std::inclusive_scan

 

C++

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Technical Specifications

 

Algorithm library

Execution policies (C++17)
is_execution_policy	execution::seqexecution::parexecution::par_unseq	execution::sequenced_policyexecution::parallel_policyexecution::parallel_unsequenced_policy
Non-modifying sequence operations
all_ofany_ofnone_of (C++11)(C++11)(C++11) for_each for_each_n (C++17)	countcount_if mismatch equal adjacent_find	findfind_iffind_if_not (C++11) find_end find_first_of	search search_n lexicographical_compare lexicographical_compare_3way (C++20)
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)
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) destroy (C++17)	uninitialized_default_construct_n (C++17) uninitialized_value_construct_n (C++17) destroy_n (C++17)
Partitioning operations
is_partitioned (C++11) partition_point (C++11)	partition partition_copy (C++11)	stable_partition
Sorting operations
is_sorted (C++11) is_sorted_until (C++11)	sort stable_sort	partial_sort partial_sort_copy	nth_element
Binary search operations
lower_bound	upper_bound	binary_search	equal_range
Set operations (on sorted ranges)
merge inplace_merge	set_difference set_intersection	set_symmetric_difference set_union	includes
Heap operations
is_heap (C++11) is_heap_until (C++11)	make_heap sort_heap	push_heap pop_heap
Minimum/maximum operations
max max_element	min min_element	minmax (C++11) minmax_element (C++11)	clamp (C++17) compare_3way (C++20)
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)	partial_sum inclusive_scan (C++17) exclusive_scan (C++17)	transform_inclusive_scan (C++17) transform_exclusive_scan (C++17)
C library
qsort	bsearch

 

Defined in header <numeric>
template< class InputIt, class OutputIt > OutputIt inclusive_scan( InputIt first,                          InputIt last, OutputIt d_first );	(1)	(since C++17)
template< class ExecutionPolicy, class ForwardIt1, class ForwardIt2 > ForwardtIt2 inclusive_scan( ExecutionPolicy&& policy, ForwardIt1 first,                             ForwardIt1 last, ForwardIt2 d_first );	(2)	(since C++17)
template< class InputIt, class OutputIt, class BinaryOperation > OutputIt inclusive_scan( InputIt first, InputIt last,                          OutputIt d_first, BinaryOperation binary_op );	(3)	(since C++17)
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)
template< class InputIt, class OutputIt, class BinaryOperation, class T > OutputIt inclusive_scan( InputIt first, InputIt last, OutputIt d_first,                          BinaryOperation binary_op, T init );	(5)	(since C++17)
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. This overload only participates in overload resolution if std::is_execution_policy_v<std::decay_t<ExecutionPolicy>> 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. and, if init is not provided, ForwardIt1's value_type must be MoveConstructible and binary_op(*first, *first) must be convertible to ForwardIt1's value type
- ForwardIt2 must meet the requirements of LegacyForwardIterator.
- 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 three 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.

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 a functor, 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)