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, InputIt last, (1) (constexpr since C++20)

OutputIt d_first );
template< class ExecutionPolicy,

class ForwardIt1, class ForwardIt2 >
ForwardIt2 inclusive_scan( ExecutionPolicy&& policy, (2) (since C++17)
ForwardIt1 first, ForwardIt1
last,

ForwardIt2 d_first );
template< class InputIt, class OutputIt, class BinaryOp
>
(since C++17)
OutputIt inclusive_scan( InputIt first, InputIt last, (3) (constexpr since C++20)

OutputIt d_first, BinaryOp op
);
template< class ExecutionPolicy,

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

ForwardIt2 d_first, BinaryOp
op );
template< class InputIt, class OutputIt,

class BinaryOp, class T > (since C++17)
OutputIt inclusive_scan( InputIt first, InputIt last, (5) (constexpr since C++20)

OutputIt d_first, BinaryOp op,
T init );
template< class ExecutionPolicy,

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

ForwardIt2 d_first, BinaryOp
op, T init );

1) Equivalent to inclusive_scan(first, last, d_first, std::plus<>().
3) Computes the inclusive prefix sum using op.
For each integer i in [0, std::distance(first, last)), performs the following
operations in order:
1. Creates a sequence which is formed by the elements of [first, iter] in order,
where iter is the next i
th iterator of first.
2. Computes the generalized noncommutative sum of the sequence over op.
3. Assigns the result to *dest, where dest is the next i
th iterator of d_first.
5) Same as (3), but each sequence created is formed by init followed by the elements
of [first, iter] in order.
2,4,6) Same as (1,3,5), but executed according to policy.
These overloads participate in overload resolution only if

std::is_execution_policy_v<std::decay_t<ExecutionPolicy>> is true. (until
C++20)
std::is_execution_policy_v<std::remove_cvref_t<ExecutionPolicy>> is true. (since
C++20)

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].

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
binary FunctionObject that will be applied in to the result of
op - dereferencing the input iterators, the results of other op, and init
(if provided)

Type requirements¶

-
InputIt must meet the requirements of LegacyInputIterator.
-
OutputIt must meet the requirements of LegacyOutputIterator.
-
ForwardIt1, ForwardIt2 must meet the requirements of LegacyForwardIterator.

Return value¶

Iterator to the element past the last element written.

Complexity¶

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

1,2) \(\scriptsize O(N)\)O(N) applications of std::plus<>().
3-6) \(\scriptsize O(N)\)O(N) applications of op.

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 or folds 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 i^th input
(C++17) element from the i^th sum
(function template)