A binary tree is Perfect if all internal nodes have two children and all leaves are at same level.

Examples:

  • Family tree

 

 

 

Time Complexity

Space Complexity

 

Average

Worst

Worst

Data Structure 

 Access 
 Search 
 Insertion 
 Deletion 
 Access 
 Search 
 Insertion 
 Deletion 
 

Binary Search Tree

Θ(log(n)) Θ(log(n)) Θ(log(n)) Θ(log(n)) O(n) O(n) O(n) O(n) O(n)

Cartesian Tree

N/A Θ(log(n)) Θ(log(n)) Θ(log(n)) N/A O(n)  O(n)  O(n)  O(n)

B-Tree

Θ(log(n)) Θ(log(n)) Θ(log(n)) Θ(log(n)) O(log(n)) O(log(n)) O(log(n)) O(log(n)) O(n)

Red-Black Tree

Θ(log(n)) Θ(log(n)) Θ(log(n)) Θ(log(n)) O(log(n)) O(log(n)) O(log(n)) O(log(n)) O(n)

Splay Tree

N/A Θ(log(n)) Θ(log(n)) Θ(log(n)) N/A O(log(n)) O(log(n)) O(log(n)) O(n)

AVL Tree

Θ(log(n)) Θ(log(n)) Θ(log(n)) Θ(log(n)) O(log(n)) O(log(n)) O(log(n)) O(log(n)) O(n)

KD Tree

Θ(log(n)) Θ(log(n)) Θ(log(n)) Θ(log(n)) O(n) O(n) O(n) O(n) O(n)