home | help 
std::partial_sum(3)	       C++ Standard Libary	     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 In-
     putIt.
	  * 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. a 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 implic-
     itly 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 rea-
     son 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 aacca of type char (the value type)
      // 2. the char arguments are used for long multiplication (char -> long)
      // 3. the long product is assigned to aacca (long -> char)
      // 4. aacca is assigned to an element of ao_arraya (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	retroac-
     tively to
	previously published C++ standards.

	   DR	   Applied  to		 Behavior as published		    Cor-
     rect behavior
	LWG 242   C++98      op could not have side effects		it  can-
     not 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)

http://cppreference.com 	   2024.06.10		     std::partial_sum(3)
home | help