Download presentation

Presentation is loading. Please wait.

Published bySammy Yeomans Modified over 3 years ago

2
Alon Efrat Computer Science Department University of Arizona SkipList

3
2 Searching a key in a Sorted linked list Searching an element x cell *p =head ; while (p->next->key next ; return p ; Note: we return the element proceeding either the element containing x, or the smallest element with a key larger than x (if x does not exists) 7142132377185117 -1 1 head find(71)

4
3 inserting a key into a Sorted linked list To insert 35 - p=find(35); CELL *p1 = (CELL *) malloc(sizeof(CELL)); p1->key=35; p1->next = p->next ; p->next = p1 ; 71421 32 377185117 -1 1 head p 35

5
4 deleteing a key from a sorted list To delete 37 - p=find(37); CELL *p1 =p->next; p->next = p1->next ; free(p1); 71421 32 377185117 -1 1 head p p1

6
5 A data structure for maintaing a set of keys in a sorted order --- SKIP LIST Consists of several levels. All keys appear in level 1 Each level is a sorted list. If key x appears in level i, then it also appears in all levels below i 7142132377185117 7137 21 7 37 21 Level 1 Level 2 Level 3 Top -1 -1 -1 1 1 1

7
6 More rules An element in level i points (via down pointer) to the element with the same key in the level below. In each level the keys - 1 and 1 appear. (In our implementation, INT_MIN and INT_MAX Top points to the smallest element in the highest level. 7142132377185117 7137 21 7 37 21 Level 1 Level 2 Level 3 Top -1 -1 -1 1 1 1 next-pointer Down-pointer

8
7 An empty SkipList Level 1 Top -1 1

9
8 Finding an element with key x p=top While(1){ while (p->next->key next; If (p->down == NULL ) return p->next p=p->down ; } Observe that we return x, if exists, or succ(x) if x is not in the SkipList 7142132377185117 7137 21 7 37 21 Level 1 Level 2 Level 3 Top -1 -1 -1 1 1 1 next-pointer down-pointer find(117), find(118)

10
9 Inserting new element X Determine k the number of levels in which x participates (explained later) Do find(x), and insert x to the appropriate places in the lowest k levels. (after the elements at which the search path turns down or terminates) Example - inserting 119. k=2 7142132377185 7137 21 7 37 21 Level 1 Level 2 Level 3 Top -1 -1 -1 1 1 1 next-pointer Down-pointer 119

11
10 Inserting an element - cont. If k is larger than the current number of levels, add new levels (and update top) Example - inser(119) when k=4 7142132377185 7137 21 7 37 21 Level 1 Level 2 Level 3 Top -1 -1 -1 1 1 1 119 1 -1

12
11 Determining k k - the number of levels at which an element x participate. Use a random function OurRnd() --- returns 1 or 0 (True/False) with equal probability. k=1 ; While( OurRnd() ) k++ ;

13
12 Deleteing a key x Find x in all the levels it participates, and delete it using the standard 'delete from a linked list' method. If one or more of the upper levels are empty, remove them (and update top) 7142132377185117 7137 21 7 37 21 Level 1 Level 2 Level 3 Top -1 -1 -1 1 1 1 next-pointer down-pointer delete(71)

14
13 Facts about SL The expected number of levels is O( log n ) (here n is the numer of elements) The expected time for insert/delete/find is O( log n ) The expected size (number of cells) is O(n )

Similar presentations

OK

Alon Efrat Computer Science Department University of Arizona Suffix Trees.

Alon Efrat Computer Science Department University of Arizona Suffix Trees.

© 2018 SlidePlayer.com Inc.

All rights reserved.

To ensure the functioning of the site, we use **cookies**. We share information about your activities on the site with our partners and Google partners: social networks and companies engaged in advertising and web analytics. For more information, see the Privacy Policy and Google Privacy & Terms.
Your consent to our cookies if you continue to use this website.

Ads by Google

Ppt on second law of thermodynamics evolution Ppt on needle stick injury images Ppt on event handling in javascript what is a number Ppt on rabindranath tagore in english Ppt on brand marketing salary Ppt on mpeg audio compression and decompression algorithms Ppt on switching networks File converter pdf to ppt online Ppt on types of internal trade Ppt on natural resources download