Presentation is loading. Please wait.

Presentation is loading. Please wait.

K-d tree k-dimensional indexing. Jaruloj Chongstitvatana k-d trees 2 Definition Let k be a positive integer. Let t be a k -d tree, with a root node p.

Published byAlison Lewis Modified over 9 years ago

Similar presentations

Presentation on theme: "K-d tree k-dimensional indexing. Jaruloj Chongstitvatana k-d trees 2 Definition Let k be a positive integer. Let t be a k -d tree, with a root node p."— Presentation transcript:

1 k-d tree k-dimensional indexing

2 Jaruloj Chongstitvatana k-d trees 2 Definition Let k be a positive integer. Let t be a k -d tree, with a root node p. Then, for any node n in t : The key j,j+1, …, j-1 of any node q in the left subtree of n is smaller than that of node p, The key j,j+1, …, j-1 of any node q in the right subtree of n is larger than that of node p.

3 Jaruloj Chongstitvatana k-d trees 3 Example 20,31 36,10 31,40 15,15 40,36 6,6 25,16

4 Jaruloj Chongstitvatana k-d trees 4 Insertion 20,31 36,10 31,40 15,15 40,36 6,6 25,16

5 Jaruloj Chongstitvatana k-d trees 5 Exact Search 20,31 36,10 31,40 15,15 40,36 6,6 25,16 (40, 36)

6 Jaruloj Chongstitvatana k-d trees 6 Range search 20,31 36,10 31,40 15,15 40,36 6,6 25,16

7 Jaruloj Chongstitvatana k-d trees 7 Deletion 20,31 36,10 38,40 15,15 40,36 32,16 28,5 45,8 Delete the blue pointCopy the pink point up

8 Jaruloj Chongstitvatana k-d trees 8 Deletion 36,10 38,40 15,15 40,36 32,1645,8 Delete the old pink point 28,5

Download ppt "K-d tree k-dimensional indexing. Jaruloj Chongstitvatana k-d trees 2 Definition Let k be a positive integer. Let t be a k -d tree, with a root node p."

Similar presentations

Info 3.3. Chapter 3.3 Recursive Data Structures Part 2 : Binary Trees.

Info 3.3. Chapter 3.3 Recursive Data Structures Part 2 : Binary Trees.
AVL Trees1 Part-F2 AVL Trees 6 3 8 4 v z. AVL Trees2 AVL Tree Definition (§ 9.2) AVL trees are balanced. An AVL Tree is a binary search tree such that.

AVL Trees1 Part-F2 AVL Trees v z. AVL Trees2 AVL Tree Definition (§ 9.2) AVL trees are balanced. An AVL Tree is a binary search tree such that.
Solution of Assignment 3 and Midterm CSC2100B. AVL Tree A binary search tree is a binary tree in which every node has larger key than the nodes in its.

Solution of Assignment 3 and Midterm CSC2100B. AVL Tree A binary search tree is a binary tree in which every node has larger key than the nodes in its.
S. Sudarshan Based partly on material from Fawzi Emad & Chau-Wen Tseng

S. Sudarshan Based partly on material from Fawzi Emad & Chau-Wen Tseng
1 Pertemuan 12 Binary Search Tree Matakuliah: T0026/Struktur Data Tahun: 2005 Versi: 1/1.

1 Pertemuan 12 Binary Search Tree Matakuliah: T0026/Struktur Data Tahun: 2005 Versi: 1/1.
Binary Search Trees Definition Of Binary Search Tree A binary tree. Each node has a (key, value) pair. For every node x, all keys in the left subtree.

Binary Search Trees Definition Of Binary Search Tree A binary tree. Each node has a (key, value) pair. For every node x, all keys in the left subtree.
AVL Trees Balanced Trees. AVL Tree Property A Binary search tree is an AVL tree if : –the height of the left subtree and the height of the right subtree.

AVL Trees Balanced Trees. AVL Tree Property A Binary search tree is an AVL tree if : –the height of the left subtree and the height of the right subtree.
C++ Programming:. Program Design Including

C++ Programming:. Program Design Including
A Binary Tree root leaf. A Binary Tree root leaf descendent of root parent of leaf.

A Binary Tree root leaf. A Binary Tree root leaf descendent of root parent of leaf.
1 Trees. 2 Outline –Tree Structures –Tree Node Level and Path Length –Binary Tree Definition –Binary Tree Nodes –Binary Search Trees.

1 Trees. 2 Outline –Tree Structures –Tree Node Level and Path Length –Binary Tree Definition –Binary Tree Nodes –Binary Search Trees.
Binary Search Trees Dictionary Operations:  IsEmpty()  Search(key)  Insert(key, value)  Delete(key)

Binary Search Trees Dictionary Operations:  IsEmpty()  Search(key)  Insert(key, value)  Delete(key)
Insert 2000 0 1 1 0 0 1 0 0 0 A tree starts with the dummy node D 0 0 0 0 0 0 0 0 0 0 D 200 D 7 Insert 1000 0 0 1 1 0 0 1 0 0 100 D 6 200 7.

Insert A tree starts with the dummy node D D 200 D 7 Insert D
AVL trees. AVL Trees We have seen that all operations depend on the depth of the tree. We don’t want trees with nodes which have large height This can.

AVL trees. AVL Trees We have seen that all operations depend on the depth of the tree. We don’t want trees with nodes which have large height This can.
AVL Trees1 6 3 8 4 v z. 2 AVL Tree Definition AVL trees are balanced. An AVL Tree is a binary search tree such that for every internal node v of T, the.

AVL Trees v z. 2 AVL Tree Definition AVL trees are balanced. An AVL Tree is a binary search tree such that for every internal node v of T, the.
1 Section 9.2 Tree Applications. 2 Binary Search Trees Goal is implementation of an efficient searching algorithm Binary Search Tree: –binary tree in.

1 Section 9.2 Tree Applications. 2 Binary Search Trees Goal is implementation of an efficient searching algorithm Binary Search Tree: –binary tree in.
B-Trees (continued) Analysis of worst-case and average number of disk accesses for an insert. Delete and analysis. Structure for B-tree node.

B-Trees (continued) Analysis of worst-case and average number of disk accesses for an insert. Delete and analysis. Structure for B-tree node.
AVL Trees / Slide 1 Deletion  To delete a key target, we find it at a leaf x, and remove it. * Two situations to worry about: (1) target is a key in some.

AVL Trees / Slide 1 Deletion  To delete a key target, we find it at a leaf x, and remove it. * Two situations to worry about: (1) target is a key in some.
Binary Search Trees CSE, POSTECH. Search Trees Search trees are ideal for implementing dictionaries – Similar or better performance than skip lists and.

Binary Search Trees CSE, POSTECH. Search Trees Search trees are ideal for implementing dictionaries – Similar or better performance than skip lists and.
K-d tree k-dimensional indexing. Jaruloj Chongstitvatana k-d trees 2 Definition Let k be a positive integer. Let t be a k -d tree, with a root node p.

K-d tree k-dimensional indexing. Jaruloj Chongstitvatana k-d trees 2 Definition Let k be a positive integer. Let t be a k -d tree, with a root node p.
Min Chen School of Computer Science and Engineering Seoul National University Data Structure: Chapter 7.

Min Chen School of Computer Science and Engineering Seoul National University Data Structure: Chapter 7.

Similar presentations

Ads by Google