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Given a function that accepts an array, a range query (,) on an array = [,..,] takes two indices and and returns the result of when applied to the subarray [, …,].For example, for a function that returns the sum of all values in an array, the range query (,) returns the sum of all values in the range [,].
Index mapping (or direct addressing, or a trivial hash function) in computer science describes using an array, in which each position corresponds to a key in the universe of possible values. [1] The technique is most effective when the universe of keys is reasonably small, such that allocating an array with one position for every possible key ...
However, the array will store pre-computed range minimum queries not for every range [i, j], but only for ranges whose size is a power of two. There are O(log n) such queries for each start position i, so the size of the dynamic programming table B is O(n log n). The value of B[i, j] is the index of the minimum of the range A[i…i+2 j-1].
The following list contains syntax examples of how a range of element of an array can be accessed. In the following table: first – the index of the first element in the slice; last – the index of the last element in the slice; end – one more than the index of last element in the slice; len – the length of the slice (= end - first)
Array data types are most often implemented as array structures: with the indices restricted to integer (or totally ordered) values, index ranges fixed at array creation time, and multilinear element addressing. This was the case in most "third generation" languages, and is still the case of most systems programming languages such as Ada, C ...
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.
Things become more interesting when we consider arrays with more than one index, for example, a two-dimensional table. We have three possibilities: make the two-dimensional array one-dimensional by computing a single index from the two; consider a one-dimensional array where each element is another one-dimensional array, i.e. an array of arrays
Matrix multiplication is an example of a 2-rank function, because it operates on 2-dimensional objects (matrices). Collapse operators reduce the dimensionality of an input data array by one or more dimensions. For example, summing over elements collapses the input array by 1 dimension.