Difference between revisions of "cpp/algorithm/partial sum"

Latest revision as of 05:02, 14 September 2024

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++20)binary_op(std::move(acc), *iter)(since C++20) 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.

[edit] Parameters

[edit] Return value

Iterator to the element past the last element written, or d_first if [first, last) is empty.

[edit] Complexity

Given \(\scriptsize N\)N as std::distance(first, last):

[edit] Possible implementation

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<>());
}

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++20
        *++d_first = acc;
    }
 
    return ++d_first;
}

[edit] 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>{});

[edit] Example

#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

[edit] Defect reports

The following behavior-changing defect reports were applied retroactively to previously published C++ standards.

[edit] See also