Preorder Traversal. Binary Tree Traversal Methods. Binary Tree Traversal Methods. Binary Tree Traversal Methods

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1 Binry Tr Trvrsl Mthos Mny inry tr oprtions r on y prorming trvrsl o th inry tr. Possil Binry Tr Oprtions: Dtrmin th hight. Dtrmin th numr o nos. Mk lon. Evlut th rithmti xprssion rprsnt y inry tr. Binry Tr Trvrsl Mthos In trvrsl o inry tr, h lmnt o th inry tr is visit xtly on. During th visit o n lmnt, ll tion (mk lon, isply, vlut th oprtor, t.) with rspt to this lmnt is tkn. Binry Tr Trvrsl Mthos Prorr Inorr Postorr Lvl orr Prorr Trvrsl tmplt <lss T> voi PrOrr(TrNo<T> *t) i (t!= NULL) Visit(t); PrOrr(t->ltChil); PrOrr(t->rightChil);

2 Prorr Exmpl (Visit = print) Prorr Exmpl (Visit = print) ghi Prorr O Exprssion Tr / * - ( ) * ( ) / ( ) / *- Givs prix orm o xprssion! Mrits O Binry Tr Form Lt n right oprns r sy to visuliz. Co optimiztion lgorithms work with th inry tr orm o n xprssion. Simpl rursiv vlution o xprssion. / * -

3 Inorr Trvrsl tmplt <lss T> voi InOrr(TrNo<T> *t) i (t!= NULL) InOrr(t->ltChil); Visit(t); InOrr(t->rightChil); Inorr Exmpl (Visit = print) Inorr Exmpl (Visit = print) Inorr By Protion (Squishing) ghi g h i

4 Inorr O Exprssion Tr * - * - / Givs inix orm o xprssion (without prnthss)! / Postorr Trvrsl tmplt <lss T> voi PostOrr(TrNo<T> *t) i (t!= NULL) PostOrr(t->ltChil); PostOrr(t->rightChil); Visit(t); Postorr Exmpl (Visit = print) Postorr Exmpl (Visit = print) ghi

5 Postorr O Exprssion Tr / Trvrsl Applitions * - Mk lon. - * / Dtrmin hight. Givs postix orm o xprssion! Dtrmin numr o nos. Lvl Orr Lvl-Orr Exmpl (Visit = print) Lt t th tr root. whil (t!= NULL) visit t n put its hilrn on FIFO quu; i FIFO quu is mpty, st t = NULL; othrwis, pop no rom th FIFO quu n ll it t; ghi

6 Binry Tr Constrution Suppos tht th lmnts in inry tr r istint. Cn you onstrut th inry tr rom whih givn trvrsl squn m? Whn trvrsl squn hs mor thn on lmnt, th inry tr is not uniquly in. Thror, th tr rom whih th squn ws otin nnot ronstrut uniquly. prorr = inorr = postorr = lvl orr = Som Exmpls Binry Tr Constrution Cn you onstrut th inry tr, givn two trvrsl squns? Dpns on whih two squns r givn. Prorr An Postorr prorr = postorr = Prorr n postorr o not uniquly in inry tr. Nor o prorr n lvl orr (sm xmpl). Nor o postorr n lvl orr (sm xmpl).

7 Inorr An Prorr inorr = g h i prorr = g h i Sn th prorr lt to right using th inorr to sprt lt n right sutrs. is th root o th tr; ghi r in th lt sutr; r in th right sutr. Inorr An Prorr ghi prorr = g h i is th nxt root; gh r in th lt sutr; i r in th right sutr. ghi gh i Inorr An Prorr gh i prorr = g h i is th nxt root; g is in th lt sutr; h is in th right sutr. Inorr An Prorr gh i prorr = g h i is th nxt root; nothing is in th lt sutr; i is in th right sutr. g h i g h i

8 Inorr An Prorr gh i prorr = g h i is th nxt root; is in th lt sutr; nothing is in th right sutr. g h i Inorr An Postorr Sn postorr rom right to lt using inorr to sprt lt n right sutrs. inorr = g h i postorr = g h i Tr root is ; ghi r in lt sutr; r in right sutr. In Clss Exris Inorr An Lvl Orr Dtrmin th tr inorr = g h i postorr = g h i Sn lvl orr rom lt to right using inorr to sprt lt n right sutrs. inorr = g h i lvl orr = Tr root is ; ghi r in lt sutr; r in right sutr.

9 Homwork S. 5.3 Exris 267 Rmrk: ADT 5.1 is P252

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