partial_sum(3C++) - partial_sum(3C++)
Standard C++ Library Copyright 1998, Rogue Wave Software, Inc.
NAMEpartial_sum
- Calculates successive partial sums of a range of values.
SYNOPSIS
#include <numeric>
template <;class InputIterator, class OutputIterator>
OutputIterator partial_sum (InputIterator first,
InputIterator last,
OutputIterator result);
template <;class InputIterator,
class OutputIterator,
class BinaryOperation>
OutputIterator partial_sum (InputIterator first,
InputIterator last,
OutputIterator result,
BinaryOperation binary_op);
DESCRIPTION
The partial_sum algorithm creates a new sequence in which every element
is formed by adding all the values of the previous elements, or, in the
second form of the algorithm, by applying the operation binary_op suc‐
cessively on every previous element. That is, partial_sum assigns to
every iterator i in the range [result, result + (last - first)) a
value equal to:
((...(*first + *(first + 1)) + ... ) +
*(first + (i - result)))
or, in the second version of the algorithm:
binary_op(binary_op(..., binary_op (*first,
*(first + 1)),...),*(first + (i - result)))
For instance, applying partial_sum to (1,2,3,4,) yields (1,3,6,10).
The partial_sum algorithm returns result + (last - first).
If result is equal to first, the elements of the new sequence successively
replace the elements in the original sequence, effectively turning partial_suminto an inplace transformation.COMPLEXITY
Exactly (last - first) - 1 applications of the default + operator or
binary_op are performed.
EXAMPLE
//
// partsum.cpp
//
#include <numeric> //for accumulate
#include <vector> //for vector
#include <functional> //for times
#include <iostream>
using namespace std;
int main()
{
//Initialize a vector using an array of ints
int d1[10] = {1,2,3,4,5,6,7,8,9,10};
vector<int> v(d1, d1+10);
//Create an empty vectors to store results
vector<int> sums((size_t)10), prods((size_t)10);
//Compute partial_sums and partial_products
partial_sum(v.begin(), v.end(), sums.begin());
partial_sum(v.begin(), v.end(), prods.begin(),
times<int>());
//Output the results
cout << "For the series: " << endl << " ";
copy(v.begin(),v.end(),
ostream_iterator<int,char>(cout," "));
cout << endl << endl;
cout << "The partial sums: " << endl << " " ;
copy(sums.begin(),sums.end(),
ostream_iterator<int,char>(cout," "));
cout <<" should each equal (N*N + N)/2" << endl << endl;
cout << "The partial products: " << endl << " ";
copy(prods.begin(),prods.end(),
ostream_iterator<int,char>(cout," "));
cout << " should each equal N!" << endl;
return 0;
}
Program OutputFor the series:
1 2 3 4 5 6 7 8 9 10
The partial sums:
1 3 6 10 15 21 28 36 45 55 should each equal (N*N + N)/2
The partial products:
1 2 6 24 120 720 5040 40320 362880 3628800 should each equal N!
WARNINGS
If your compiler does not support default template parameters, then you
always need to include the Allocator template argument. For instance,
you need to write:
vector<int, allocator<int> >
instead of:
vector<int>
If your compiler does not support namespaces, then you do not need the
using declaration for std.
Rogue Wave Software 02 Apr 1998 partial_sum(3C++)
