std::transform_inclusive_scan

 

C++

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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)

 

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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>
	(1)
template< class InputIt, class OutputIt,           class BinaryOperation, class UnaryOperation > OutputIt transform_inclusive_scan( InputIt first, InputIt last,                                    OutputIt d_first,                                    BinaryOperation binary_op,                                    UnaryOperation unary_op );			(since C++17) (until C++20)
template< class InputIt, class OutputIt,           class BinaryOperation, class UnaryOperation > constexpr OutputIt transform_inclusive_scan( InputIt first, InputIt last,                                              OutputIt d_first,                                              BinaryOperation binary_op,                                              UnaryOperation unary_op );			(since C++20)
template< class ExecutionPolicy, class ForwardIt1, class ForwardIt2,           class BinaryOperation, class UnaryOperation > ForwardIt2 transform_inclusive_scan( ExecutionPolicy&& policy,                                      ForwardIt1 first, ForwardIt1 last,                                      ForwardIt2 d_first,                                      BinaryOperation binary_op,                                      UnaryOperation unary_op );		(2)	(since C++17)
		(3)
template< class InputIt, class OutputIt,           class BinaryOperation, class UnaryOperation, class T > OutputIt transform_inclusive_scan( InputIt first, InputIt last,                                    OutputIt d_first,                                    BinaryOperation binary_op,                                    UnaryOperation unary_op,                                    T init );				(since C++17) (until C++20)
template< class InputIt, class OutputIt,           class BinaryOperation, class UnaryOperation, class T > constexpr OutputIt transform_inclusive_scan( InputIt first, InputIt last,                                              OutputIt d_first,                                              BinaryOperation binary_op,                                              UnaryOperation unary_op,                                              T init );				(since C++20)
template< class ExecutionPolicy, class ForwardIt1, class ForwardIt2,           class BinaryOperation, class UnaryOperation, class T > ForwardIt2 transform_inclusive_scan( ExecutionPolicy&& policy,                                      ForwardIt1 first, ForwardIt1 last,                                      ForwardIt2 d_first,                                      BinaryOperation binary_op,                                      UnaryOperation unary_op,                                      T init );			(4)	(since C++17)

Transforms each element in the range [first, last) with unary_op, then computes an inclusive prefix sum operation using binary_op over the resulting range, optionally with init as the initial value, 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 (1,2), the generalized noncommutative sum of unary_op(*j)... for every j in [first, first + (i - d_first + 1)) over binary_op,
• for overloads (3,4), the generalized noncommutative sum of init, unary_op(*j)... for every j in [first, first + (i - d_first + 1)) over binary_op,

where generalized noncommutative sum GNSUM(op, a1, ..., aN) is defined as follows:

• if N = 1, a1
• if N > 1, op(GNSUM(op, a1, ..., aK), GNSUM(op, aM, ..., aN)) 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) are 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)

unary_op and 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
unary_op	-	unary FunctionObject that will be applied to each element of the input range. The return type must be acceptable as input to binary_op.
binary_op	-	binary FunctionObject that will be applied in to the result of unary_op, 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(unary_op(*first), unary_op(*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, unary_op(*first)), binary_op(init, init), and binary_op(unary_op(*first), unary_op(*first)) must be convertible to T.

Return value

Iterator to the element past the last element written.

Complexity

O(last - first) applications of each of binary_op and unary_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.

Notes

unary_op is not applied to init.

The parameter init appears last, differing from std::transform_exclusive_scan, because it is optional for this function.

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};
 
    auto times_10 = [](int x) { return x * 10; };
 
    std::cout << "10 times exclusive sum: ";
    std::transform_exclusive_scan(data.begin(), data.end(),
                                  std::ostream_iterator<int>(std::cout, " "),
                                  0, std::plus<int>{}, times_10);
    std::cout << "\n10 times inclusive sum: ";
    std::transform_inclusive_scan(data.begin(), data.end(),
                                  std::ostream_iterator<int>(std::cout, " "),
                                  std::plus<int>{}, times_10);
    std::cout << '\n';
}

Output:

10 times exclusive sum: 0 30 40 80 90 140 230 250 
10 times inclusive sum: 30 40 80 90 140 230 250 310

See also

partial_sum	computes the partial sum of a range of elements (function template)
transform	applies a function to a range of elements, storing results in a destination range (function template)
inclusive_scan (C++17)	similar to std::partial_sum, includes the ith input element in the ith sum (function template)
transform_exclusive_scan (C++17)	applies an invocable, then calculates exclusive scan (function template)