It is about advanced tree

1. Prepared by:- Suraksha Sanghavi

2. • Invented in 1970s by Jon Bentley
• It is a binary tree
• K-tree is also known as KD tree
(k-diamensional)
Where D=1,2,3……
• But we have in study is 2D Tree
• Each level has a “cutting
dimension”
• Each node contains a point
P = (x,y)

3. Complexity
Insert:
Average and balanced trees: O(log N)
Worst case: O(N)
Print:
Range query: for M matches Perfectly
balanced tree:
K-D trees: O(M + kN (1-1/k) )
2-D trees: O(M + N)

4. • Its left side with space known as left
subtree
• Its right side with points known as right
subtree
• Its first node is root (Grand parent)
• While inserting its child (parent) it checks
with x-cordinate
• While inserting next node at next level it
checks with y-co-dinate

5. • It is reprsenting in two way
• 1)Tree 2)Graph
• 0 level - x-alinged (vertical line)-compare with
x-co-ordinate.
• 1-level – y-alinged (horizontal line –it depend
on child on which side) – compare with y-co-
ordinate.
• 2-level – x-alinged-compare x-cordinate.
• 3-level – y alinged-compare y –corinate.

7. 1.Nearest neighbour Search
2.Database Queries