std::inclusive_scan

 

C++

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Freestanding and hosted

Language

Standard library

Standard library headers

Named requirements

Feature test macros (C++20)

Language support library

Concepts library (C++20)

Metaprogramming library (C++11)

Diagnostics library

General utilities library

Strings library

Containers library

Iterators library

Ranges library (C++20)

Algorithms library

Numerics library

Localizations library

Input/output library

Filesystem library (C++17)

Regular expressions library (C++11)

Concurrency support library (C++11)

Execution support library (C++26)

Technical specifications

Symbols index

External libraries

 

Algorithm library

Constrained algorithms and algorithms on ranges (C++20)
Constrained algorithms, e.g. ranges::copy, ranges::sort, ...
Execution policies (C++17)
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)
Non-modifying sequence operations Batch operations for_each for_each_n (C++17) Search operations all_ofany_ofnone_of (C++11)                (C++11)(C++11) countcount_if mismatch equal findfind_iffind_if_not (C++11) find_end find_first_of adjacent_find search search_n Modifying sequence operations Copy operations copycopy_if (C++11) copy_backward copy_n (C++11) move (C++11) move_backward (C++11) Swap operations swap iter_swap swap_ranges Transformation operations replacereplace_if transform replace_copyreplace_copy_if Generation operations fill fill_n generate generate_n Removing operations removeremove_if unique remove_copyremove_copy_if unique_copy Order-changing operations reverse reverse_copy rotate rotate_copy random_shuffleshuffle (until C++17)(C++11) shift_leftshift_right (C++20)(C++20) Sampling operations sample (C++17)	Sorting and related operations Partitioning operations partition partition_copy (C++11)   stable_partition is_partitioned (C++11) partition_point (C++11) Sorting operations sort stable_sort partial_sort partial_sort_copy is_sorted (C++11) is_sorted_until (C++11) nth_element Binary search operations (on partitioned ranges) lower_bound upper_bound equal_range binary_search Set operations (on sorted ranges) includes set_union set_intersection set_difference set_symmetric_difference Merge operations (on sorted ranges) merge inplace_merge Heap operations push_heap pop_heap make_heap sort_heap is_heap (C++11) is_heap_until (C++11) Minimum/maximum operations max min minmax (C++11) clamp (C++17) max_element min_element minmax_element (C++11) Lexicographical comparison operations lexicographical_compare lexicographical_compare_three_way (C++20) Permutation operations next_permutation prev_permutation is_permutation (C++11) C library qsort bsearch
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)
Operations on uninitialized memory
uninitialized_copy uninitialized_move (C++17)    uninitialized_fill uninitialized_copy_n (C++11) uninitialized_move_n (C++17) uninitialized_fill_n	destroy (C++17) destroy_n (C++17) destroy_at (C++17) construct_at (C++20)       uninitialized_default_construct (C++17) uninitialized_value_construct (C++17) uninitialized_default_construct_n (C++17) uninitialized_value_construct_n (C++17)

 

Numerics library

Common mathematical functions
Mathematical special functions (C++17)
Mathematical constants (C++20)
Basic linear algebra algorithms (C++26)
Floating-point environment (C++11)
Complex numbers
Numeric array (valarray)
Pseudo-random number generation
Factor operations
gcd (C++17)	lcm (C++17)
Interpolations
midpoint (C++20)	lerp (C++20)
Saturation arithmetic
add_sat (C++26) sub_sat (C++26) saturate_cast (C++26)	mul_sat (C++26) div_sat (C++26)
Generic numeric operations
iota (C++11) ranges::iota (C++23) accumulate inner_product adjacent_difference partial_sum	reduce (C++17) transform_reduce (C++17) inclusive_scan (C++17) exclusive_scan (C++17) transform_inclusive_scan (C++17) transform_exclusive_scan (C++17)
Bit operations
has_single_bit (C++20)     bit_cast (C++20) bit_ceil (C++20) bit_floor (C++20) bit_width (C++20) rotl (C++20) rotr (C++20)	popcount (C++20) countl_zero (C++20) countl_one (C++20) countr_zero (C++20) countr_one (C++20) byteswap (C++23) endian (C++20)

 

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 [​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 ith 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 ith 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
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.

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

adjacent_difference	computes the differences between adjacent elements in a 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 (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)