Editing Pancake sorting (section)

{{short description|Mathematics problem}}
{{Use mdy dates|date=October 2014}}
[[File:Pancake sort operation.png|right|frame|Demonstration of the primary operation. The spatula is flipping over the top three pancakes, with the result seen below. In the burnt pancake problem, their top sides would now be burnt instead of their bottom sides.]]

'''Pancake sorting''' is the mathematical problem of sorting a disordered stack of pancakes in order of size when a [[spatula]] can be inserted at any point in the stack and used to flip all pancakes above it.  A ''pancake number'' is the minimum number of flips required for a given number of pancakes. In this form, the problem was first discussed by American geometer [[Jacob E. Goodman]].<ref>{{cite news|first=Simon |last=Singh |authorlink=Simon Singh | title=Flipping pancakes with mathematics|newspaper=[[The Guardian]]| date=November 14, 2013| url=https://www.theguardian.com/science/blog/2013/nov/14/flipping-pancakes-mathematics-jacob-goodman| access-date=March 25, 2014}}</ref> A variant of the problem is concerned with ''burnt'' pancakes, where each pancake has a burnt side and all pancakes must, in addition, end up with the burnt side on bottom.

All sorting methods require pairs of elements to be compared. For the traditional [[sorting problem]], the usual problem studied is to minimize the [[Comparison sort#Number of comparisons required to sort a list|number of comparisons required to sort a list]]. The number of actual operations, such as swapping two elements, is then irrelevant. For pancake sorting problems, in contrast, the aim is to minimize the number of operations, where the only allowed operations are reversals of the elements of some ''[[prefix (computer science)|prefix]]'' of the sequence. Now, the number of comparisons is irrelevant.