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An array data structure can be mathematically modeled as an abstract data structure (an abstract array) with two operations get(A, I): the data stored in the element of the array A whose indices are the integer tuple I. set(A, I, V): the array that results by setting the value of that element to V. These operations are required to satisfy the ...
Slicing of higher-dimensional arrays works similarly: A[-1, *] % The last row of A A[[1:5], [2:7]] % 2d array using rows 1-5 and columns 2-7 A[[5:1:-1], [2:7]] % Same as above except the rows are reversed Array indices can also be arrays of integers. For example, suppose that I = [0:9] is an
In a 1999 paper, [18] Brodnik et al. describe a tiered dynamic array data structure, which wastes only n 1/2 space for n elements at any point in time, and they prove a lower bound showing that any dynamic array must waste this much space if the operations are to remain amortized constant time. Additionally, they present a variant where growing ...
Box-drawing characters, also known as line-drawing characters, are a form of semigraphics widely used in text user interfaces to draw various geometric frames and boxes. These characters are characterized by being designed to be connected horizontally and/or vertically with adjacent characters, which requires proper alignment.
Thus, if a two-dimensional array has rows and columns indexed from 1 to 10 and 1 to 20, respectively, then replacing B by B + c 1 − 3c 2 will cause them to be renumbered from 0 through 9 and 4 through 23, respectively. Taking advantage of this feature, some languages (like FORTRAN 77) specify that array indices begin at 1, as in mathematical ...
Integer overflow can be demonstrated through an odometer overflowing, a mechanical version of the phenomenon. All digits are set to the maximum 9 and the next increment of the white digit causes a cascade of carry-over additions setting all digits to 0, but there is no higher digit (1,000,000s digit) to change to a 1, so the counter resets to zero.
These graphs include the complete graph K 6, the Petersen graph, the graph formed by removing an edge from the complete bipartite graph K 4,4, and the complete tripartite graph K 3,3,1. Every planar graph has a flat and linkless embedding: simply embed the graph into a plane and embed the plane into space. If a graph is planar, this is the only ...
In numerical analysis and scientific computing, a sparse matrix or sparse array is a matrix in which most of the elements are zero. [1] There is no strict definition regarding the proportion of zero-value elements for a matrix to qualify as sparse but a common criterion is that the number of non-zero elements is roughly equal to the number of ...