std::partial_sum() algorithm
- since C++20
- until C++20
// (1)
template< class InputIt, class OutputIt >
constexpr OutputIt partial_sum( InputIt first, InputIt last, OutputIt d_first );
// (2)
template< class InputIt, class OutputIt, class BinaryOperation >
constexpr OutputIt partial_sum( InputIt first, InputIt last, OutputIt d_first, BinaryOperation op );
// (1)
template< class InputIt, class OutputIt >
OutputIt partial_sum( InputIt first, InputIt last, OutputIt d_first );
// (2)
template< class InputIt, class OutputIt, class BinaryOperation >
OutputIt partial_sum( InputIt first, InputIt last, OutputIt d_first, BinaryOperation op );
If [first
; last
) is not empty, computes the partial sums of the elements in its subranges and writes the sums to the range beginning at d_first
, both applying std::move
to their operands on the left hand side (since C++11).
- (1) Uses
operator+
to sum up the elements. Equivalent to:
std::iterator_traits<InputIt>::value_type acc = *first;
*d_first = acc;
acc = std::move(acc) + *(first + 1);
*(d_first + 1) = acc;
acc = std::move(acc) + *(first + 2);
*(d_first + 2) = acc;
acc = std::move(acc) + *(first + 3);
*(d_first + 3) = acc;
// ...
- (2) Uses the given binary function op. Equivalent to:
std::iterator_traits<InputIt>::value_type acc = *first;
*d_first = acc;
acc = op(std::move(acc), *(first + 1));
*(d_first + 1) = acc;
acc = op(std::move(acc), *(first + 2));
*(d_first + 2) = acc;
acc = op(std::move(acc), *(first + 3));
*(d_first + 3) = acc;
// ...
If op
invalidates any iterators (including the end iterators) or modifies any elements of the range involved, the behavior is undefined
Parameters
first last | The range of elements to fold. |
init | Initial value of the fold. |
op | Binary operation function object that will be applied. The signature of the function should be equivalent to the following:
|
Type requirements
InputIt | LegacyInputIterator |
OutputIt | LegacyOutputIterator |
InputIt
's value type must be constructible from*first
.acc
must be writable tod_first
.
Return value
Iterator to the element past the last element written, or d_first
if [first
; last
) is empty.
Complexity
Given N
as std::distance(first, last) - 1
:
- (1) Exactly
N
applications ofoperator+
. - (2) Exactly
N
applications of the binary functionop
.
Exceptions
(none)
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 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 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 calculating the differences 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-
orop
- The return type of
operator-
orop
acc
serves as the intermediate object to cache values of the iterated elements:
- Its type is the value type of
InputIt
- The value written to
d_first
(which is the return value ofoperator-
orop
) is assigned to it - Its value is passed to
operator-
orop
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>{});
Examples
#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';
}
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
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