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 (12)) 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 ith input element is included in the ith sum.
Formally, assigns through each iterator i
in [
d_first
,
d_first + (last  first)
)
the value of:
*j...
for every j
in [
first
,
first + (i  d_first + 1)
)
over binary_op
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:
In other words, the summation operations may be performed in arbitrary order, and the behavior is nondeterministic if binary_op
is not associative. Overloads.
policy
. These overloads do not participate in overload resolution unless
 (until C++20) 
 (since C++20) 
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.
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. 
Iterator to the element past the last element written.
O(last  first) applications of the binary operation.
The overloads with a template parameter named ExecutionPolicy
report errors as follows:
ExecutionPolicy
is one of the standard policies, std::terminate
is called. For any other ExecutionPolicy
, the behavior is implementationdefined. std::bad_alloc
is thrown. #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
computes the differences between adjacent elements in a range (function template) 

sums up or folds a range of elements (function template) 

computes the partial sum of a range of elements (function template) 

(C++17)  applies an invocable, then calculates inclusive scan (function template) 
(C++17)  similar to std::partial_sum , excludes the ith input element from the ith sum (function template) 
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