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std::inclusive_scan

From cppreference.com
< cpp‎ | algorithm
 
 
Algorithm library
Constrained algorithms and algorithms on ranges (C++20)
Concepts and utilities: std::Sortable, std::projected, ...
Constrained algorithms: std::ranges::copy, std::ranges::sort, ...
Execution policies (C++17)
Non-modifying sequence operations
(C++11)(C++11)(C++11)
(C++17)
Modifying sequence operations
Operations on uninitialized storage
Partitioning operations
Sorting operations
(C++11)
Binary search operations
Set operations (on sorted ranges)
Heap operations
(C++11)
Minimum/maximum operations
(C++11)
(C++17)

Permutations
Numeric operations
inclusive_scan
(C++17)
C library
 
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.

Contents

[edit] 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

[edit] Return value

Iterator to the element past the last element written.

[edit] Complexity

O(last - first) applications of the binary operation

[edit] 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.

[edit] Example

#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

[edit] See also

computes the differences between adjacent elements in a range
(function template) [edit]
sums up a range of elements
(function template) [edit]
computes the partial sum of a range of elements
(function template) [edit]
applies a functor, then calculates inclusive scan
(function template) [edit]
similar to std::partial_sum, excludes the ith input element from the ith sum
(function template) [edit]