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 last, (1) (constexpr since C++20)
                        OutputIt d_first );
   template< class InputIt, class OutputIt, class BinaryOp
   >
                        (2) (constexpr since C++20)
   OutputIt partial_sum( InputIt first, InputIt last,
                        OutputIt d_first, BinaryOp op );
   1) If [first, last) is empty, does nothing.
   Otherwise, performs the following operations in order:
    1. Creates an accumulator acc, whose type is the value type of InputIt, and
       initializes it with *first.
    2. Assigns acc to *d_first.
    3. For each integer i in [1, std::distance(first, last)), performs the following
       operations in order:
   a) Computes
   acc + *iter
   (until C++11)
   std::move(acc) + *iter
   (since C++11), where iter is the next i
   th iterator of first.
   b) Assigns the result to acc.
   c) Assigns acc^[1] to *dest, where dest is the next i
   th iterator of d_first.
   2) Same as (1), but computes
   op(acc, *iter)
   (until C++11)
   op(std::move(acc), *iter)
   (since C++11) instead.
   Given binary_op as the actual binary operation:
     * If any of the following conditions is satisfied, the program is ill-formed:
     * The value type of InputIt is not constructible from *first.
     * acc is not writable to d_first.
     * The result of
       binary_op(acc, *iter)
       (until C++11)
       binary_op(std::move(acc), *iter)
       (since C++11) is not implicitly convertible to the value type of InputIt.
     * Given d_last as the iterator to be returned, if any of the following conditions
       is satisfied, the behavior is undefined:
     * binary_op modifies any element of [first, last) or [d_first, d_last).
     * binary_op invalidates any iterator or subrange in [first, last] or
       [d_first, d_last].
    1. ↑ The actual value to be assigned is the result of the assignment in the
       previous step. We assume the assignment result is acc here.

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
                 std::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 InputIt can be dereferenced
                 and 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, or d_first if [first, last)
   is empty.

Complexity
   Given \(\scriptsize N\)N as std::distance(first, last):
   1) Exactly \(\scriptsize N-1\)N-1 applications of operator+.
   2) Exactly \(\scriptsize N-1\)N-1 applications of the binary function op.

Possible implementation
                        partial_sum (1)
   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++11
           *++d_first = sum;
       }
       return ++d_first;
       // or, since C++14:
       // return std::partial_sum(first, last, d_first, std::plus<>());
   }
                        partial_sum (2)
   template<class InputIt, class OutputIt, class BinaryOp>
   constexpr // since C++20
   OutputIt partial_sum(InputIt first, InputIt last,
                        OutputIt d_first, BinaryOp op)
   {
       if (first == last)
           return d_first;
       typename std::iterator_traits<InputIt>::value_type acc = *first;
       *d_first = acc;
       while (++first != last)
       {
           acc = op(std::move(acc), *first); // std::move since C++11
           *++d_first = acc;
       }
       return ++d_first;
   }

Notes
   acc was introduced because of the resolution of LWG issue 539. The reason of using
   acc rather than directly summing up the results (i.e. *(d_first + 2) = (*first +
   *(first + 1)) + *(first + 2);) is because the semantic of the latter is confusing if
   the following types mismatch:
     * the value type of InputIt
     * the writable type(s) of OutputIt
     * the types of the parameters of operator+ or op
     * the return type of operator+ or op
   acc serves as the intermediate object to store and provide the values for each step
   of the computation:
     * its type is the value type of InputIt
     * it is written to d_first
     * its value is passed to operator+ or op
     * it stores the return value of operator+ or op
 enum not_int { x = 1, y = 2 };
 char i_array[4] = {100, 100, 100, 100};
 not_int e_array[4] = {x, x, y, y};
 int o_array[4];
 // OK: uses operator+(char, char) and assigns char values to int array
 std::partial_sum(i_array, i_array + 4, o_array);
 // Error: cannot assign not_int values to int array
 std::partial_sum(e_array, e_array + 4, o_array);
 // OK: performs conversions when needed
 // 1. creates “acc” of type char (the value type)
 // 2. the char arguments are used for long multiplication (char -> long)
 // 3. the long product is assigned to “acc” (long -> char)
 // 4. “acc” is assigned to an element of “o_array” (char -> int)
 // 5. go back to step 2 to process the remaining elements in the input range
 std::partial_sum(i_array, i_array + 4, o_array, std::multiplies<long>{});

Example
// Run this code
 #include <functional>
 #include <iostream>
 #include <iterator>
 #include <numeric>
 #include <vector>
 int main()
 {
     std::vector<int> v(10, 2); // v = {2, 2, 2, 2, 2, 2, 2, 2, 2, 2}
     std::cout << "The first " << v.size() << " even numbers are: ";
     // write the result to the cout stream
     std::partial_sum(v.cbegin(), v.cend(),
                      std::ostream_iterator<int>(std::cout, " "));
     std::cout << '\n';
     // write the result back to the vector v
     std::partial_sum(v.cbegin(), v.cend(),
                      v.begin(), std::multiplies<int>());
     std::cout << "The first " << v.size() << " powers of 2 are: ";
     for (int 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
   Defect reports
   The following behavior-changing defect reports were applied retroactively to
   previously published C++ standards.
      DR Applied to Behavior as published Correct behavior
   LWG 242 C++98 op could not have side effects it cannot modify the
                        ranges involved
                        the type requirements needed for the
   LWG 539 C++98 result added
                        evaluations and assignments to be valid
                        were missing
   LWG 2055 C++11 acc was not moved while being accumulated it is moved
   (P0616R0)

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