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The lazy initialization technique allows us to do this in just O(m) operations, rather than spending O(m+n) operations to first initialize all array cells. The technique is simply to allocate a table V storing the pairs ( k i , v i ) in some arbitrary order, and to write for each i in the cell T [ k i ] the position in V where key k i is stored ...
In Rule 90, each cell's value is computed as the exclusive or of the two neighboring values in the previous time step. Rule 90 is an elementary cellular automaton.That means that it consists of a one-dimensional array of cells, each of which holds a single binary value, either 0 or 1.
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 ...
An empty matrix is a matrix in which the number of rows or columns (or both) is zero. [ 73 ] [ 74 ] Empty matrices help to deal with maps involving the zero vector space . For example, if A is a 3-by-0 matrix and B is a 0-by-3 matrix, then AB is the 3-by-3 zero matrix corresponding to the null map from a 3-dimensional space V to itself, while ...
A Sudoku starts with some cells containing numbers (clues), and the goal is to solve the remaining cells. Proper Sudokus have one solution. [1] Players and investigators use a wide range of computer algorithms to solve Sudokus, study their properties, and make new puzzles, including Sudokus with interesting symmetries and other properties.
MATLAB allows matrix manipulations, plotting of functions and data, implementation of algorithms, creation of user interfaces, and interfacing with programs written in other languages. Although MATLAB is intended primarily for numeric computing, an optional toolbox uses the MuPAD symbolic engine allowing access to symbolic computing abilities.
Note how the use of A[i][j] with multi-step indexing as in C, as opposed to a neutral notation like A(i,j) as in Fortran, almost inevitably implies row-major order for syntactic reasons, so to speak, because it can be rewritten as (A[i])[j], and the A[i] row part can even be assigned to an intermediate variable that is then indexed in a separate expression.
Lloyd's algorithm starts by an initial placement of some number k of point sites in the input domain. In mesh-smoothing applications, these would be the vertices of the mesh to be smoothed; in other applications they may be placed at random or by intersecting a uniform triangular mesh of the appropriate size with the input domain.