Wata BST mai sauqi na iya raguwa zuwa jerin linki (ayyuka O(n)) idan makallau suka zo a tsarin da aka tsara. Self-balancing BSTs — kamar AVL da red-black trees — suna aiwatar da juyi na nodes a baje jiya/baje don jiyya ajiye tsayi ~log n, wanda yake tabbatar da ayyuka .
Unbalanced (insert 1,2,3,4): Balanced after rotations:
1 2
\ / \
2 1 3
\ \
3 4
height ~ n (BAD) height ~ log n (GOOD)
| AVL tree | red-black tree | |
|---|---|---|
| Tsikitaccen abalanci | tsikitaci (a ma'amalarancewa) | mafi kai a cuci |
| Bincike | mafi sauri (gajere) | a taushi mai yin wajen |
| Insert/delete | juyi mai yawa | juyi kaɗan |
| Mafi kyau don | aikin karantawa mai nauyi | aikin rubuta mai nauyi |
| Aiki | Lokaci |
|---|---|
| search | O(log n) |
| insert | O(log n) |
| delete | O(log n) |
Duka biyu suna kula da abalanci ta hanyar juyi — tsoffin sake girki na O(1) da ke kiyayewa TSK tsari sannan sami rage tsayi.
Bilajjuwar balanced suna taimaka wa taswirori masu odar da saiti a cibiyoyin lissafi na ilimi (misali, Java TreeMap, C++ std::map suna amfani da red-black trees), suna ba da odar bayar da ayyuka na logarithmic.
Su ne amsa lokacin da kake buƙatar tsarin TSK da tabbaci aiki mafi tsanani a gida buguwe na aiki.