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

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{{par begin}}
 
{{par begin}}
 
{{par | first, last | the range of elements to sum}}
 
{{par | first, last | the range of elements to sum}}
−
{{par | d_first | the beginning of the destination range}}
+
{{par | d_first | the beginning of the destination range; may be equal to {{tt|first}}}}
 
{{par op2 | op | t1=iterator_traits<InputIt>::value_type | p2=InputIt | rt=iterator_traits<InputIt>::value_type}}
 
{{par op2 | op | t1=iterator_traits<InputIt>::value_type | p2=InputIt | rt=iterator_traits<InputIt>::value_type}}
 
{{par hreq}}
 
{{par hreq}}
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===Complexity===
 
===Complexity===
 
Exactly {{tt|(last - first) - 1}} applications of the binary operation
 
Exactly {{tt|(last - first) - 1}} applications of the binary operation
−
 
−
===Notes===
 
−
{{tt|d_first}} may be equal to {{tt|first}}
 
 
   
 
   
 
===Possible implementation===
 
===Possible implementation===

Revision as of 17:28, 14 June 2016

 
C++
 
Algorithm library
Constrained algorithms and algorithms on ranges (C++20)
Constrained algorithms, e.g. ranges::copy, ranges::sort, ...
Execution policies (C++17)
Non-modifying sequence operations
Batch operations
(C++17)
Search operations
(C++11)                (C++11)(C++11)

Modifying sequence operations
Copy operations
(C++11)
(C++11)
(C++11)
Swap operations
Transformation operations
Generation operations
Removing operations
Order-changing operations
(until C++17)(C++11)
(C++20)(C++20)
Sampling operations
(C++17)

Sorting and related operations
Partitioning operations
Sorting operations
Binary search operations
(on partitioned ranges)
Set operations (on sorted ranges)
Merge operations (on sorted ranges)
Heap operations
Minimum/maximum operations
(C++11)
(C++17)
Lexicographical comparison operations
(C++20)
Permutation operations
C library
Numeric operations
partial_sum
(C++17)   
(C++17)
Operations on uninitialized memory
 
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)

Contents

Parameters

first, last - the range of elements to sum
d_first - the beginning of the destination range; may be equal to first
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

Template:par req concept Template:par req concept

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

 computes the differences between adjacent elements in a range
(function template) [edit]
sums up or folds a range of elements
(function template) [edit]
(C++17)
 similar to std::partial_sum, includes the ith input element in the ith sum
(function template) [edit]
(C++17)
 similar to std::partial_sum, excludes the ith input element from the ith sum
(function template) [edit]
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