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4
2
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Quick-Sort(A, 0, 7)
Quick-Sort(A, 0, 7) , done!
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7
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Quick-Sort Algorithm Analysis: Best, Average, and Worst Cases, Slides of Design and Analysis of Algorithms
An analysis of the quick-sort algorithm, discussing its best, average, and worst-case scenarios. The best case occurs when the input is already sorted or reversely sorted, resulting in a time complexity of o(nlogn). The average case assumes a split of 1/10: 9/10, leading to an average time complexity of o(nlogn). The worst case, with an unbalanced partition, results in a time complexity of o(n^2). The document also mentions that quick-sort sorts in-place and requires minimal additional space.
Typology: Slides
2011/2012
1 / 6
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76
Quick-Sort(A, 0, 7)
Quick-Sort(A, 0, 7)
, done!
77
Quick-Sort: Best Case
Even Partition
Total time: (nlogn)
cn
2 × cn/2 = cn
4 × c/4 = cn
n/3 × 3c = cn
log n levels
n
n/
n/
n/
n/
n/ n/
79
Quick-Sort: an Average Case
Suppose the split is 1/10 : 9/
Quick-Sort: an Average Case
cn
cn
cn
≤cn
n
0.1n
0.9n
0.01n
0.09n
0.09n
Total time: (nlogn)
0.81n
log
10
n
log
10/
n
≤cn
80
Quick-Sort Summary
Time
Most of the work done in partitioning.
Average case takes (n log(n)) time.
Worst case takes (n
2