?? Share?? Share?? Share??
2/29/2016 Binary?Tree?to?Binary?Search?Tree?Conversion???GeeksforGeeks http://www.geeksforgeeks.org/binary?tree?to?binary?search?tree?conversion/ 12/13 ? Reply ???2 ＠ ? ? Reply ? algobard? ? ?4?years?ago Can?you?guys?please?post?the?approach?which?uses?O(ht.)?space? ?＠ ? ? Reply ? Arun? ? ?4?years?ago do no times ?＠ ? ? Reply ? Dipanjan? ? ? ?4?years?ago>?Arun ?＠ ? ? Reply ? Pramod? ? ?4?years?ago see?more import /**? ?*?Given?a?Binary?Tree,?convert?it?to?a?Binary?Search?Tree.?The?conversion?must? ?*?be?done?in?such?a?way?that?keeps?the?original?structure?of?Binary?Tree.? ?*?? ?*?@author?ppatil? ?*?? ?*?Example?1? Input:? ??????????10? ?????????/??? ????????2????7? ???????/?? ??????8???4? Output:? ??????????8? ?????????/??? ????????4????10? ?＠ ? Venki? ? ?4?years?ago I?guess?we?can?use?modified?head?sort?method.?Use?an?explicit?pointer?to?point?next?slot?in the?inorder?traversal,?fill?it?from?the?top?of?heap.?Algorithmically, Share?? Share?? Share?? Share?? Share??
2/29/2016 Binary?Tree?to?Binary?Search?Tree?Conversion???GeeksforGeeks http://www.geeksforgeeks.org/binary?tree?to?binary?search?tree?conversion/ 13/13 ? Reply ? the?inorder?traversal,?fill?it?from?the?top?of?heap.?Algorithmically, 1.?Min?heapify?the?binary?tree?(you?need?parent?pointer). 2.?Set?inorder?successor?pointer?to?left?most?element. 3.?Copy?root?to?successor?node. 4.?Move?the?successor?node?to?next?node?in?inorder?traversal. 5.?Heapify?the?binary?tree?(excluding?subtrees?of?inorder?successor,?little?trick?needed here). 6.?Repeat?3?to?5?till?all?nodes?are?placed. Binary?tree?is?nothing?but?random?shuffle?or?data,?the?any?algorithm?must?atleast?take?O(N log?N)?time. ?＠ ? ? Reply ? Keshava? ? ?4?years?ago Would?it?not?be?better?to?make?the?BST?balanced?while?we?are?at?it? selecting?arr[n/2]?as?root?recursively?would?do?that ?＠ ? Subscribe? Add?Disqus?to?your?site?Add?Disqus?Addd Privacy? Share?? Share?? @geeksforgeeks,?Some?rights?reserved????????Contact?Us!????????About?Us!???????????????Advertise?with?us!???????

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