computer science 101 a survey of computer science quicksort
TRANSCRIPT
Computer Science 101A Survey of Computer Science
QuickSort
Divide and Conquer
Divide and Conquer
• Divide and Conquer is a common strategy used in computer science.
• The idea is that for a given problem, we try to break it into smaller problems (perhaps of the same type and then solve the smaller problems)
• Of course, we must consider how to solve the smaller problems.
Sorting -Quicksort
• Strategy - Divide and Conquer:– Partition list with small elements in first part and
large elements in second part
– Sort the first part.
– Sort the second part.
Quicksort (cont.)
• Question - How do we sort the sections?Answer - Apply Quicksort to them.
• Recursive algorithm - one which makes use of itself to solve smaller problems of the same type.
Quicksort (cont.)
• Question - Will this recursive process ever stop?
• Answer - Yes, when the problem is “small enough” , we no longer use recursion. Such cases are called “anchor cases”.
Recursion Example
• The factorial function could be defined this way:
n! = { 1 if n=1 { n ((n-1)!) otherwise
• Example: 4! = 4 x 3! = 4 x 3 x 2! = 4 x 3 x 2 x 1! = 4 x 3 x 2 x 1
Smaller problem of same type
Anchor case
Quicksort - Partitioning
• To partition, we choose a “pivot element” from the list.
• The elements which are less than or equal to the pivot go into the first section.
• The elements larger than the pivot go into the second section.
Quicksort - The Pivot
• Ideal would be to choose the median as the pivot, but this would take too long.
• Some programs just choose the first element.
• Our choice - choose the median of the first three elements.
Quicksort Partition
• Variables:N(I),N(I+1), … , N(K) - list to partition
P - position of the pivot element
L - Right hand marker for the first section
U - Left hand marker for the second section
Quicksort Partition Algorithm Exchange the median of the first 3
elements with the first elementSet P to first position of listSet L to second position of listSet U to last position of listWhile L ≤ U do
While N(L) N(P) doSet L to L+1
end-of-loopWhile N(U) > N(P) do
Set U to U-1end-of-loopIf L < U then
Exchange N(L) and N(U)end-of-loopExchange N(P) and N(U)
Left markercharges to right
Right markercharges to left
QuickSort - The Algorithm
If the list to sort has more than 1 element thenIf the list has exactly two elements then If the elements are out of order thenExchange themelse Perform the Partition Algorithm on list Apply QuickSort to the first section Apply QuickSort to the second section
Note: Anchor cases are when the list has 1 or 2 elements – recursion is used for 3 or more.
Quicksort Example
15 8 19 5 30 20 10 1 28 25 12
19 8 15 5 30 20 10 1 28 25 12Original
19 8 15 5 30 20 10 1 28 25 12Pivot
15 8 19 5 30 20 10 1 28 25 12Move L
15 8 19 5 30 20 10 1 28 25 12Move U
15 8 12 5 30 20 10 1 28 25 19Swap
Quicksort Example (Cont.)
15 8 12 5 30 20 10 1 28 25 19Move L
15 8 12 5 30 20 10 1 28 25 19
15 8 12 5 30 20 10 1 28 25 19Move U
15 8 12 5 30 20 10 1 28 25 19
15 8 12 5 30 20 10 1 28 25 19
15 8 12 5 1 20 10 30 28 25 19Swap
Quicksort Example (Cont.)15 8 12 5 1 20 10 30 28 25 19Move L
15 8 12 5 1 10 20 30 28 25 19Swap
15 8 12 5 1 20 10 30 28 25 19Move U
15 8 12 5 1 10 20 30 28 25 19Move L
15 8 12 5 1 10 20 30 28 25 19Move U
10 8 12 5 1 15 20 30 28 25 19PivotSwap
Quicksort Example (Cont.)
10 8 12 5 1Move L
10 8 12 5 1
10 8 12 5 1Move U
10 8 1 5 12Swap
10 8 1 5 12Move L
10 8 1 5 12
Pivot 10 8 12 5 1 20 30 28 25 1915
Quicksort Example (Cont.)10 8 1 5 12Move U
5 8 1 10 12PivotSwap
Pivot 5 8 1 10 12 20 30 28 25 1915
Move L 5 8 1
Move U 5 8 1
Swap 5 1 8
Quicksort Example (Cont.)
Move L 5 1 8
Move U 5 1 8
PivotSwap 1 5 8
Size 1 11 5 8 10 12 20 30 28 25 1915
Size 1 1 5 8 10 12 20 30 28 25 1915
Size 1 11 5 8 10 12 20 30 28 25 1915
Quicksort Example (Cont.)20Pivot 11 5 108 12 30 28 25 1915
28Move L 30 20 25 19
28Move U 30 20 25 19
28Swap 19 20 25 30
Move L 28 19 20 25 30
28 19 20 25 30
28 19 20 25 30
Quicksort Example (Cont.)
Move L 20 19 25
PivotSwap 25 19 20 28 30
25Pivot 11 85 10 12 19 20 28 3015
Move U 28 19 20 25 30
20 19 25
Move U 20 19 25
PivotSwap 19 20 25
Quicksort Example (Cont.)
19Size 1 11 85 10 12 20 25 28 3015
19Size 1 11 85 10 12 20 25 28 3015
19Size 1 11 85 10 12 20 25 28 3015
19Finished 11 85 10 12 20 25 28 3015
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