Sorting LinkedLists.

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Presentation transcript:

Sorting LinkedLists

QuickSort Review What is needed to do quick sort efficiently?

QuickSort Review What is needed to do quick sort efficiently? partitionFunction must be O(n)

QuickSort Review What is needed to partition in O(n)? Partition Array between low and high: pivotValue = value at low i = low+1 //left maker j = high //right marker while i <= j while i points to value <= pivotValue and i <= j increase i while j points to value >= pivotValue and i <= j decrease j if i < j swap values at i and j   swap values at low and j return new location of pivot

QuickSort Review What is needed to partition in O(n)? O(n) : set i, j, pivot Partition Array between low and high: pivotValue = value at low i = low+1 //left maker j = high //right marker while i <= j while i points to value <= pivotValue and i <= j increase i while j points to value >= pivotValue and i <= j decrease j if i < j swap values at i and j   swap values at low and j return new location of pivot

QuickSort Review What is needed to partition in O(n)? O(n) : O(1) : set i, j, pivot O(1) : move left or right one element compare elements swap elements Partition Array between low and high: pivotValue = value at low i = low+1 //left maker j = high //right marker while i <= j while i points to value <= pivotValue and i <= j increase i while j points to value >= pivotValue and i <= j decrease j if i < j swap values at i and j   swap values at low and j return new location of pivot

QuickSort Could use existing algorithm with DLL

QuickSort Could use existing algorithm with DLL Could adapt for Singly Linked List

QuickSort Use pivot pointer and two new lists for small and large items

QuickSort Grab first node as pivot

QuickSort Iterate through list, removing each node and adding to small or large

QuickSort Iterate through list, removing each node and adding to small or large

QuickSort Iterate through list, removing each node and adding to small or large

QuickSort Iterate through list, removing each node and adding to small or large

QuickSort Recursively sort small and large

QuickSort Recursively sort small and large

QuickSort Reassemble into one list

QuickSort Reassemble into one list

QuickSort Reassemble into one list

QuickSort Reassemble into one list

QuickSort Log(n) levels of recursion (hopefully) O(n) work to partition O(n) work to reassemble – or O(1) with tail pointer

MergeSort MergeSort with array Disadvantages?

MergeSort MergeSort with array Need O(n) extra storage Lots of copy overhead In place trades LOTS of copying for less storage

MergeSort What is needed to do efficiently?

MergeSort What is needed to do efficiently? Slice in half in O(n) Merge in O(n)

Slice Slice list in half: Produce second linked list with second half

Slice Slice list in half: Walk to last node before halfway point

Slice Slice list in half: Attach otherlist to second half of list

Slice Slice list in half: Break list, update tail and length of mylist

Merge Merge : Combine elements from two sorted lists

Merge Merge : Combine elements from two sorted lists One by one move smallest value to Merged list

Merge Merge : Combine elements from two sorted lists One by one move smallest value to Merged list

Merge Merge : Combine elements from two sorted lists One by one move smallest value to Merged list

Merge Merge : Combine elements from two sorted lists One by one move smallest value to Merged list

Merge Steal nodes back into original list

Merge And remove from Merged

Merge And remove from Merged

Final Sort With split/merge, sort part is easy