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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.
In mathematics, summation is the addition of a sequence of numbers, called addends or summands; the result is their sum or total.Beside numbers, other types of values can be summed as well: functions, vectors, matrices, polynomials and, in general, elements of any type of mathematical objects on which an operation denoted "+" is defined.
This list of mathematical series contains formulae for finite and infinite sums. It can be used in conjunction with other tools for evaluating sums. It can be used in conjunction with other tools for evaluating sums.
A Harshad number in base 10 is an integer that is divisible by the sum of its digits (when written in base 10). A005349: Factorions: 1, 2, 145, 40585, ... A natural number that equals the sum of the factorials of its decimal digits. A014080: Circular primes: 2, 3, 5, 7, 11, 13, 17, 37, 79, 113, ...
var c = 0.0 // The array input has elements indexed for i = 1 to input.length do // c is zero the first time around. var y = input[i] + c // sum + c is an approximation to the exact sum. (sum,c) = Fast2Sum(sum,y) // Next time around, the lost low part will be added to y in a fresh attempt. next i return sum
The list type is an additive monad, with nil as the monadic zero and append as monadic sum. Lists form a monoid under the append operation. The identity element of the monoid is the empty list, nil. In fact, this is the free monoid over the set of list elements.
The cardinality or "size" of a multiset is the sum of the multiplicities of all its elements. For example, in the multiset { a , a , b , b , b , c } the multiplicities of the members a , b , and c are respectively 2, 3, and 1, and therefore the cardinality of this multiset is 6.
Binary search Visualization of the binary search algorithm where 7 is the target value Class Search algorithm Data structure Array Worst-case performance O (log n) Best-case performance O (1) Average performance O (log n) Worst-case space complexity O (1) Optimal Yes In computer science, binary search, also known as half-interval search, logarithmic search, or binary chop, is a search ...