7 sorting scheme
THE SEVEN SORTING SCHEME
1. BUBBLE SORT
The bubble sort is generally considered to be the simplest sorting algorithm. Because of its simplicity and ease of visualization, it is often taught in introductory computer science courses. Because of its abysmal O(n2) performance, it is not used often for large (or even medium-sized) datasets.
ALGORITHM:
for i = 1:n, swapped = false for j = n:i+1, if a[j] < a[j-1], swap a[j,j-1] swapped = true → invariant: a[1..i] in final position break if not swapped end RUNNING TIME:
BEST CASE: The term best-case performance is used in computer science to describe an algorithm's behavior under optimal conditions. For example, the best case for a simple linear search on a list occurs when the desired element is the first element of the list.
Development and choice of algorithms is rarely based on best-case performance: most academic and commercial enterprises are more interested in improving average performance and worst-case performance. Algorithms may also be trivially modified to have good best-case running time by hard-coding solutions to a finite set of inputs, making the measure almost meaningless.[1]
AVERAGE CASE: Average performance is the most used in algorithm analysis. Less widely found is best-case performance, but it does have uses: for example, where the best cases of individual tasks are known, they can be used to improve the accuracy of an overall worst-case analysis. Computer scientists use probabilistic analysis techniques, especially expected value, to determine expected running times.
WORST CASE:
Worst-case performance analysis and average case performance analysis have some similarities, but in practice usually require different tools and approaches.
Determining what average input means is difficult, and often that average input has properties which make it difficult to characterise mathematically (consider, for instance,
1. BUBBLE SORT
The bubble sort is generally considered to be the simplest sorting algorithm. Because of its simplicity and ease of visualization, it is often taught in introductory computer science courses. Because of its abysmal O(n2) performance, it is not used often for large (or even medium-sized) datasets.
ALGORITHM:
for i = 1:n, swapped = false for j = n:i+1, if a[j] < a[j-1], swap a[j,j-1] swapped = true → invariant: a[1..i] in final position break if not swapped end RUNNING TIME:
BEST CASE: The term best-case performance is used in computer science to describe an algorithm's behavior under optimal conditions. For example, the best case for a simple linear search on a list occurs when the desired element is the first element of the list.
Development and choice of algorithms is rarely based on best-case performance: most academic and commercial enterprises are more interested in improving average performance and worst-case performance. Algorithms may also be trivially modified to have good best-case running time by hard-coding solutions to a finite set of inputs, making the measure almost meaningless.[1]
AVERAGE CASE: Average performance is the most used in algorithm analysis. Less widely found is best-case performance, but it does have uses: for example, where the best cases of individual tasks are known, they can be used to improve the accuracy of an overall worst-case analysis. Computer scientists use probabilistic analysis techniques, especially expected value, to determine expected running times.
WORST CASE:
Worst-case performance analysis and average case performance analysis have some similarities, but in practice usually require different tools and approaches.
Determining what average input means is difficult, and often that average input has properties which make it difficult to characterise mathematically (consider, for instance,