namespace tf {

/** @page ParallelScan Parallel Scan

%Taskflow provide template methods that construct tasks
to perform parallel scan over a range of items.

@tableofcontents

@section ParallelScanInclude Include the Header

You need to include the header file, <tt>taskflow/algorithm/scan.hpp</tt>,
for creating a parallel-scan task.

@code{.cpp}
#include <taskflow/algorithm/scan.hpp>
@endcode

@section WhatIsAScanOperation What is a Scan Operation?

A parallel scan task
performs the cumulative sum, also known as <i>prefix sum</i> or @em scan, 
of the input range and writes the result to the output range.
Each element of the output range contains the
running total of all earlier elements using the given binary operator
for summation.

@image html images/scan.png

@section CreateAParallelInclusiveScanTask Create a Parallel Inclusive Scan Task
  
tf::Taskflow::inclusive_scan(B first, E last, D d_first, BOP bop)
generates an @em inclusive scan, meaning that the N-th element
of the output range is the sum of the first N input elements,
so the N-th input element is included.
For example, the code below performs an inclusive scan over five elements:

@code{.cpp}
std::vector<int> input = {1, 2, 3, 4, 5};
std::vector<int> output(input.size())
taskflow.inclusive_scan(
  input.begin(), input.end(), output.begin(), std::plus<int>{}
);
executor.run(taskflow).wait();
// output is {1, 3, 6, 10, 15}
@endcode

The output range may be the same as the input range, in which
the scan operation is @em in-place with results written to
the input range.
For example, the code below performs an in-place inclusive
scan over five elements:

@code{.cpp}
std::vector<int> input = {1, 2, 3, 4, 5};
taskflow.inclusive_scan(
  input.begin(), input.end(), input.begin(), std::plus<int>{}
);
executor.run(taskflow).wait();
// input is {1, 3, 6, 10, 15}
@endcode

  
Similar to tf::Taskflow::inclusive_scan(B first, E last, D d_first, BOP bop),
tf::Taskflow::inclusive_scan(B first, E last, D d_first, BOP bop, T init)
performs an inclusive scan but with an additional initial value @c init.
For example, the code below performs an inclusive scan
over five elements plus an initial value:

@code{.cpp}
std::vector<int> input = {1, 2, 3, 4, 5};
std::vector<int> output(input.size());
// performs inclusive scan with an initial value
taskflow.inclusive_scan(
  input.begin(), input.end(), output.begin(), std::plus<int>{}, -1
);
executor.run(taskflow).wait();
// output is {0, 2, 5, 9, 14}
@endcode

@section CreateAParallelTransformInclusiveScanTask Create a Parallel Transform-Inclusive Scan Task

You can transform elements in the input range before running inclusive scan
using tf::Taskflow::transform_inclusive_scan(B first, E last, D d_first, BOP bop, UOP uop)
and tf::Taskflow::transform_inclusive_scan(B first, E last, D d_first, BOP bop, UOP uop, T init).
For example, the code below performs an inclusive scan over five
transformed elements:

@code{.cpp}
std::vector<int> input = {1, 2, 3, 4, 5};
std::vector<int> output(input.size());
taskflow.transform_inclusive_scan(
  input.begin(), input.end(), output.begin(), std::plus<int>{}, 
  [] (int item) { return -item; }
);
executor.run(taskflow).wait();
// output is {-1, -3, -6, -10, -15}
@endcode

You can also associate the transform-inclusive scan with an initial value
using tf::Taskflow::transform_inclusive_scan(B first, E last, D d_first, BOP bop, UOP uop, T init).
Only elements in the input range will be transformed using @c uop,
i.e., the initial value @c init does not participate in @c uop.

@code{.cpp}
std::vector<int> input = {1, 2, 3, 4, 5};
std::vector<int> output(input.size());
taskflow.transform_inclusive_scan(
  input.begin(), input.end(), output.begin(), std::plus<int>{}, 
  [] (int item) { return -item; },
  -1
);
executor.run(taskflow).wait();
// output is {-2, -4, -7, -11, -16}
@endcode

@section CreateAParallelExclusiveScanTask Create a Parallel Exclusive Scan Task

tf::Taskflow::exclusive_scan(B first, E last, D d_first, T init, BOP bop)
generates an @em exclusive scan with the given initial value.
The N-th element of the output range is the sum of the first N-1 input elements,
so the N-th input element is included.
For example, the code below performs an exclusive scan over five elements
with an initial value -1:

@code{.cpp}
std::vector<int> input = {1, 2, 3, 4, 5};
std::vector<int> output(input.size())
taskflow.exclusive_scan(
  input.begin(), input.end(), output.begin(), -1, std::plus<int>{}
);
executor.run(taskflow).wait();
// output is {-1, 0, 2, 5, 9}
@endcode

The output range may be the same as the input range, in which
the scan operation is @em in-place with results written to
the input range.
For example, the code below performs an in-place exclusive
scan over five elements with an initial -1:

@code{.cpp}
std::vector<int> input = {1, 2, 3, 4, 5};
std::vector<int> output(input.size());
taskflow.exclusive_scan(
  input.begin(), input.end(), output.begin(), -1, std::plus<int>{}
);
executor.run(taskflow).wait();
// output is {-1, 0, 2, 5, 9}
@endcode

@section CreateAParallelTransformExclusiveScanTask Create a Parallel Transform-Exclusive Scan Task

You can transform elements in the input range before running exclusive scan using
tf::Taskflow::transform_exclusive_scan(B first, E last, D d_first, T init, BOP bop, UOP uop).
For example, the code below performs an exclusive scan over five
transformed elements:
  
@code{.cpp}
std::vector<int> input = {1, 2, 3, 4, 5};
std::vector<int> output(input.size());
taskflow.transform_exclusive_scan(
  input.begin(), input.end(), input.begin(), -1, std::plus<int>{},
  [](int item) { return -item; }
);
executor.run(taskflow).wait();
// output is {-1, -2, -4, -7, -11}
@endcode

*/

}