partial_sum

Artikel
12/17/2007

Computes a series of sums in an input range from the first element through the ith element and stores the result of each such sum in the ith element of a destination range or computes the result of a generalized procedure where the sum operation is replaced by another specified binary operation.

template<class InputIterator, class OutIt>
   OutputIterator partial_sum(
      InputIterator _First, 
      InputIterator _Last,
      OutputIterator _Result
   );

template<class InputIterator, class OutIt, class Fn2>
   OutputIterator partial_sum(
      InputIterator _First, 
      InputIterator _Last,
      OutputIterator _Result, 
      BinaryOperation _Binary_op
   );

Parameters

_First
An input iterator addressing the first element in the range to be partially summed or combined according to a specified binary operation.
_Last
An input iterator addressing the last element in the range to be partially summed or combined according to a specified binary operation that is one position beyond the final element actually included in the iterated accumulation.
_Result
An output iterator addressing the first element a destination range where the series of partial sums or the results of the specified operation is to be stored.
_Binary_op
The binary operation that is to be applied in the generalized operation replacing the operation of sum in the partial sum procedure.

Return Value

An output iterator addressing the end of the destination range: _Result + (_Last - _First),

Remarks

The output iterator _Result is allowed to be the same iterator as the input iterator _First, so that partial sums may be computed in place.

For a sequence of values a₁, a₂, a₃, in an input range, the first template function stores successive partial sums in the destination range, where the ith element is given by ( ( (a₁ + a₂) + a₃) a_i).

For a sequence of values a₁, a₂, a₃, in an input range, the second template function stores successive partial sums in the destination range, where the ith element is given by ( ( ( a₁ _Binary_op a₂ ) _Binary_op a₃ ) a_i).

The binary operation _Binary_op is not required to be either associative or commutative, because the order of operations applies is completely specified.

partial_sum has two related forms:

If you pass a checked iterator to one of the forms of partial_sum, you get checked iterator behavior. If you pass an unchecked iterator, you get unchecked behavior. For more information, see Checked Iterators.

Example

// numeric_partial_sum.cpp
// compile with: /EHsc
#include <vector>
#include <list>
#include <numeric>
#include <functional>
#include <iostream>

int main( ) 
{
   using namespace std;   
   vector<int> V1( 10 ), V2( 10 );
   vector<int>::iterator VIter1, VIter2, VIterend, VIterend2;

   list <int> L1;
   list <int>::iterator LIter1, LIterend;

   int t;
   for ( t = 1 ; t <= 10 ; t++ )
   {
      L1.push_back( t );
   }

   cout << "The input list L1 is:\n ( " ;
   for ( LIter1 = L1.begin( ) ; LIter1 != L1.end( ) ; LIter1++ )
      cout << *LIter1 << " ";
   cout << ")." << endl;

   // The first member function for the partial sums of
   // elements in a list output to a vector
   VIterend = partial_sum ( L1.begin ( ) , L1.end ( ) , 
      V1.begin ( ) );
   
   cout << "The output vector containing the partial sums is:\n ( " ;
   for ( VIter1 = V1.begin( ) ; VIter1 != VIterend ; VIter1++ )
      cout << *VIter1 << " ";
   cout << ")." << endl;

   // The second member function used to compute
   // the partial product of the elements in a list
   VIterend2 = partial_sum ( L1.begin ( ) , L1.end ( ) , V2.begin ( ) , 
      multiplies<int>( ) );
   
   cout << "The output vector with the partial products is:\n ( " ;
   for ( VIter2 = V2.begin( ) ; VIter2 != VIterend2 ; VIter2++ )
      cout << *VIter2 << " ";
   cout << ")." << endl;

   // Computation of partial sums in place
   LIterend = partial_sum ( L1.begin ( ) , L1.end ( ) , L1.begin ( ) );
   cout << "The in place output partial_sum list L1 is:\n ( " ;
   for ( LIter1 = L1.begin( ) ; LIter1 != LIterend ; LIter1++ )
      cout << *LIter1 << " ";
   cout << ")." << endl;
}

Output

The input list L1 is:
 ( 1 2 3 4 5 6 7 8 9 10 ).
The output vector containing the partial sums is:
 ( 1 3 6 10 15 21 28 36 45 55 ).
The output vector with the partial products is:
 ( 1 2 6 24 120 720 5040 40320 362880 3628800 ).
The in place output partial_sum list L1 is:
 ( 1 3 6 10 15 21 28 36 45 55 ).

Requirements

Header: <numeric>

Namespace: std

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