Trace of QuickSort Algorithm. quickSort(array, lower, upper) { // Base Case if (lower >= upper) { we’re done } else { partition array around pivot value.

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Presentation transcript:

Trace of QuickSort Algorithm

quickSort(array, lower, upper) { // Base Case if (lower >= upper) { we’re done } else { partition array around pivot value array[lower] pos contains the new location of pivot value quickSort array up to pos: quickSort(array,lower,pos) quickSort array after pos: quickSort(array,pos+1,upper) }

partition(array, lower, upper) { pivot is array[lower] while (true) { scan from right to left using index called RIGHT STOP when locate an element that should be left of pivot scan from left to right using index called LEFT stop when locate an element that should be right of pivot swap array[RIGHT] and array[LEFT] if (RIGHT and LEFT cross) pos = location where LEFT/RIGHT cross swap pivot and array[pos] all values left of pivot are <= pivot all values right of pivot are >= pivot return pos end pos }

quickSort(arr,0,5)

partition(arr,0,5)

quickSort(arr,0,5) partition(arr,0,5) pivot= ? Partition Initialization...

quickSort(arr,0,5) partition(arr,0,5) pivot=6 Partition Initialization...

quickSort(arr,0,5) partition(arr,0,5) left pivot=6 Partition Initialization...

quickSort(arr,0,5) partition(arr,0,5) left right pivot=6 Partition Initialization...

quickSort(arr,0,5) partition(arr,0,5) left right pivot=6 right moves to the left until value that should be to left of pivot...

quickSort(arr,0,5) partition(arr,0,5) left right pivot=6

quickSort(arr,0,5) partition(arr,0,5) left right pivot=6 left moves to the right until value that should be to right of pivot...

quickSort(arr,0,5) partition(arr,0,5) left right pivot=6

quickSort(arr,0,5) partition(arr,0,5) left right pivot=6

quickSort(arr,0,5) partition(arr,0,5) left right pivot=6 swap arr[left] and arr[right]

quickSort(arr,0,5) partition(arr,0,5) left right pivot=6 repeat right/left scan UNTIL left & right cross

quickSort(arr,0,5) partition(arr,0,5) left right pivot=6 right moves to the left until value that should be to left of pivot...

quickSort(arr,0,5) partition(arr,0,5) left right pivot=6

quickSort(arr,0,5) partition(arr,0,5) left right pivot=6 left moves to the right until value that should be to right of pivot...

quickSort(arr,0,5) partition(arr,0,5) leftright pivot=6

quickSort(arr,0,5) partition(arr,0,5) leftright pivot=6 swap arr[left] and arr[right]

quickSort(arr,0,5) partition(arr,0,5) leftright pivot=6 swap arr[left] and arr[right]

quickSort(arr,0,5) partition(arr,0,5) leftright pivot=6 repeat right/left scan UNTIL left & right cross

quickSort(arr,0,5) partition(arr,0,5) leftright pivot=6 right moves to the left until value that should be to left of pivot...

quickSort(arr,0,5) partition(arr,0,5) left right pivot=6

quickSort(arr,0,5) partition(arr,0,5) left right pivot=6 right & left CROSS!!!

quickSort(arr,0,5) partition(arr,0,5) left right pivot=6 right & left CROSS!!! 1 - Swap pivot and arr[right]

quickSort(arr,0,5) partition(arr,0,5) left right pivot=6 right & left CROSS!!! 1 - Swap pivot and arr[right]

quickSort(arr,0,5) partition(arr,0,5) left right pivot=6 right & left CROSS!!! 1 - Swap pivot and arr[right] 2 - Return new location of pivot to caller return 3

quickSort(arr,0,5) Recursive calls to quickSort() using partitioned array... pivot position

quickSort(arr,0,5) quickSort(arr,0,3) quickSort(arr,4,5)

quickSort(arr,0,5) quickSort(arr,0,3) quickSort(arr,4,5) partition(arr,0,3)

quickSort(arr,0,3) quickSort(arr,4,5) partition(arr,0,3) Partition Initialization... quickSort(arr,0,5)

quickSort(arr,0,3) quickSort(arr,4,5) partition(arr,0,3) Partition Initialization... quickSort(arr,0,5)

quickSort(arr,0,3) quickSort(arr,4,5) partition(arr,0,3) Partition Initialization... left quickSort(arr,0,5)

quickSort(arr,0,3) quickSort(arr,4,5) partition(arr,0,3) Partition Initialization... left right quickSort(arr,0,5)

right moves to the left until value that should be to left of pivot... quickSort(arr,0,3) quickSort(arr,4,5) partition(arr,0,3) left right quickSort(arr,0,5)

quickSort(arr,0,3) quickSort(arr,4,5) partition(arr,0,3) left right quickSort(arr,0,5)

quickSort(arr,0,3) quickSort(arr,4,5) partition(arr,0,3) left right quickSort(arr,0,5)

quickSort(arr,0,3) quickSort(arr,4,5) partition(arr,0,3) left right quickSort(arr,0,5)

quickSort(arr,0,3) quickSort(arr,4,5) partition(arr,0,3) left right right & left CROSS!!! quickSort(arr,0,5)

quickSort(arr,0,3) quickSort(arr,4,5) partition(arr,0,3) left right right & left CROSS!!! 1 - Swap pivot and arr[right] quickSort(arr,0,5)

quickSort(arr,0,3) quickSort(arr,4,5) partition(arr,0,3) left right right & left CROSS!!! 1 - Swap pivot and arr[right] right & left CROSS!!! 1 - Swap pivot and arr[right] 2 - Return new location of pivot to caller return 0 quickSort(arr,0,5)

quickSort(arr,0,3) quickSort(arr,4,5) quickSort(arr,0,5) Recursive calls to quickSort() using partitioned array...

quickSort(arr,0,3) quickSort(arr,4,5) quickSort(arr,0,5) quickSort(arr,0,0) 3 0 quickSort(arr,1,3)

quickSort(arr,0,3) quickSort(arr,4,5) quickSort(arr,0,5) quickSort(arr,0,0) 3 0 quickSort(arr,1,3) Base case triggered... halting recursion.

quickSort(arr,0,3) quickSort(arr,4,5) quickSort(arr,0,5) quickSort(arr,0,0) 3 0 quickSort(arr,1,3) Base Case: Return

quickSort(arr,0,3) quickSort(arr,4,5) quickSort(arr,0,5) quickSort(arr,0,0) 3 0 quickSort(arr,1,3) partition(arr,1,3) Partition Initialization...

quickSort(arr,0,3) quickSort(arr,4,5) quickSort(arr,0,5) quickSort(arr,0,0) 3 0 quickSort(arr,1,3) partition(arr,1,3) Partition Initialization...

quickSort(arr,0,3) quickSort(arr,4,5) quickSort(arr,0,5) quickSort(arr,0,0) 3 0 quickSort(arr,1,3) partition(arr,1,3) Partition Initialization... left

quickSort(arr,0,3) quickSort(arr,4,5) quickSort(arr,0,5) quickSort(arr,0,0) 3 0 quickSort(arr,1,3) partition(arr,1,3) left right right moves to the left until value that should be to left of pivot...

quickSort(arr,0,3) quickSort(arr,4,5) quickSort(arr,0,5) quickSort(arr,0,0) 3 0 quickSort(arr,1,3) partition(arr,1,3) left right

quickSort(arr,0,3) quickSort(arr,4,5) quickSort(arr,0,5) quickSort(arr,0,0) 3 0 quickSort(arr,1,3) partition(arr,1,3) left right left moves to the right until value that should be to right of pivot...

quickSort(arr,0,3) quickSort(arr,4,5) quickSort(arr,0,5) quickSort(arr,0,0) 3 0 quickSort(arr,1,3) partition(arr,1,3) left right

quickSort(arr,0,3) quickSort(arr,4,5) quickSort(arr,0,5) quickSort(arr,0,0) 3 0 quickSort(arr,1,3) partition(arr,1,3) left right right & left CROSS!

quickSort(arr,0,3) quickSort(arr,4,5) quickSort(arr,0,5) quickSort(arr,0,0) 3 0 quickSort(arr,1,3) partition(arr,1,3) left right right & left CROSS! 1- swap pivot and arr[right]

quickSort(arr,0,3) quickSort(arr,4,5) quickSort(arr,0,5) quickSort(arr,0,0) 3 0 quickSort(arr,1,3) partition(arr,1,3) left right right & left CROSS! 1- swap pivot and arr[right]

quickSort(arr,0,3) quickSort(arr,4,5) quickSort(arr,0,5) quickSort(arr,0,0) 3 0 quickSort(arr,1,3) partition(arr,1,3) left right right & left CROSS! 1- swap pivot and arr[right] 2 – return new position of pivot return 2

quickSort(arr,0,3) quickSort(arr,4,5) quickSort(arr,0,5) quickSort(arr,0,0) 3 0 quickSort(arr,1,3) quickSort(arr,1,2)quickSort(arr,3,3)

quickSort(arr,0,3) quickSort(arr,4,5) quickSort(arr,0,5) quickSort(arr,0,0) 3 0 quickSort(arr,1,3) quickSort(arr,1,2)quickSort(arr,3,3) partition(arr,1,2)

quickSort(arr,0,3) quickSort(arr,4,5) quickSort(arr,0,5) quickSort(arr,0,0) 3 0 quickSort(arr,1,3) quickSort(arr,1,2)quickSort(arr,3,3)

quickSort(arr,0,3) quickSort(arr,4,5) quickSort(arr,0,5) quickSort(arr,0,0) 3 0 quickSort(arr,1,3) quickSort(arr,1,2)quickSort(arr,3,3) 6 3 quickSort(arr,1,1)quickSort(arr,2,2) 45 12

quickSort(arr,0,3) quickSort(arr,4,5) quickSort(arr,0,5) quickSort(arr,0,0) 3 0 quickSort(arr,1,3) quickSort(arr,1,2)quickSort(arr,3,3) 6 3 quickSort(arr,1,1)quickSort(arr,2,2) partition(arr,4,5)

quickSort(arr,0,3) quickSort(arr,4,5) quickSort(arr,0,5) quickSort(arr,0,0) 3 0 quickSort(arr,1,3) quickSort(arr,1,2)quickSort(arr,3,3) 6 3 quickSort(arr,1,1)quickSort(arr,2,2) partition(arr,4,5)

quickSort(arr,0,3) quickSort(arr,4,5) quickSort(arr,0,5) quickSort(arr,0,0) 3 0 quickSort(arr,1,3) quickSort(arr,1,2)quickSort(arr,3,3) 6 3 quickSort(arr,1,1)quickSort(arr,2,2) quickSort(arr,4,5) quickSort(arr,6,5)

quickSort(arr,0,3) quickSort(arr,4,5) quickSort(arr,0,5) quickSort(arr,0,0) 3 0 quickSort(arr,1,3) quickSort(arr,1,2)quickSort(arr,3,3) 6 3 quickSort(arr,1,1)quickSort(arr,2,2) quickSort(arr,4,5) partition(arr,4,5) quickSort(arr,6,5)

quickSort(arr,0,3) quickSort(arr,4,5) quickSort(arr,0,5) quickSort(arr,0,0) 3 0 quickSort(arr,1,3) quickSort(arr,1,2)quickSort(arr,3,3) 6 3 quickSort(arr,1,1)quickSort(arr,2,2) quickSort(arr,4,5) quickSort(arr,6,5)

quickSort(arr,0,3) quickSort(arr,4,5) quickSort(arr,0,5) quickSort(arr,0,0) 3 0 quickSort(arr,1,3) quickSort(arr,1,2)quickSort(arr,3,3) 6 3 quickSort(arr,1,1)quickSort(arr,2,2) quickSort(arr,4,5) quickSort(arr,4,4) quickSort(arr,5,5) quickSort(arr,6,5)