std::inclusive_scan

 

C++

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Algorithm library

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Constrained algorithms, e.g. ranges::copy, ranges::sort, ...
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is_execution_policy (C++17)	execution::seqexecution::parexecution::par_unseqexecution::unseq (C++17)(C++17)(C++17)(C++20)	execution::sequenced_policyexecution::parallel_policyexecution::parallel_unsequenced_policyexecution::parallel_unsequenced (C++17)(C++17)(C++17)(C++20)
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all_ofany_ofnone_of (C++11)(C++11)(C++11) for_each for_each_n (C++17)	countcount_if mismatch equal adjacent_find	search search_n lexicographical_compare lexicographical_compare_three_way (C++20)	findfind_iffind_if_not (C++11) find_end find_first_of
Modifying sequence operations
copycopy_if (C++11) copy_n (C++11) copy_backward move (C++11) move_backward (C++11) shift_leftshift_right (C++20)(C++20) transform	fill fill_n generate generate_n swap iter_swap swap_ranges sample (C++17)	removeremove_if replacereplace_if reverse rotate unique random_shuffle (until C++17)	remove_copyremove_copy_if replace_copyreplace_copy_if reverse_copy rotate_copy unique_copy shuffle (C++11)
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is_partitioned (C++11) partition_point (C++11)	partition partition_copy (C++11)	stable_partition
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is_sorted (C++11) is_sorted_until (C++11)	sort stable_sort	partial_sort partial_sort_copy	nth_element
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Permutations
is_permutation (C++11)	next_permutation	prev_permutation
Numeric operations
iota (C++11) inner_product adjacent_difference	accumulate reduce (C++17) transform_reduce (C++17)	transform_inclusive_scan (C++17) transform_exclusive_scan (C++17)	partial_sum inclusive_scan (C++17) exclusive_scan (C++17)
Operations on uninitialized storage
uninitialized_copy uninitialized_move (C++17) uninitialized_fill	uninitialized_copy_n (C++11) uninitialized_move_n (C++17) uninitialized_fill_n	uninitialized_default_construct (C++17) uninitialized_value_construct (C++17) uninitialized_default_construct_n (C++17) uninitialized_value_construct_n (C++17)	destroy (C++17) destroy_n (C++17) destroy_at (C++17) construct_at (C++20)
C library
qsort	bsearch

 

Defined in header <numeric>
	(1)
template< class InputIt, class OutputIt > OutputIt inclusive_scan( InputIt first,                          InputIt last, OutputIt d_first );			(since C++17) (until C++20)
template< class InputIt, class OutputIt > constexpr OutputIt inclusive_scan( InputIt first,                                    InputIt last, OutputIt d_first );			(since C++20)
template< class ExecutionPolicy, class ForwardIt1, class ForwardIt2 > ForwardtIt2 inclusive_scan( ExecutionPolicy&& policy, ForwardIt1 first,                             ForwardIt1 last, ForwardIt2 d_first );		(2)	(since C++17)
		(3)
template< class InputIt, class OutputIt, class BinaryOperation > OutputIt inclusive_scan( InputIt first, InputIt last,                          OutputIt d_first, BinaryOperation binary_op );				(since C++17) (until C++20)
template< class InputIt, class OutputIt, class BinaryOperation > constexpr OutputIt inclusive_scan( InputIt first, InputIt last,                                    OutputIt d_first, BinaryOperation binary_op );				(since C++20)
template< class ExecutionPolicy, class ForwardIt1, class ForwardIt2,           class BinaryOperation > ForwardIt2 inclusive_scan( ExecutionPolicy&& policy,                            ForwardIt1 first, ForwardIt1 last,                            ForwardIt2 d_first, BinaryOperation binary_op );			(4)	(since C++17)
			(5)
template< class InputIt, class OutputIt, class BinaryOperation, class T > OutputIt inclusive_scan( InputIt first, InputIt last, OutputIt d_first,                          BinaryOperation binary_op, T init );					(since C++17) (until C++20)
template< class InputIt, class OutputIt, class BinaryOperation, class T > constexpr OutputIt inclusive_scan( InputIt first, InputIt last, OutputIt d_first,                                    BinaryOperation binary_op, T init );					(since C++20)
template< class ExecutionPolicy, class ForwardIt1, class ForwardIt2,           class BinaryOperation, class T > ForwardIt2 inclusive_scan( ExecutionPolicy&& policy,                            ForwardIt1 first, ForwardIt1 last, ForwardIt2 d_first,                            BinaryOperation binary_op, T init );				(6)	(since C++17)

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_op	-	binary FunctionObject that will be applied in to the result of 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

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