NAME¶

std::inclusive_scan - std::inclusive_scan

Synopsis¶

Defined in header <numeric>
template< class InputIt, class OutputIt
>
(since C++17)
OutputIt inclusive_scan( InputIt first, (until C++20)

InputIt last, OutputIt d_first );
template< class InputIt, class OutputIt
>

constexpr OutputIt inclusive_scan( (since C++20)
InputIt first,

InputIt last, OutputIt d_first );
template< class ExecutionPolicy, class
ForwardIt1, class ForwardIt2 >

ForwardtIt2 inclusive_scan( (2) (since C++17)
ExecutionPolicy&& policy, ForwardIt1
first,

ForwardIt1 last, ForwardIt2 d_first );
template< class InputIt, class OutputIt,
class BinaryOperation >

OutputIt inclusive_scan( InputIt first, (since C++17)
InputIt last, (until C++20)

OutputIt d_first, BinaryOperation
binary_op );
template< class InputIt, class OutputIt,
class BinaryOperation >

constexpr OutputIt inclusive_scan( (since C++20)
InputIt first, InputIt last,

OutputIt d_first, BinaryOperation (1)
binary_op );
template< class ExecutionPolicy, class
ForwardIt1, class ForwardIt2,

class BinaryOperation >
ForwardIt2 inclusive_scan( (4) (since C++17)
ExecutionPolicy&& policy,
ForwardIt1 first, ForwardIt1 last,

ForwardIt2 d_first, BinaryOperation
binary_op ); (3)
template< class InputIt, class OutputIt,
class BinaryOperation, class T > (since
C++17)
OutputIt inclusive_scan( InputIt first, (until
InputIt last, OutputIt d_first, C++20)

BinaryOperation binary_op, T init );
template< class InputIt, class OutputIt,
class BinaryOperation, class T >

constexpr OutputIt inclusive_scan( (since
InputIt first, InputIt last, OutputIt C++20)
d_first, (5)

BinaryOperation binary_op, T init );
template< class ExecutionPolicy, class
ForwardIt1, class ForwardIt2,

class BinaryOperation, class T >
ForwardIt2 inclusive_scan( (6) (since
ExecutionPolicy&& policy, C++17)
ForwardIt1 first, ForwardIt1 last,
ForwardIt2 d_first,

BinaryOperation binary_op, T init );

Computes an inclusive prefix sum operation using binary_op (or std::plus<>() for
overloads (1-2)) for the range [first, last), using init as the initial value (if
provided), and writes the results to the range beginning at d_first. "inclusive"
means that the i-th input element is included in the i-th sum.

Formally, assigns through each iterator i in [d_first, d_first + (last - first)) the
value of:

* for overloads (1-4), the generalized noncommutative sum of *j... for every j in
[first, first + (i - d_first + 1)) over binary_op
* for overloads (5-6), the generalized noncommutative sum of init, *j... for every
j in [first, first + (i - d_first + 1)) over binary_op

where generalized noncommutative sum GNSUM(op, a
1, ..., a
N) is defined as follows:

* if N=1, a
1
* if N > 1, op(GNSUM(op, a
1, ..., a
K), GNSUM(op, a
M, ..., a
N)) for any K where 1 < K+1 = M ≤ N

In other words, the summation operations may be performed in arbitrary order, and
the behavior is nondeterministic if binary_op is not associative.

Overloads (2,4,6) are executed according to policy. These overloads do not
participate in overload resolution unless
std::is_execution_policy_v<std::decay_t<ExecutionPolicy>>
(until C++20)
std::is_execution_policy_v<std::remove_cvref_t<ExecutionPolicy>>
(since C++20) is true.

binary_op shall not invalidate iterators (including the end iterators) or subranges,
nor modify elements in the ranges [first, last) or [d_first, d_first + (last -
first)). Otherwise, the behavior is undefined.

Parameters¶

first, last - the range of elements to sum
d_first - the beginning of the destination range; may be equal to first
policy - the execution policy to use. See execution policy for details.
init - the initial value (optional)
binary FunctionObject that will be applied in to the result of
binary_op - dereferencing the input iterators, the results of other
binary_op, and init (if provided).

Type requirements¶

-
InputIt must meet the requirements of LegacyInputIterator.
-
OutputIt must meet the requirements of LegacyOutputIterator.
-
ForwardIt1 must meet the requirements of LegacyForwardIterator.
-
ForwardIt2 must meet the requirements of LegacyForwardIterator.
-
If init is not provided, decltype(first)'s value_type must be MoveConstructible and
binary_op(*first, *first) must be convertible to decltype(first)'s value type.
-
T (if init is provided) must meet the requirements of MoveConstructible. All of
binary_op(init, *first), binary_op(init, init), and binary_op(*first, *first) must
be convertible to T

Return value¶

Iterator to the element past the last element written.

Complexity¶

O(last - first) applications of the binary operation

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.

Example¶

// Run this code

#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<>{});
}

Output:¶

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

See also¶

computes the differences between adjacent elements in a
adjacent_difference range
(function template)
accumulate sums up a range of elements
(function template)
partial_sum computes the partial sum of a range of elements
(function template)
transform_inclusive_scan applies an invocable, then calculates inclusive scan
(C++17) (function template)
exclusive_scan similar to std::partial_sum, excludes the ith input element
(C++17) from the ith sum
(function template)