CSC 172 DATA STRUCTURES. SKIP LISTS Read Weiss 10.4.2.
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Transcript of CSC 172 DATA STRUCTURES. SKIP LISTS Read Weiss 10.4.2.
CSC 172 DATA STRUCTURES
SKIP LISTSRead Weiss 10.4.2
SKIP LISTS Dictionary Data Structure Efficient
SKIP LISTS Dictionary Data Structure (insert delete lookup) Efficient O(lg n)
SKIP LISTS Dictionary Data Structure (insert delete lookup) Efficient O(lg n)
SKIP LISTS Dictionary Data Structure Efficient (with high probability) Randomized
SKIP LISTS Dictionary Data Structure Efficient (with high probability) Randomized Easy to implement
LISTS
How much time does it take to search a sorted linked list?
How can this be improved?
EXAMPLE
EXAMPLE What is this sequence?
14,23,28,34,42,50,59,66,72,79,86,96,103,110
EXAMPLE What is this sequence?
14,23,34,42,50,59,66,72,79,86,96,103,110
EXAMPLE What is this sequence?
14,23,34,42,50,59,66,72,79,86,96,103,110,116,125
SKIP LISTS Use two lists L
2 stores all element
L1 stores some elements
Links between shared elements
Lookup on a skip list
Lookup on a skip list
1)Take L1 until you go too far2)Back up one3)Transfer to L24)Take L2 until you find element
(or go too far – not found – or insert)
Lookup on a skip list
How should we distribute the L1 list? What is the time cost of a search?
Lookup on a skip list
How should we distribute the L1 list? What is the time cost of a search?
Minimize : L1.length + (L2.length/L1.length)
NEXT STEP 2 linked lists 2(n^(1/2)) Can we improve this further?
NEXT STEP 2 linked lists 2(n^(1/2)) Can we improve this further? 3 linked lists 3(n^(1/3)) k linked lists k(n^(1/k)) N linked lists ???? lg n linked lists lg n (n^(1/lg n))
BALLANCED SKIP LISTS Ideal as long as structure is maintained
BALLANCED SKIP LISTS Ideal as long as structure is maintained Insertions and deletions mess up structure
INSERTION ON SKIP LISTS Search to find location Must insert on bottom list Which other lists? FLIP A COIN
If heads add to level above and flip again. If tails done.
INSERTION ON SKIP LISTS FLIP A COIN
If heads add to level above and flip again. If tails done.
½ of the elements go up one level¼ of the elements go up 2 levels1/8 of the elements go up 3 levels
INSERTION ON SKIP LISTS EXAMPLE
ANALYSIS Intuitively:
Height of the structure is O(lg n)How many coin flips do we need to get lg n heads?