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Topic: Pancake sorting

Related Topics

Stupid sort

Comb sort

Bucket sort

Shell sort

Pigeonhole sort

Cocktail sort

Counting sort

Merge sort

Bead sort

Bogosort

List of algorithms

Several Unique Sort

Topological sorting

Smoothsort

Binary tree sort

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	Pancake sorting (via CobWeb/3.1 planetlab1.netlab.uky.edu) (Site not responding. Last check: 2007-10-10)
		Pancake sorting is a variation of the sorting problem in which the only allowed operation is to reverse the elements of some prefix of the sequence.
		Whereas in the regular sorting problem one usually seeks to minimize the number of comparisons, in pancake sorting the operation is different.
		Because of this, pancake sorting can be accomplished in linear time, which is not possible for comparison sorting.
	publicliterature.org.cob-web.org:8888 /en/wikipedia/p/pa/pancake_sorting.html (494 words)

	CPS 6 : Spring 1999 : Pancake (Site not responding. Last check: 2007-10-10)
		Given a stack of pancakes, you are to write a program that indicates how the stack can be sorted so that the largest pancake is on the bottom and the smallest pancake is on the top.
		The pancake on the bottom of the whole stack has position 1 and the pancake on the top of a stack of n pancakes has position n.
		For each stack of pancakes, the output should echo the original stack on one line, followed by some sequence of flips that results in the stack of pancakes being sorted so that the largest diameter pancake is on the bottom and the smallest on top.
	www.cs.duke.edu /courses/cps006/spring99/asgn/pancake.html (486 words)

	Pancake sorting - Wikipedia, the free encyclopedia
		In the burnt pancake problem, their top sides would now be burnt instead of their bottom sides.
		The goal is to sort the sequence in as few reversals as possible.
		Because of this, pancake sorting can be accomplished in a linear number of operations, which is not possible for comparison sorting.
	en.wikipedia.org /wiki/Pancake_sorting (645 words)

	MathTrek: Pancake Sorting
		The original pancake problem was posed in 1975 in the American Mathematical Monthly by Jacob E. Goodman, writing under the name "Harry Dweighter" (or "Harried Waiter").
		When you are left with just two pancakes to be sorted, the final step requires only a single flip.
		In general, a pancake stack is an example of a data structure, and the pancake problem is relevant, for example, to the construction of networks of parallel processors, in which pancake sorting can provide an effective routing algorithm between processors.
	blog.sciencenews.org /2006/10/pancake_sorting.html (827 words)

	Al Zimmermann's Pancakes Programming Contest
		The pancake problem is to determine the shortest sequence of flips which will sort a given stack.
		Not all stacks of pancakes are equally difficult to sort.
		The fraction is the length of the shortest sequence of flips submitted for that stack, divided by the length of your sequence for that stack.
	members.aol.com /bitzenbeitz/Contests/Pancakes/index.html (1459 words)

	Cosc 300 - Pancake Sorting (Site not responding. Last check: 2007-10-10)
		Your goal is to put the stack of pancakes in order, so the largest pancake is on the bottom and the smallest one is on the top.
		Remember the problem is not to actually sort the stack of regular or blueberry pancakes (it generally takes more flips to sort a stack of blueberry pancakes), but rather to calculate the smallest number of flips needed to do so.
		Thus calculating the number of flips need to sort a stack of blueberry pancakes is the same as figuring out the minimum number of evolutionary changes needed to transform one ring of mitochondrial DNA into another.
	www.mathcs.duq.edu /simon/Fall05/cs300notes1.html (610 words)

	Flipping pancakes
		The purpose is to arrange pancakes according to their size with the biggest at the bottom.
		For each flip, you must (on Pete's behalf): Choose a number k between 1 and N. Pick a pancake in the kth position (counting from the topmost pancake) and insert your spatula under it (between the pancakes in position k and (k+1).
		Date: April/27/2000 8:35 AM Subject: Re: Pancake puzzle Before Bill Gates decided to become the richest man on earth, he was doing research on the fundamentals of algorithms.
	www.cut-the-knot.org /SimpleGames/Flipper.shtml (1475 words)

	Godfrey's Cockatiel Family & Friends, A Tribute to Pancake Page
		Pancake would come sleep with me. She would settle in in on my left side on the pillow, look at me decide anything was OK and very quickly go to sleep.
		Pancake was a very private bird for example she would not bath if there were strangers looking even if they were in the other room.
		Pancake would only allow about five or six people to go near her or even touch her.
	www.cockatiel.za.net /pancake/pancake_memories.php3 (1493 words)

	Reference.com/Encyclopedia/Sorting algorithm
		Although many consider it a solved problem, useful new sorting algorithms are still being invented to this day (for example, library sort was first published in 2004).
		Sort algorithms which only use an abstract key comparison operation always need at least Ω(n log n) comparisons on average.
		No This table describes some sorting algorithms that are impractical for real-life use due to extremely poor performance or a requirement for specialized hardware.
	www.reference.com /browse/wiki/Sorting_algorithm (2776 words)

	"The Pancake Problems"
		We represent the condition that pancake i is "burnt side up" by putting a negative element i' in place of i in the permutation.
		For the Burnt Pancake Problem, the lower and upper bounds provided by Gates and Papadimitriou were improved slightly by Cohen and Blum [CB] to 3n/2 and 2n-2.
		A sequence of flips that sorts a burnt permutation also sorts the corresponding ordinary permutation when sign of elements is ignored, so the sorting complexity of each unburnt permutation is bounded by the complexities of its burnt versions.
	www.math.uiuc.edu /~west/openp/pancake.html (716 words)

	Pancake day - Miamidolphins.co.uk > Forum
		To toss a pancake successfully takes a combination of the perfect pancake and good technique - it's so easy to get it wrong and end up with half the pancake still stuck to the pan while the other half is stuck to the ceiling or floor.
		Russian blinis, usually prepared with buckwheat, are thin, crisp pancakes, and commonly served with caviar and sour cream or folded over and filled with cream cheese or jam.
		Pancake tossing is also a very serious pastime for some people - Ralf Laue from Leipzig broke the world record by tossing a pancake 416 times in two minutes and Mike Cuzzacrea ran a marathon while continually tossing a pancake for three hours, two minutes and 27 seconds.
	www.miamidolphins.co.uk /forum/showthread.php?t=378 (1168 words)

	CSE 648 - Phylogenic Trees and Evolution (Lectures 17-19) (Site not responding. Last check: 2007-10-10)
		Thus a sorting problem can be signed or unsigned depending upon whether we know/care or do not know/care about the orientation of each gene.
		Suppose we seek to sort a stack of pancakes by size using a spatula.
		The gaps between strips are breakpoints, and the number of breakpoints is a lower bound on the number of reversals needed to sort.
	www.cs.sunysb.edu /~skiena/549/lectures/phylogeny/phylogeny.html (2147 words)

	Sorting algorithm - Wikipedia, the free encyclopedia
		Some algorithms are either recursive or non recursive, while others may be both (e.g., merge sort).
		Unstable sorting algorithms can be specially implemented to be stable.
		Shell sort was invented by Donald Shell in 1959.
	en.wikipedia.org /wiki/Sorting_algorithm (2704 words)

	Untitled Document
		For seven pancakes, there are 35 worst cases, each taking 8 flips to solve.
		For 7 pancakes, there are 35 worst case stacks with 8-flop solutions.
		pancakes, the maximum number of flops needed is 8.
	www.mathpuzzle.com /pancakes.htm (1965 words)

	MathTrek: Pancake Sorting (via CobWeb/3.1 planetlab1.netlab.uky.edu) (Site not responding. Last check: 2007-10-10)
		Additional information about pancake sorting can be found at http://mathworld.wolfram.com.cob-web.org:8888/PancakeSorting.html and http://en.wikipedia.org.cob-web.org:8888/wiki/Pancake_sorting.
		The terms of the pancake sequence and other information is available at http://www.research.att.com.cob-web.org:8888/cgi-bin/access.cgi/as/
		To do pancake sorting as a game, go to http://www.cut-the-knot.org.cob-web.org:8888/SimpleGames/Flipper.shtml.
	blog.sciencenews.org.cob-web.org:8888 /mathtrek/2006/10/pancake_sorting.html (827 words)

	Blue Pancakes and Homemade Coffee
		Any other attempt he might have made at sorting out the enigma was immediately over ridden by his brain’s insistence that he make coffee before he forced it to work any more.
		It didn’t take long, and he suspected that even if she did wake up, Dom wouldn’t emerge from the cocoon she’d wrapped herself in until the house was good and warm.
		Right, like she wouldn’t mock the mess he’d made of the kitchen already, or the fact that he was going to the trouble of making her breakfast at all.
	members.tripod.com /morrioghan/bluepancakes.htm (1079 words)

	1999-2000 AFLB Calendar
		Sorting by Reversals is Hard to Approximate Within Certain Constant.
		We prove that the problem MIN-SBR of sorting a permutation by the minimum number of reversals is hard to approximate (NP-hard by randomized reductions) within any constant factor less than some explicit threshold.
		This problem connects also to the well known problem of sorting by prefix reversals (or, so called, pancake sorting).
	theory.stanford.edu /~aflb/1999-00.html (2589 words)

	Question About Sorting an Array of Structs - dBforums
		When you sort an array of structs, it appears that it might be very quick.
		an to be sorted array, the number of sorts done during the runtime of an application
		Sorting structs by just swapping pointers to those structs tends to be faster than
	www.dbforums.com /showthread.php?t=327623 (3290 words)

	VG Scribbles (via CobWeb/3.1 planetlab1.netlab.uky.edu) (Site not responding. Last check: 2007-10-10)
		External sorting -- When data being sorted doesnt fit into the main memory of a computing device(usually RAM) and a slower kind of memory(usually a hard drive) needs to be used.Suppose we have 10 MB of RAM and data is 12 MB to be sorted then in this case external sort is used.
		Merge sort is one example of external sort as a core.
		For sorting N elements, O(logn) extra space is required.This is reasonable because in a purely mathematical analysis of the algorithms, any sorting algorithm that operates on a contiguous array requires O(log n) extra space, since this is the number of bite required to represent an index into the array.
	vinodgupta.blogspot.com.cob-web.org:8888 (3743 words)

	CMPSCI H04 (Honors for CMPSCI 311), Fall 2003
		The pancake number is the diameter of this graph, which is the longest distance from one point to another.
		The n=3 pancake graph is a hexagon, and the n=4 graph with 24 vertices looks a bit like a soccer ball though we don't have a good picture of it.
		Generalizing Vitaly's generating set, we noted that the diameter of this graph is (n choose 2) because bubblesort and insertion sort operate by exchanging adjacent items, and we proved that any such sort needs (n choose 2) exchanges in the worst case.
	www.cs.umass.edu /~barring/cs311f03/honors (2411 words)

	Club Information
		Each year the Martin Kiwanis Club assists Santa's Village by counting the food items that are donated during the event.
		Club members assist in the sorting during the actual event, and then on the following Monday, club members help distribute the items to the organizations, such as We Care, that make up Christmas boxes for the needy in Weakley and Obion counties.
		The annual Pancake Day fundraiser will be held on Saturday, February 24.
	www.utm.edu /organizations/kiwanis/calendar.html (201 words)

	CAL: Digests: Ten Common Fallacies About Bilingual Education
		In this 3-week unit, Frederike introduced her third-grade German students to a story based on a Grimm's fairy tale about a pancake (Pfannküchen) by singing the song "Ich Habe Hunger" ("I Am Hungry") with them, then preparing batter (measuring in grams) and cooking a pancake in class.
		Finally, the pancake meets two hungry orphans, jumps into their laps and begs, "Eat me, I will give you strength." The orphans then eat the pancake.
		The students practiced new vocabulary by drawing pictures on the board as Frederike recited the scene and by sequencing sentences about the story using sentence strips and a pocket chart.
	www.cal.org /resources/digest/0004thematic.html (1525 words)

	Grades of Maple Syrup - Pure Maple Syrup - Gourmet Maple Syrup - Gourmet Food Finder - THE NIBBLE Gourmet Food Magazine
		It’s easy to read a label that says “pancake syrup” or “maple-flavored syrup” and translate that in your mind to “maple syrup,” so read carefully.
		Pancake syrups are usually corn syrup or sugar based, and either artificially—flavored or flavored with 1 to 5 percent maple syrup.
		Grade A Medium Amber is the most popular grade sold, but that doesn’t mean it’s the connoisseur’s choice—it’s closest to the artificial supermarket pancake syrup we grew up with.
	www.thenibble.com /reviews/main/honey/grades-of-maple-syrup.asp?r=rss (850 words)

	CS 577 In-Class Questions
		Q: In the case of Insertion Sort, how many comparisons are needed in each of these situations?
		Q: In pancake flipping, how many flips are there in the worst case?
		In looking at an example of a 6 element array in reverse sorted order, we determined it to be a worst case scenario for Quick Sort.
	www.cs.wisc.edu /~gage/cs577/cs577.htm (517 words)

	Pancake sorting at AllExperts (via CobWeb/3.1 planetlab1.netlab.uky.edu) (Site not responding. Last check: 2007-10-10)
		As an interesting piece of trivia, the only well-known paper ever published by Microsoft Chairman and billionaire Bill Gates, entitled "Bounds for Sorting by Prefix Reversal", describes an efficient algorithm for pancake sorting.
		* Gates, W. and Papadimitriou, C. "Bounds for Sorting by Prefix Reversal." Discrete Mathematics.
		* Cut-the-Knot: Flipping pancakes puzzle, including a Java applet for the pancake problem and some discussion.
	experts.about.com.cob-web.org:8888 /e/p/pa/Pancake_sorting.htm (555 words)

	Untitled Document
		When the spatula reaches the last pancake, the stack is flopped so that larger pancakes are on the bottom.
		If you have a spatula, and 7 pancakes of size 1-7 on a plate, what is the minimum number of flops you'll need to get the pancakes sorted from smallest to largest?
		The worst case for 7 pancakes is unknown, so far as I know.
	www.mathpuzzle.com /25Feb.htm (3973 words)

	I want a perfect body.. (Site not responding. Last check: 2007-10-10)
		You are required to sort 15 applications per sorting session.
		If you sort 15 right away, you do not have to sort any for the rest of the session.
		If you believe you are not a good fit for the house you have be sorted into, you apply here to be moved.
	swedish-pancake.livejournal.com (1444 words)

	USO Canteen FReeper Style ~ Pancakes on Wednesday ~ 27 August 2003
		Then the pancake sorting problem asks how many such "prefix reversals" are sufficient to sort an arbitrary stack (Skiena 1990, p.
		needed to sort a random stack of n = 1, 2, 3,...
		pancakes are 0, 1, 3, 4, 5, 7, 8, 9, 10, 11, 13,...
	www.freerepublic.com /focus/f-news/971179/posts (2896 words)

	Thematic, Communicative Language Teaching in the K-8 Classroom. ERIC Digests.
		"A German Fairy Tale" In this 3-week unit, Frederike introduced her third-grade German students to a story based on a Grimm's fairy tale about a pancake ("Pfannkuchen") by singing the song "Ich Habe Hunger" ("I Am Hungry") with them, then preparing batter (measuring in grams) and cooking a pancake in class.
		"The Thick, Fat Pancake" ("Der Dicke Fette Pfannkuchen") is the story of an old woman who bakes a pancake that does not want to be eaten.
		* pretending to become animals and pancakes when the teacher waved her magic wand, then role playing their actions in the story
	www.ericdigests.org /2001-2/thematic.html (1498 words)

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