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The most common problem being solved is the 0-1 knapsack problem, which restricts the number of copies of each kind of item to zero or one. Given a set of items numbered from 1 up to , each with a weight and a value , along with a maximum weight capacity ,
Packing different rectangles in a rectangle: The problem of packing multiple rectangles of varying widths and heights in an enclosing rectangle of minimum area (but with no boundaries on the enclosing rectangle's width or height) has an important application in combining images into a single larger image. A web page that loads a single larger ...
Circle packing in a circle is a two-dimensional packing problem with the objective of packing unit circles into the smallest possible larger circle.
Circle packing in a square is a packing problem in recreational mathematics, where the aim is to pack n unit circles into the smallest possible square. Equivalently, the problem is to arrange n points in a unit square aiming to get the greatest minimal separation, d n , between points. [ 1 ]
Square packing in a square is the problem of determining the maximum number of unit squares (squares of side length one) that can be packed inside a larger square of side length . If a {\displaystyle a} is an integer , the answer is a 2 , {\displaystyle a^{2},} but the precise – or even asymptotic – amount of unfilled space for an arbitrary ...
The most efficient way to pack different-sized circles together is not obvious. In geometry, circle packing is the study of the arrangement of circles (of equal or varying sizes) on a given surface such that no overlapping occurs and so that no circle can be enlarged without creating an overlap.
[[Category:Route diagram templates]] to the <includeonly> section at the bottom of that page. Otherwise, add <noinclude>[[Category:Route diagram templates]]</noinclude> to the end of the template code, making sure it starts on the same line as the code's last character.
A 30 L top and bottom-loading Deuter Trans Alpine hiking backpack A 12 L front-loading Canon 200EG photography backpack. A backpack—also called knapsack, schoolbag, rucksack, pack, booksack, bookbag, haversack, packsack, or backsack—is, in its simplest frameless form, a fabric sack carried on one's back and secured with two straps that go over the shoulders; but it can have an external or ...