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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 [,].
Prefix sums are trivial to compute in sequential models of computation, by using the formula y i = y i − 1 + x i to compute each output value in sequence order. However, despite their ease of computation, prefix sums are a useful primitive in certain algorithms such as counting sort, [1] [2] and they form the basis of the scan higher-order function in functional programming languages.
Let A be the sum of the negative values and B the sum of the positive values; the number of different possible sums is at most B-A, so the total runtime is in (()). For example, if all input values are positive and bounded by some constant C , then B is at most N C , so the time required is O ( N 2 C ) {\displaystyle O(N^{2}C)} .
INT sum sq := 0; FOR i WHILE print(("So far:", i, new line)); # Interposed for tracing purposes. # sum sq ≠ 70↑2 # This is the test for the WHILE # DO sum sq +:= i↑2 OD Subsequent extensions to the standard ALGOL 68 allowed the to syntactic element to be replaced with upto and downto to achieve a small optimization.
find the value (if any) that is bound to a given key. The argument to this operation is the key, and the value is returned from the operation. If no value is found, some lookup functions raise an exception, while others return a default value (such as zero, null, or a specific value passed to the constructor).
In applications such as in radix sort, a bound on the maximum key value k will be known in advance, and can be assumed to be part of the input to the algorithm. However, if the value of k is not already known then it may be computed, as a first step, by an additional loop over the data to determine the maximum key value.
Elements of a newly created array may have undefined values (as in C), or may be defined to have a specific "default" value such as 0 or a null pointer (as in Java). In C++ a std::vector object supports the store, select, and append operations with the performance characteristics discussed above. Vectors can be queried for their size and can be ...
In array languages, operations are generalized to apply to both scalars and arrays. Thus, a+b expresses the sum of two scalars if a and b are scalars, or the sum of two arrays if they are arrays. An array language simplifies programming but possibly at a cost known as the abstraction penalty.