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std::inclusive_scan

From cppreference.com
< cpp‎ | algorithm
 
 
Algorithm library
Constrained algorithms and algorithms on ranges (C++20)
Constrained algorithms, e.g. ranges::copy, ranges::sort, ...
Execution policies (C++17)
Non-modifying sequence operations
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(C++17)
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(C++11)                (C++11)(C++11)

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(C++11)
(C++11)
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(until C++17)(C++11)
(C++20)(C++20)
Sampling operations
(C++17)

Sorting and related operations
Partitioning operations
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(on partitioned ranges)
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(C++11)
(C++17)
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C library
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inclusive_scan
(C++17)   
Operations on uninitialized memory
 
 
Defined in header <numeric>
template< class InputIt, class OutputIt >

OutputIt inclusive_scan( InputIt first, InputIt last,

                         OutputIt d_first );
(1) (since C++17)
(constexpr since C++20)
template< class ExecutionPolicy,

          class ForwardIt1, class ForwardIt2 >
ForwardIt2 inclusive_scan( ExecutionPolicy&& policy,
                           ForwardIt1 first, ForwardIt1 last,

                           ForwardIt2 d_first );
(2) (since C++17)
template< class InputIt, class OutputIt, class BinaryOp >

OutputIt inclusive_scan( InputIt first, InputIt last,

                         OutputIt d_first, BinaryOp op );
(3) (since C++17)
(constexpr since C++20)
template< class ExecutionPolicy,

          class ForwardIt1, class ForwardIt2, class BinaryOp >
ForwardIt2 inclusive_scan( ExecutionPolicy&& policy,
                           ForwardIt1 first, ForwardIt1 last,

                           ForwardIt2 d_first, BinaryOp op );
(4) (since C++17)
template< class InputIt, class OutputIt,

          class BinaryOp, class T >
OutputIt inclusive_scan( InputIt first, InputIt last,

                         OutputIt d_first, BinaryOp op, T init );
(5) (since C++17)
(constexpr since C++20)
template< class ExecutionPolicy,

          class ForwardIt1, class ForwardIt2,
          class BinaryOp, class T >
ForwardIt2 inclusive_scan( ExecutionPolicy&& policy,
                           ForwardIt1 first, ForwardIt1 last,

                           ForwardIt2 d_first, BinaryOp op, T init );
(6) (since C++17)
1) Equivalent to inclusive_scan(first, last, d_first, std::plus<>().
3) Computes the inclusive prefix sum using op.
For each integer i in [0std::distance(first, last)), performs the following operations in order:
  1. Creates a sequence which is formed by the elements of [firstiter] 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 [firstiter] 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 [firstlast).
  • binary_op invalidates any iterator or subrange of [firstlast].

Contents

[edit] 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
op - binary FunctionObject that will be applied in to the result of 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.

[edit] Return value

Iterator to the element past the last element written.

[edit] Complexity

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

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

[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<>{});
}

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

[edit] See also

computes the differences between adjacent elements in a range
(function template) [edit]
sums up or folds a range of elements
(function template) [edit]
computes the partial sum of a range of elements
(function template) [edit]
applies an invocable, then calculates inclusive scan
(function template) [edit]
similar to std::partial_sum, excludes the ith input element from the ith sum
(function template) [edit]