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    std::exclusive_scan

    From cppreference.com
     
    C++
     
    Algorithm library
    Constrained algorithms and algorithms on ranges (C++20)
    Constrained algorithms, e.g. ranges::copy, ranges::sort, ...
    Execution policies (C++17)
    Non-modifying sequence operations
    Batch operations
    (C++17)
    Search operations
    (C++11)                (C++11)(C++11)

    Modifying sequence operations
    Copy operations
    (C++11)
    (C++11)
    (C++11)
    Swap operations
    Transformation operations
    Generation operations
    Removing operations
    Order-changing operations
    (until C++17)(C++11)
    (C++20)(C++20)
    Sampling operations
    (C++17)

    Sorting and related operations
    Partitioning operations
    Sorting operations
    Binary search operations
    (on partitioned ranges)
    Set operations (on sorted ranges)
    Merge operations (on sorted ranges)
    Heap operations
    Minimum/maximum operations
    (C++11)
    (C++17)
    Lexicographical comparison operations
    (C++20)
    Permutation operations
    C library
    Numeric operations
    Operations on uninitialized memory
     
    Numerics library
     
    Defined in header <numeric>
    template< class InputIt, class OutputIt, class T > OutputIt exclusive_scan( InputIt first, InputIt last, OutputIt d_first, T init );
    		 (1) (since C++17)
    (constexpr since C++20)
    template< class ExecutionPolicy, class ForwardIt1, class ForwardIt2, class T > ForwardIt2 exclusive_scan( ExecutionPolicy&& policy, ForwardIt1 first, ForwardIt1 last, ForwardIt2 d_first, T init );
    		 (2) (since C++17)
    template< class InputIt, class OutputIt, class T, class BinaryOp > OutputIt exclusive_scan( InputIt first, InputIt last, OutputIt d_first, T init, BinaryOp op );
    		 (3) (since C++17)
    (constexpr since C++20)
    template< class ExecutionPolicy, class ForwardIt1, class ForwardIt2, class T, class BinaryOp > ForwardIt2 exclusive_scan( ExecutionPolicy&& policy, ForwardIt1 first, ForwardIt1 last, ForwardIt2 d_first, T init, BinaryOp op );
    		 (4) (since C++17)
    1) Equivalent to exclusive_scan(first, last, d_first, init, std::plus<>().
    3) Computes the exclusive 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 init followed 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.
    2,4) Same as (1,3), but executed according to policy.
    These overloads participate in overload resolution only if all following conditions are satisfied:
    See More

    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).
    • 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:
    • 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 pair of iterators defining 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
    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
    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 N as std::distance(first, last):

    1,2) O(N) applications of std::plus<>().
    3,4) 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

    		 computes the differences between adjacent elements in a range
    (function template) [edit]
    		sums up or folds a range of elements
    (function template) [edit]
    		computes the partial sum of a range of elements
    (function template) [edit]
    (C++17)
    		 applies an invocable, then calculates exclusive scan
    (function template) [edit]
    (C++17)
    		 similar to std::partial_sum, includes the ith input element in the ith sum
    (function template) [edit]