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One discrete problem that is expensive to solve on many computers is that of counting the number of bits that are set to 1 in a (binary) number, sometimes called the population function. For example, the decimal number "37" is "00100101" in binary, so it contains three bits that are set to binary "1".
To use column-major order in a row-major environment, or vice versa, for whatever reason, one workaround is to assign non-conventional roles to the indexes (using the first index for the column and the second index for the row), and another is to bypass language syntax by explicitly computing positions in a one-dimensional array.
Excel offers many user interface tweaks over the earliest electronic spreadsheets; however, the essence remains the same as in the original spreadsheet software, VisiCalc: the program displays cells organized in rows and columns, and each cell may contain data or a formula, with relative or absolute references to other cells. Excel 2.0 for ...
A vector treated as an array of numbers by writing as a row vector or column vector (whichever is used depends on convenience or context): = (), = Index notation allows indication of the elements of the array by simply writing a i, where the index i is known to run from 1 to n, because of n-dimensions. [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)
A two-dimensional array stored as a one-dimensional array of one-dimensional arrays (rows) Many languages support only one-dimensional arrays. In those languages, a multi-dimensional array is typically represented by an Iliffe vector, a one-dimensional array of references to arrays of one dimension less. A two-dimensional array, in particular ...
General array slicing can be implemented (whether or not built into the language) by referencing every array through a dope vector or descriptor – a record that contains the address of the first array element, and then the range of each index and the corresponding coefficient in the indexing formula.
This is an injective relation: each combination of the values of the headers row (row 0, for lack of a better term) and the headers column (column 0 for lack of a better term) is related to a unique cell in the table: Column 1 and row 1 will only correspond to cell (1,1); Column 1 and row 2 will only correspond to cell (2,1) etc.