std::partial_sum(3)

NAME
std::partial_sum - std::partial_sum

Synopsis
   Defined in header <numeric>
   template< class InputIt, class OutputIt >
   OutputIt partial_sum( InputIt first, InputIt (until C++20)
   last, OutputIt d_first );
   template< class InputIt, class OutputIt >
   constexpr OutputIt partial_sum( InputIt first, (since C++20)
   InputIt last, OutputIt d_first );
   template< class InputIt, class OutputIt, class
   BinaryOperation >
   OutputIt partial_sum( InputIt first, InputIt (1) (until C++20)
   last, OutputIt d_first,
   BinaryOperation op ); (2)
   template< class InputIt, class OutputIt, class
   BinaryOperation >
   constexpr OutputIt partial_sum( InputIt first, (since C++20)
   InputIt last, OutputIt d_first,
   BinaryOperation op );
   Computes the partial sums of the elements in the subranges of the range [first,
   last) and writes them to the range beginning at d_first. The first version uses
   operator+ to sum up the elements, the second version uses the given binary function
   op
   , both applying std::move to their operands on the left hand side
   (since C++20).
   Equivalent operation:
 *(d_first) = *first;
 *(d_first+1) = *first + *(first+1);
 *(d_first+2) = *first + *(first+1) + *(first+2);
 *(d_first+3) = *first + *(first+1) + *(first+2) + *(first+3);
 ...
   op must not have side effects. (until C++11)
   op must not invalidate any iterators, including the end iterators, or (since C++11)
   modify any elements of the range involved.

Parameters
   first, last - the range of elements to sum
   d_first - the beginning of the destination range; may be equal to first
                 binary operation function object that will be applied.
                 The signature of the function should be equivalent to the following:
                 Ret fun(const Type1 &a, const Type2 &b);
   op - The signature does not need to have const &.
                 The type Type1 must be such that an object of type
                 iterator_traits<InputIt>::value_type can be implicitly converted to
                 Type1. The type Type2 must be such that an object of type InputIt can
                 be dereferenced and then implicitly converted to Type2. The type Ret
                 must be such that an object of type
                 iterator_traits<InputIt>::value_type can be assigned a value of type
                 Ret.

Type requirements
   -
   InputIt must meet the requirements of LegacyInputIterator.
   -
   OutputIt must meet the requirements of LegacyOutputIterator.

Return value
   Iterator to the element past the last element written.

Complexity
   Exactly (last - first) - 1 applications of the binary operation

Possible implementation

First version
   template<class InputIt, class OutputIt>
   constexpr // since C++20
   OutputIt partial_sum(InputIt first, InputIt last,
                        OutputIt d_first)
   {
       if (first == last) return d_first;
       typename std::iterator_traits<InputIt>::value_type sum = *first;
       *d_first = sum;
       while (++first != last) {
          sum = std::move(sum) + *first; // std::move since C++20
          *++d_first = sum;
       }
       return ++d_first;
       // or, since C++14:
       // return std::partial_sum(first, last, d_first, std::plus<>());
   }

Second version
   template<class InputIt, class OutputIt, class BinaryOperation>
   constexpr // since C++20
   OutputIt partial_sum(InputIt first, InputIt last,
                        OutputIt d_first, BinaryOperation op)
   {
       if (first == last) return d_first;
       typename std::iterator_traits<InputIt>::value_type sum = *first;
       *d_first = sum;
       while (++first != last) {
          sum = op(std::move(sum), *first); // std::move since C++20
          *++d_first = sum;
       }
       return ++d_first;
   }

Example
// Run this code
 #include <numeric>
 #include <vector>
 #include <iostream>
 #include <iterator>
 #include <functional>
 int main()
 {
     std::vector<int> v = {2, 2, 2, 2, 2, 2, 2, 2, 2, 2}; // or std::vector<int>v(10, 2);
     std::cout << "The first 10 even numbers are: ";
     std::partial_sum(v.begin(), v.end(),
                      std::ostream_iterator<int>(std::cout, " "));
     std::cout << '\n';
     std::partial_sum(v.begin(), v.end(), v.begin(), std::multiplies<int>());
     std::cout << "The first 10 powers of 2 are: ";
     for (auto n : v) {
         std::cout << n << " ";
     }
     std::cout << '\n';
 }

Output:
 The first 10 even numbers are: 2 4 6 8 10 12 14 16 18 20
 The first 10 powers of 2 are: 2 4 8 16 32 64 128 256 512 1024

See also
   adjacent_difference computes the differences between adjacent elements in a range
                       (function template)
   accumulate sums up a range of elements
                       (function template)
   inclusive_scan similar to std::partial_sum, includes the ith input element in
   (C++17) the ith sum
                       (function template)
   exclusive_scan similar to std::partial_sum, excludes the ith input element from
   (C++17) the ith sum
                       (function template)