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Before we get into the gritty details of various sorting algorithms, let me point out: We usually don't build an automobile engine from scratch. Instead, we usually use an off-the-shelf automobile engine already built into the automobile we are using. Likewise, we usually don't write yet another sort function. Instead, we usually use an off-the-shelf sort function already supplied with the API we are using.

• Binary Tree Sort
• Bogosort
• Bubble sort
• Bucket sort
• Check sort
• Cocktail sort
• Comb sort
• Counting sort
• Gnome sort
• Heapsort
• Insertion sort
• Introsort
• Library sort
• Merge sort
• Patience sort
• Pigeonhole sort
• Quicksort
• Radix sort
• Rapid sort
• Schwartzian transform
• Selection sort
• Shell sort
• Smoothsort
  • Some proofs

Further reading

• When we discuss the details of these algorithms, we assume you are already familiar with Data Structures.
• Optimizing C++/General optimization techniques/Sorting—explains how to use the standard, off-the-shelf sorting algorithm implementations in the standard template library (STL)
• c2: SortingAlgorithms