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Topic: Binary insertion sort

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	Shell Sort Algorithm (Site not responding. Last check: 2007-10-29)
		Sorting algorithms are important in computer science because of the need to organize data into ascending or descending order according to each data records key.
		Sorting by selection is where the largest or smallest number in a set is put at the end or beginning.
		Sorting by distribution is where all items are compared to each other and a position index is given to each one based on how many are smaller or larger than it is. Radix sort is a sorting by distribution method.
	www2.hawaii.edu /~deubelbe/ShellSortAlgorithm.htm (986 words)

	Ira Pohl CMPS 012A: Homework 5
		Binary lookup takes a key as input (the key which is being looked for) and looks in the middle of the sorted array of data.
		Insertion sort has an inner loop which varies j from the value of the outer loop variable, i, down to the beginning of the array.
		Insertion sort starts with as little work as possible, and with every iteration of the outer loop, it adds a bit of work, and by the time it reaches the last iteration of the outer loop, it has to consider the entire array.
	www.cse.ucsc.edu /~pohl/CBDCourse/hw/hw5.html (2186 words)

	[No title]
		Linear insertion is quadratic in both worst and average cases, and linear in best cases.
		Each bucket is sorted (with respect to the order of two reference objects), and the list of buckets is sorted on the minimum of the buckets (w.r.t.
		Compared to insertion sort into a list of single objects (Full, Half, or Zoom) this saves calls (over 2000 in the worst case of the task), because only a partial order instead of a total order is constructed.
	olympiads.win.tue.nl /ioi/ioi2000/contest/day1/median/median-handout.txt (1389 words)

	PlanetMath: insertion sort
		Even the optimization of using a binary search does not help us here, because the deciding factor in this case is the insertion.
		A similar algorithm to the insertion sort is the selection sort, which requires fewer data movements than the insertion sort, but requires more comparisons.
		This is version 7 of insertion sort, born on 2001-10-08, modified 2005-01-21.
	planetmath.org /encyclopedia/InsertionSort.html (234 words)

	Insertion Sort
		Sorting algorithms were measured by a standard called big O. Big O measures algorithms by taking the worst-case that the algorithm could have and timing it.
		Insertion sort is also used in other sorting algorithms such as shell sort, merge sort and quick sort.
		Although both of these sorts are faster than insertion sort, insertion sort is the basis of these sorts and is therefore a good foundation to start teaching sorting.
	www2.hawaii.edu /~lestery/insertsort.htm (1149 words)

	[No title] (Site not responding. Last check: 2007-10-29)
		Theorem: For the perfect binary tree of height h containing 2h + 1 — 1 nodes, the sum of the heights of the nodes is 2h + 1 — 1 — (h + 1).
		The unexpected things that occurred in the data was, as in insertion sort, we expected N to take longer than E, but as we said before, it could be because of the data itself and since it has happened with more than one sort, it gets more and more likely it’s the data itself.
		This sort seems to be slower than the merge sort routine for the most part; only that it’s a bit faster with sorting family N. Overall, this would be an ideal sort to implement if data sets needed to be sorted because it does not dramatically take longer as the size increases.
	www.calpoly.edu /~bqduong/Files/103Project.doc (2874 words)

	Sorting -- Getting it Straight
		binary search techniques we know that only about lg i compares need to be made to determine where to insert an item into a sorted list.
		Binary insertion was mentioned by John Mauchly in 1946 in the first published discussion of computer sorting.
		That is, a heap is a binary tree which is completely filled at all levels except possibly the last, which is filled from left to right and the key in each node is larger than (or equal to) the keys of its children.
	www.cs.fit.edu /~wds/classes/cse5081/Sort/sort/sort.html (5028 words)

	[No title]
		For example, the N value for each node of the binary tree in Figure 2 is shown by the value inside the node.
		Insertion sort is based on the idea of repeatedly inserting a new element into a list of already sorted elements so that the resulting list is still sorted.
		In binary insertion sort, a binary search is used (instead of linear search) to locate the position in the sorted sublist x[1], x[2], ., x[i-1] where the next item x[i] is to be inserted.
	www.ececs.uc.edu /~wjone/DATA_STRUCTURE_04/Midterm.doc (840 words)

	insertion sort (Site not responding. Last check: 2007-10-29)
		Note: Sorting can be done in place by moving the next item into place by repeatedly swapping it with the preceding item until it is in place - a linear search and move combined.
		If comparing items is very expensive, use binary search to reduce the number of comparisons needed to find where the item should be inserted, then open a space by moving all later items down one.
		However a binary search is likely to make this not a stable sort.
	www.nist.gov /dads/HTML/insertionSort.html (222 words)

	sort from FOLDOC
		Sorting is the subject of a great deal of study since it is a common operation which can consume a lot of computer time.
		There are many well-known sorting algorithms with different time and space behaviour and programming complexity.
		Examples are quicksort, insertion sort, bubble sort, heap sort, and tree sort.
	foldoc.org /foldoc/foldoc.cgi?sort (193 words)

	Insertion sort
		The regular insertion sort is the most efficient of the 3 main naive approaches.
		Dichotomic insertion (also called binary search insertion sort) consists in using a dichotomic search to determine where to insert the new item, taking advantage of the fact the sub array is already sorted.
		Unfortunately, this algorithm is not efficient in practice, because, to the opposite of Selection sort, it does on average of n*n exchanges.
	thomas.baudel.name /Visualisation/VisuTri/insertionsort.html (229 words)

	10.2.3 Insertion Sort
		The two sorting algorithms we have looked at so far are useful when all of the data is already present in an array, and we wish to rearrange it into sorted order.
		Figure 10.12 shows the complete function for inserting one new element in a sorted array, given the array, the new item, and the next free position (which, incidentally, is the current size of the array).
		Insertion sort can be adapted to sorting an existing array.
	www-ee.eng.hawaii.edu /Courses/EE150/Book/chap10/subsection2.1.2.3.html (903 words)

	Introduction to Algorithms: Insertion Sort (Site not responding. Last check: 2007-10-29)
		This is the proof of correctness for insertion sort, using a loop invariant diagram.
		says that the ``sorted'' part is empty (or has exactly one element), so is trivially sorted, whilst the ``untouched'' part is the whole (or rest) of the array, i.e.
		(e) When the insertion sort algorithm was presented to you in lectures, two subroutines (methods) were used inside the main loop of the algorithm.
	www.cs.man.ac.uk /~pt/algorithms/insertion_sort.html (1095 words)

	Binary Sort
		We have that when k is 1 to 5 the worst case total comparisons required to sort are 1,5, 17, 49, and 129, respectively.
		I could not find an example in any of the textbooks in my room to verify this; however, it is a simple proof by induction.
		An interesting thing is it seems that if we take into account the hidden constants, the worst case for this algorithm still outperforms the average case for quicksort.
	www.geneffects.com /briarskin/theory/binary (267 words)

	Sorting Algorithms
		Bucket sort initially creates a "counts" array whose size is the size of the range of all possible values for the data we are sorting, eg.
		This time, several bucket like sorts are performed (one for each digit), but instead of having a counts array representing the range of all possible values for the data, it represents all of the possible values for each individual digit, which in decimal numbering is only 10.
		Firstly a bucked sort is performed, using only the least significant digit to sort it by, then another is done using the next least significant digit, until the end, when you have done the number of bucket sorts equal to the maximum number of digits of your biggest number.
	tanksoftware.com /tutes/uni/sorting.html (1784 words)

	UnrealWiki: Insertion Sort
		Insertion Sort is an iterative sorting algorithm like Bubble Sort.
		If the removed input element is higher than the current result element, the element's correct location is found; remove it from its original location, insert it at the new location and start again from (2) with the next input element.
		For numeric arrays the last two steps can be optimized using BinarySearch to search the new location in the sorted part of the array if it's not already in the correct location.
	wiki.beyondunreal.com /wiki/Insertion_Sort (620 words)

	Python owns us
		The initial implementation was fine with many aspects, but there were two annoyances, namely the fact that the new sort introduces 2*N extra bytes memory burden and that with a specific data profile timsort was significantly slower.
		Tim implemented also the Edelkamp and Stiegeler's "Next-to-m" refinement of weak heapsort, but the first refinement of their algorithm proved to be so far from promising that he dropped it.
		Eventually the tuning got into point where timsort for troublesome sample data was at the same level or even faster than the current sort, so the speed issue went practically away.
	py-stablesort.sourceforge.net /doc/2002_07_28_pythonowns_archive.html (850 words)

	Insertion sort
		Insertion sort always maintains two zones in the array to be sorted: sorted and unsorted.
		binary insertion sort -- an optimization of the insertion sort where the proper location is found by binary search.
		Dichotomic insertion consists in using a dichotomic search to determine where to insert the new item, taking advantage of the fact the sub array is already sorted.
	www.softpanorama.org /Algorithms/Sorting/insertion_sort.shtml (1069 words)

	prog1 (Site not responding. Last check: 2007-10-29)
		Implement the Insertion Sort and Merge Sort algorithms to sort a vector in place, as it is described in the book.
		This algorithm is like Merge Sort but it calls Insertion Sort on subvectors with fewer than 100 elements.
		Then, after each sorting, your program will scan all elements of A and for each element of A it will check using binary search whether the element exists in B; if it is not, it will report an error.
	lambda.uta.edu /cse2320/prog1 (388 words)

	[No title]
		# # # # # # where the number represents the sorts to be run on the corresponding data set.
		Sort Source code: Written by Len Myers and John Araujo /** * binaryInsertionSort * the recursive version; this method first * checks to see if a sort needs to occur, * then calls 'place' specifying the area to the * left of the current array index.
		As predicted by the theoretic run-time analysis of the recursive binary insertion sort algorithm, the ordered (best-case) data returned linear data and the backwards (worst-case) sets showed a quadratic (n^2) trend.
	www.csc.calpoly.edu /~lmyers/Cpe103/BinInsetRec/Project.doc (605 words)

	Ingres Data Sorts
		A single sort output work file is used to gather all the runs, which are then merged into a second output work file.
		The QEF sort used to be an insertion sort (not a bubble sort) which used a binary search to determine the location of each added row.
		And that algorithm is a heap sort, which I'm told is one of the more reasonable algorithms kicking around (according to my data structures and algorithms text, it has n log n performance, as does Quicksort).
	ariel.ucs.unimelb.edu.au /~yuan/Ingres/ingsort.html (841 words)

	[No title]
		{0, 1} is a binary alphabet, and {1} is a unary alphabet.
		Sequential search, binary search, insertion sort, quick sort, and merge sort are some examples of such approaches.
		is a binary representation over {0, 1} of the natural numbers if it assigns to the ith natural number the set consisting of the ith canonically smallest binary string.
	www.cse.ohio-state.edu /~gurari/theory-bk/theory-bk-onese1.html (1122 words)

	[No title]
		Number of moves is at most number of comparisons in straight insertion sort.
		Definition of P. ``Is this array sorted?'' is in P. ``Is there a path from x to y in this digraph of length under L?'' is in P. A problem that is not in P. Definition of NP.
		How close we are to proving that ``Is the input composite?'' is in P: there is a nearly-polynomial-time algorithm that answers the question; there is a polynomial-time algorithm that is believed to answer the question; there is a random algorithm that takes polynomial time on average.
	cr.yp.to /1998-401/inclass.html (1270 words)

	Anguilla Computer Club: Sorting and Speed (Site not responding. Last check: 2007-10-29)
		Spreadsheet lesson #4 sorted rows of information into order by the values in one column, but we did not explore how the data was actually sorted into order.
		One performance attribute of a sort algorithm is whether it is linear: as the number of sort items increases, does the sort time increase proportionally, or does it increase faster.
		If any sort takes more than 60 seconds, press ESC to stop the sort and try again with a number of items halfway between the last test and the aborted test.
	www.news.ai /club/sorting.html (338 words)

	Binary Insertion Sort
		The straight insertion algorithm presented in the preceding section does a linear search to find the position in which to do the insertion.
		In each iteration, a binary search search is done to determine the position at which to do the insertion (lines 13-23).
		The worst-case running time of the binary insertion sort is dominated by the i swaps needed to do the insertion.
	www.brpreiss.com /books/opus4/html/page491.html (334 words)

	[No title]
		Both of these searches are forms of the same search, referred to as a LINEAR search, because the computation cost increases linearly as the number of elements increase.
		Binary Search Now we will describe a search algorithm that is an ORDER OF MAGNITUDE improvement over our previous search, the linear search.
		Insertion Sort We've now talked about how we can search through a list of numbers, but what about sorting a list of numbers?
	www.owlnet.rice.edu /~comp200/02spring/Lecture-notes/lec15.txt (1058 words)

	CSCI 3650, Summer 2001
		We looked at a very naive sorting, the insertion sort algorithm, binary insertion sort, and the mergesort algorithm.
		(n!) on the number of comparisons that must be done, in the worst case, for sorting n numbers by a general comparison algorithm.
		Bucket sort is discussed in Section 9.4 of the text.
	www.cs.ecu.edu /~karl/3650/sum01 (1035 words)

	[No title]
		4) In binary insertion sort, one inserts each element by performing a binary search to find the position, and then inserting the element.
		Analyze the worst case number of comparisons and time complexity of binary insertion sort; state the data structures used in your implementation.
		Design an O(n+kn) algorithm which sorts a sequence with at most k changes of direction.
	www.vuse.vanderbilt.edu /~spin/finalans.html (1019 words)

	[No title]
		If we were to implement a Binary tree with 100 nodes as: a general tree, an N-ary tree (with N=2) and a Binary tree, which technique would require the most space (assume all pointers are the same size and that the tree uses indirect containment).
		Both types of rotations assume that no node higher in the tree than the lowest node with a new balance factor of magnitude 2 will be affected by the insertion...
		Explain the differences between bucket sorting and radix sorting.
	www.pads.uwaterloo.ca /Wayne.Loucks/Teaching/ece250/f1998_wml/complete.htm (3895 words)

	Data Structures
		Quick sort is then applied to the left and right recursively.
		Binary Tree: Each node has two children that are either null or trees themselves.
		Trees with nodes that include keys so that the nodes are sorted with nodes on the left being lesser than those on the right.
	home.att.net /~gobruen/progs/datastruct.html (1405 words)

	Week 11 Wednesday (Site not responding. Last check: 2007-10-29)
		In the basic insertion sort, how many inversions are corrected for each movement/comparison?
		What is the performance of the best/average/worst case basic insertion sort?
		What is the performance of the best/average/worst case binary insertion sort?
	www.pads.uwaterloo.ca /Wayne.Loucks/Teaching/ece250/f1998_wml/question30.htm (81 words)

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