A comparison sort examines the data only by comparing two elements with a comparison operator. General methods: insertion , exchange , selection , merging , etc. Adaptability : Whether or not the presortedness of the input affects the running time.
Algorithms that take this into account are known to be adaptive. Stable sorting algorithms maintain the relative order of records with equal keys. If all keys are different then this distinction is not necessary.
But if there are equal keys, then a sorting algorithm is stable if whenever there are two records let's say R and S with the same key, and R appears before S in the original list, then R will always appear before S in the sorted list.
When equal elements are indistinguishable, such as with integers, or more generally, any data where the entire element is the key, stability is not an issue.
However, assume that the following pairs of numbers are to be sorted by their first component:. In this case, two different results are possible, one which maintains the relative order of records with equal keys, and one which does not:. Bubble Sort Bubble sort is a simple sorting algorithm.
It works by repeatedly stepping through the list to be sorted, comparing each pair of adjacent items and swapping them if they are in the wrong order. The pass through the list is repeated until no swaps are needed, which indicates that the list is sorted. Because it only uses comparisons to operate on elements, it is a comparison sort. Step-by-Step Example. Assume we have an array "5 1 4 2 8" and we want to sort the array from the lowest number to the greatest number using bubble sort.
Selection Sort Selection sort is an in-place comparison sort. It has O n 2 complexity, making it inefficient on large lists, and generally performs worse than the similar insertion sort. Selection sort is noted for its simplicity, and also has performance advantages over more complicated algorithms in certain situations. Effectively, we divide the list into two parts: the sublist of items already sorted and the sublist of items remaining to be sorted.
How many comparisons does the algorithm need to perform? How many swaps does the algorithm perform in the worst case? Selecting the lowest element requires scanning all n elements this takes n -1 comparisons and then swapping it into the first position. Each of these scans requires one swap for n -1 elements. Every iteration of insertion sort removes an element from the input data, inserting it into the correct position in the already-sorted list, until no input elements remain.
The choice of which element to remove from the input is arbitrary, and can be made using almost any choice algorithm. Sorting is typically done in-place. In each iteration the first remaining entry of the input is removed, inserted into the result at the correct position, thus extending the result.
Among simple average-case O n 2 algorithms, selection sort almost always outperforms bubble sort, but is generally outperformed by insertion sort. Experiments show that insertion sort usually performs about half as many comparisons as selection sort. Selection sort will perform identically regardless of the order the array, while insertion sort's running time can vary considerably.
Insertion sort runs much more efficiently if the array is already sorted or "close to sorted. Selection sort always performs O n swaps, while insertion sort performs O n 2 swaps in the average and worst case. Selection sort is preferable if writing to memory is significantly more expensive than reading. Insertion sort or selection sort are both typically faster for small arrays i. A useful optimization in practice for the recursive algorithms is to switch to insertion sort or selection sort for "small enough" subarrays.
Merge Sort Merge sort is an O n log n comparison-based sorting algorithm. It is an example of the divide and conquer algorithmic paradigm.
We can solve the recurrence relation given above. We'll write n instead of O n in the first line below because it makes the algebra much simpler. Insertion sort and quicksort use different instructions and hava different memory access patterns. So the running time of quicksort versus insertion sort for any particular dataset on any particular system will depend both on the instructions used to implement those two sorting routines and the memory access patterns of the data.
Given the different mixes of instructions, it's perfectly possible that insertion sort is faster for lists of up to ten items on one system, but only for lists up to six items on some other system. The relative costs of various operations are different on different machines, and compilers have varying degrees of ability to optimize various constructs.
David Richerby goes into somewhat more detail on that, but the last half-sentence of the highlighted quote is perhaps the most important.
In many cases where one algorithm is more efficient than another for small data sets, and another is more efficient for large data sets, the performance differences between the two algorithms are apt to be rather small for data sets near the "break-even" point. Then consider the relative behaviors for two sets of constants. Hand-write an insertion sort and a merge sort for a list with 3 items, down to assembly code.
Pay attention to:. Now see if you can give different weights to the operations that might represent two different systems - for instance, one that's comparison-optimized and one that's register loading-optimized, and compute total. If you can get different results, then it's systems-dependent.
If you always get the same result, the one algorithm is always faster. Imagine an implementation where a function call is very, very expensive. Say so expensive that in the time it takes to do one function call, you can sort an array of elements with insertion sort.
When a partition reaches the size that can fit in a machine dependent sized cache, then it will be faster. It's more interesting to look at the mathematics behind the machine independent answer of 10 being the cut off point. Then there are recursive calls on the left and right partitions either side of the partitioning element. This is a student answer mine to an Exercise from the AofA website, Introduction Analysis of Algorithms Sedgewick The answer is a middle school algebra expansion of some answers found on a discussion forum, mainly this thread : Flores, Yao and Spreng , and a it's a good idea to try to independently reach their answers.
Sign up to join this community. The best answers are voted up and rise to the top. Stack Overflow for Teams — Collaborate and share knowledge with a private group. Insertion sort is the sorting mechanism where the sorted array is built having one item at a time.
The array elements are compared with each other sequentially and then arranged simultaneously in some particular order. How much faster is insertion sort with a element array than with a element array? The time efficiency of selection sort is quadratic, so there are a number of sorting techniques which have better time complexity than selection sort.
Merge sort is a recursive algorithm that continually splits a list in half. If the list is empty or has one item, it is sorted by definition the base case. Overview of quicksort.
The way that quicksort uses divide-and-conquer is a little different from how merge sort does. In merge sort, the divide step does hardly anything, and all the real work happens in the combine step. Quick Sort is also a cache friendly sorting algorithm as it has good locality of reference when used for arrays. Quick Sort is also tail recursive, therefore tail call optimizations is done. Begin typing your search term above and press enter to search.
Press ESC to cancel. Skip to content Home Engineering Which is faster insertion sort or merge sort? Ben Davis November 4, Which is faster insertion sort or merge sort? Which sorting technique is better between quick sort and merge sort and why? What is the difference between quick sort and merge sort?
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