std::partial_sum

 

C++

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Technical Specifications

 

Algorithm library

Functions
Non-modifying sequence operations
all_ofany_ofnone_of (C++11)(C++11)(C++11) for_each countcount_if mismatch equal	findfind_iffind_if_not (C++11) find_end find_first_of adjacent_find search search_n
Modifying sequence operations
copycopy_if (C++11) copy_n (C++11) copy_backward move (C++11) move_backward (C++11) fill fill_n transform generate generate_n removeremove_if remove_copyremove_copy_if	replacereplace_if replace_copyreplace_copy_if swap swap_ranges iter_swap reverse reverse_copy rotate rotate_copy random_shuffleshuffle (until C++17)(C++11) unique unique_copy
Partitioning operations
is_partitioned (C++11) partition partition_copy (C++11)	stable_partition partition_point (C++11)
Sorting operations (on sorted ranges)
is_sorted (C++11) is_sorted_until (C++11) sort	partial_sort partial_sort_copy stable_sort nth_element
Binary search operations (on sorted ranges)
lower_bound upper_bound	binary_search equal_range
Set operations (on sorted ranges)
merge inplace_merge includes	set_difference set_intersection set_symmetric_difference set_union
Heap operations
is_heap (C++11) is_heap_until (C++11) make_heap	push_heap pop_heap sort_heap
Minimum/maximum operations
max max_element min min_element minmax (C++11) minmax_element (C++11)	lexicographical_compare is_permutation (C++11) next_permutation prev_permutation
Numeric operations
iota (C++11) accumulate inner_product	adjacent_difference partial_sum
C library
qsort	bsearch

 

Defined in header <numeric>
template< class InputIt, class OutputIt > OutputIt partial_sum( InputIt first, InputIt last, OutputIt d_first );	(1)
template< class InputIt, class OutputIt, class BinaryOperation > OutputIt partial_sum( InputIt first, InputIt last, OutputIt d_first,                       BinaryOperation op );	(2)

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.

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 modify any elements of the ranges involved.	(since C++11)

Parameters

first, last	-	the range of elements to sum
d_first	-	the beginning of the destination range
op	-	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); 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 InputIterator.
- OutputIt must meet the requirements of OutputIterator.

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> 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 = sum + *first; *++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> 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(sum, *first); *++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 (parallelism TS)	similar to std::partial_sum, includes the ith input element in the ith sum (function template)
exclusive_scan (parallelism TS)	similar to std::partial_sum, excludes the ith input element from the ith sum (function template)