Read: Insertion Sort link

Insertion sort is a simple sorting algorithm that builds the final sorted array (or list) one item at a time. It is much less efficient on large lists than more advanced algorithms such as quicksort, heapsort, or merge sort. However, insertion sort provides several advantages:

• Simple implementation: Jon Bentley shows a three-line C version, and a five-line optimized version[2]
• Efficient for (quite) small data sets, much like other quadratic sorting algorithms
• More efficient in practice than most other simple quadratic (i.e., O(n2)) algorithms such as selection sort or bubble sort
• Adaptive, i.e., efficient for data sets that are already substantially sorted: the time complexity is O(kn) when each element in the input is no more than k places away from its sorted position
• Stable; i.e., does not change the relative order of elements with equal keys
• In-place; i.e.,** only requires a constant amount O(1)** of additional memory space
• Online; i.e., can sort a list as it receives it
• When people manually sort cards in a bridge hand, most use a method that is similar to insertion sort

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Read: Merge Sortlink

• In computer science, merge sort (also commonly spelled mergesort) is an efficient, general-purpose, comparison-based sorting algorithm. Most implementations produce a stable sort, which means that the order of equal elements is the same in the input and output.

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Read: Quick Sort link

• quicksort (sometimes called partition-exchange sort) is an efficient sorting algorithm, serving as a systematic method for placing the elements of a random access file or an array in order. Developed by British computer scientist Tony Hoare in 1959[1] and published in 1961,[2] it is still a commonly used algorithm for sorting. When implemented well, it can be about two or three times faster than its main competitors, merge sort and heapsort.[3][contradictory]

• Quicksort is a comparison sort, meaning that it can sort items of any type for which a "less-than" relation (formally, a total order) is defined. Efficient implementations of Quicksort are not a stable sort, meaning that the relative order of equal sort items is not preserved. Quicksort can operate in-place on an array, requiring small additional amounts of memory to perform the sorting. It is very similar to selection sort, except that it does not always choose worst-case partition.

• Mathematical analysis of quicksort shows that, on average, the algorithm takes O(n log n) comparisons to sort n items. In the worst case, it makes O(n2) comparisons, though this behavior is rare.

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