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For example, a two-dimensional array A with three rows and four columns might provide access to the element at the 2nd row and 4th column by the expression A[1][3] in the case of a zero-based indexing system. Thus two indices are used for a two-dimensional array, three for a three-dimensional array, and n for an n-dimensional array.
The definition of matrix multiplication is that if C = AB for an n × m matrix A and an m × p matrix B, then C is an n × p matrix with entries = =. From this, a simple algorithm can be constructed which loops over the indices i from 1 through n and j from 1 through p, computing the above using a nested loop:
Flood fill, also called seed fill, is a flooding algorithm that determines and alters the area connected to a given node in a multi-dimensional array with some matching attribute. It is used in the "bucket" fill tool of paint programs to fill connected, similarly colored areas with a different color, and in games such as Go and Minesweeper for ...
In contrast, two-dimensional arrays are always rectangular [4] so jagged arrays should not be confused with multidimensional arrays, but the former is often used to emulate the latter. Arrays of arrays in languages such as Java, PHP, Python (multidimensional lists), Ruby, C#.NET, Visual Basic.NET , Perl, JavaScript, Objective-C, Swift, and ...
More generally, there are d! possible orders for a given array, one for each permutation of dimensions (with row-major and column-order just 2 special cases), although the lists of stride values are not necessarily permutations of each other, e.g., in the 2-by-3 example above, the strides are (3,1) for row-major and (1,2) for column-major.
Common examples of array slicing are extracting a substring from a string of characters, the "ell" in "hello", extracting a row or column from a two-dimensional array, or extracting a vector from a matrix. Depending on the programming language, an array slice can be made out of non-consecutive elements.
The point quadtree [3] is an adaptation of a binary tree used to represent two-dimensional point data. It shares the features of all quadtrees but is a true tree as the center of a subdivision is always on a point. It is often very efficient in comparing two-dimensional, ordered data points, usually operating in O(log n) time.
In computer programming, the stride of an array (also referred to as increment, pitch or step size) is the number of locations in memory between beginnings of successive array elements, measured in bytes or in units of the size of the array's elements. The stride cannot be smaller than the element size but can be larger, indicating extra space ...