## accumulate

`Generalized Numeric Operation`

### Summary

Accumulate all elements within a range into a single value.

None

### Synopsis

```#include <numeric>
template <class InputIterator, class T>
T accumulate (InputIterator first,
InputIterator last,
T init);

template <class InputIterator,
class T,
class BinaryOperation>
T accumulate (InputIterator first,
InputIterator last,
T init,
BinaryOperation binary_op);
```

### Description

accumulate applies a binary operation to init and each value in the range [first,last). The result of each operation is returned in init. This process aggregates the result of performing the operation on every element of the sequence into a single value.

Accumulation is done by initializing the accumulator acc with the initial value init and then modifying it with acc = acc + *i or acc = binary_op(acc, *i) for every iterator i in the range [first, last) in order. If the sequence is empty, accumulate returns init.

### Complexity

accumulate performs exactly last-first applications of the binary operation (operator+ by default).

### Example

```//
// accum.cpp
//
#include <numeric>   //for accumulate
#include <vector>    //for vector
#include <functional> //for times
#include <iostream.h>

int main()
{
//
//Typedef for vector iterators
//
typedef vector<int>::iterator iterator;
//
//Initialize a vector using an array of ints
//
int d1[10] = {1,2,3,4,5,6,7,8,9,10};
vector<int> v1(d1, d1+10);
//
//Accumulate sums and products
//
int sum = accumulate(v1.begin(), v1.end(), 0);
int prod = accumulate(v1.begin(), v1.end(),
1, times<int>());
//
//Output the results
//
cout << "For the series: ";
for(iterator i = v1.begin(); i != v1.end(); i++)
cout << *i << " ";

cout << " where N = 10." << endl;
cout << "The sum = (N*N + N)/2 = " << sum << endl;
cout << "The product = N! = " << prod << endl;
return 0;
}
Output :
For the series: 1 2 3 4 5 6 7 8 9 10  where N = 10.
The sum = (N*N + N)/2 = 55
The product = N! = 3628800
```

### Warnings

If your compiler does not support default template parameters then you need to always supply the Allocator template argument. For instance you'll have to write:

```vector<int,allocator<int> >
```

```vector<int>