Difference between revisions of "cpp/algorithm/inclusive scan"

Latest revision as of 14:43, 29 May 2024

The generalized, noncommutative sum of a sequence of elements over a binary operation binary_op is defined as follows:

• If the sequence only has one element, the sum is the value of the element.
• Otherwise, performs the following operations in order:

1. Selects any two adjacent elements elem1 and elem2 from the sequence.
2. Calculates binary_op(elem1, elem2) and replaces the two elements in the sequence with the result.
3. Repeats steps 1 and 2 until there is only one element in the sequence.

Given binary_op as the actual binary operation:

• The result is non-deterministic if the binary_op is not associative (such as floating-point addition).

• For overloads (1-4), if binary_op(*first, *first) is not convertible to the value type of decltype(first), the program is ill-formed.

• For overloads (5,6), if any of the following values is not convertible to T, the program is ill-formed:

• binary_op(init, *first)
• binary_op(init, init)
• binary_op(*first, *first)

• If any of the following conditions is satisfied, the behavior is undefined:

• For overloads (1-4), the value type of decltype(first) is not MoveConstructible.
• For overloads (5,6), T is not MoveConstructible.
• binary_op modifies any element of [first, last).
• binary_op invalidates any iterator or subrange of [first, last].

[edit] Parameters

[edit] Return value

Iterator to the element past the last element written.

[edit] Complexity

Given \(\scriptsize N\)N as std::distance(first, last):

[edit] Exceptions

The overloads with a template parameter named ExecutionPolicy report errors as follows:

• If execution of a function invoked as part of the algorithm throws an exception and ExecutionPolicy is one of the standard policies, std::terminate is called. For any other ExecutionPolicy, the behavior is implementation-defined.
• If the algorithm fails to allocate memory, std::bad_alloc is thrown.

[edit] Example

#include <functional>
#include <iostream>
#include <iterator>
#include <numeric>
#include <vector>
 
int main()
{
    std::vector data{3, 1, 4, 1, 5, 9, 2, 6};
 
    std::cout << "Exclusive sum: ";
    std::exclusive_scan(data.begin(), data.end(),
                        std::ostream_iterator<int>(std::cout, " "),
                        0);
 
    std::cout << "\nInclusive sum: ";
    std::inclusive_scan(data.begin(), data.end(),
                        std::ostream_iterator<int>(std::cout, " "));
 
    std::cout << "\n\nExclusive product: ";
    std::exclusive_scan(data.begin(), data.end(),
                        std::ostream_iterator<int>(std::cout, " "),
                        1, std::multiplies<>{});
 
    std::cout << "\nInclusive product: ";
    std::inclusive_scan(data.begin(), data.end(),
                        std::ostream_iterator<int>(std::cout, " "),
                        std::multiplies<>{});
}

Exclusive sum: 0 3 4 8 9 14 23 25
Inclusive sum: 3 4 8 9 14 23 25 31
 
Exclusive product: 1 3 3 12 12 60 540 1080
Inclusive product: 3 3 12 12 60 540 1080 6480

[edit] See also