< 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
Modifying sequence operations
Operations on uninitialized storage
Partitioning operations
Sorting operations
Binary search operations
Set operations (on sorted ranges)
Heap operations
Minimum/maximum operations
Numeric operations

C library
Defined in header <numeric>
template< class InputIt, class OutputIt, class T,

          class BinaryOperation, class UnaryOperation>
OutputIt transform_exclusive_scan( InputIt first, InputIt last, OutputIt d_first, T init,

                                   BinaryOperation binary_op, UnaryOperation unary_op);
(1) (since C++17)
template< class ExecutionPolicy,

          class ForwardIt1, class ForwardIt2,
          class T, class BinaryOperation, class UnaryOperation >
ForwardIt2 transform_exclusive_scan( ExecutionPolicy&& policy,
                                     ForwardIt1 first, ForwardIt1 last,
                                     ForwardIt2 d_first, T init,

                                     BinaryOperation binary_op, UnaryOperation unary_op );
(2) (since C++17)

Transforms each element in the range [first, last) with unary_op, then computes an exclusive prefix sum operation using binary_op over the resulting range, with init as the initial value, and writes the results to the range beginning at d_first. "exclusive" means that the i-th input element is not included in the i-th sum.

Formally, assigns through each iterator i in [d_first, d_first + (last - first)) the value of the generalized noncommutative sum of init, unary_op(*j)... for every j in [first, first + (i - d_first)) over binary_op,

where generalized noncommutative sum GNSUM(op, a
, ..., a
is defined as follows:

  • if N=1, a
  • if N > 1, op(GNSUM(op, a
    , ..., a
    ), GNSUM(op, a
    , ..., a
    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.

Overload (2) is executed according to policy, and does not participate in overload resolution unless std::is_execution_policy_v<std::decay_t<ExecutionPolicy>> is true.

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.


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.
Type requirements
InputIt must meet the requirements of LegacyInputIterator.
OutputIt must meet the requirements of LegacyOutputIterator.
ForwardIt1, ForwardIt2 must meet the requirements of LegacyForwardIterator.
T 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.


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


The overload with a template parameter named ExecutionPolicy reports 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.


unary_op is not applied to init.


#include <functional>
#include <iostream>
#include <iterator>
#include <numeric>
#include <vector>
int times_10(int x)
  return x * 10;
int main()
  std::vector data {3, 1, 4, 1, 5, 9, 2, 6};
  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);


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

computes the partial sum of a range of elements
(function template)
similar to std::partial_sum, excludes the ith input element from the ith sum
(function template)
applies a functor, then calculates inclusive scan
(function template)