# Taskflow Algorithms » Parallel Scan

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

## Include the Header

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

    #include <taskflow/algorithm/scan.hpp>

## What is a Scan Operation?

A parallel scan task performs the cumulative sum, also known as prefix sum or 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.

## Create a Parallel Inclusive Scan Task

tf::Taskflow::inclusive_scan(B first, E last, D d_first, BOP bop) generates an 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:

    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}

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

    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}

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 `init`. For example, the code below performs an inclusive scan over five elements plus an initial value:

    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}

## 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:

    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}

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 `uop`, i.e., the initial value `init` does not participate in `uop`.

    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}

## Create a Parallel Exclusive Scan Task

tf::Taskflow::exclusive_scan(B first, E last, D d_first, T init, BOP bop) generates an 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:

    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}

The output range may be the same as the input range, in which the scan operation is 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:

    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}

## 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:

    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}

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