Sorting --- Quick Sort

Steven J. Zeil

Old Dominion University, Dept. of Computer Science

Table of Contents

1. Partitioning the Array
1.1. Analysis of pivotIndex
1.2. Analysis of pivotIndex (cont.)
2. Quick Sort
3. Quick Sort Analysis
3.1. Best Case
3.2. Average Case
3.3. Worst Case
3.4. Great Average, Dreadful Worst
4. Optimizing the Algorithm
5. Average Case Analysis of Quick Sort

Quick sort is a sorting algorithm with the optimal O(n log n) average case, but a O(n2) worst case.

Despite its slower worst case behavior, the Quick sort is generally preferred over Merge sort when sorting array-like structures (including vectors and deques). This is because the constant multiplier on quick sort's average case is much smaller, and, if we are careful, we can make the worst case input of quick sort a relatively obscure case that would seldom be seen in practice.

Like Merge sort, Quick sort also works by dividing the array into progressively smaller parts, but instead of chopping at an arbitrary point (e.g., halfway), it divides into pieces in which

This is often called partitioning the array.

For example, given the array

1 4 3 9 5 8 7 6

it's not hard to see that we can split the array this way

1 4 3
9 5 8 7 6

so that all items to the left are less than or equal to a pivot value 4, and all items on the right are greater than 4.

On the other hand, for some arrays:

9 1 8 7 2 6 4 0

there's really no place were we can divide the array as is to meet these requirements.

So an algorithm to partition the array must, in some case, move elements around to make the partition possible. The pivotIndex algorithm from your text does just this.

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