Reduce and Accumulate

A detailed guide to generating a single object from collections using the std::reduce and std::accumulate algorithms
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Ryan McCombe
Ryan McCombe
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In this lesson and the next, we introduce a range of algorithms that are designed to simplify large collections of objects into simpler outputs.

For example, we might have a collection of objects representing bank transactions, and we want to generate a simple object that includes some aggregate data. That could perhaps include information like:

  • What was the total amount of all transactions
  • How many transactions were there
  • What is the average transaction value

In this lesson, we’ll introduce the reduce() and accumulate() algorithms, which remain the most popular way of implementing logic like this.

In the next lesson, we’ll introduce fold algorithms, which were added to the language in C++23, and give us more ways to accomplish tasks like this.

The std::reduce() Algorithm

The std::reduce() algorithm is available within the standard library’s <numeric> header.

The most basic form of a std::reduce() call involves two iterators, denoting the first and last element of our input.

The algorithm will return the result of adding all the objects in that range together:

#include <numeric> 
#include <iostream>
#include <vector>

int main(){
  std::vector Numbers{1, 2, 3, 4, 5};

  int Result{
    std::reduce(Numbers.begin(), 
                Numbers.end())}; 

  std::cout << "Result: " << Result;
}
Result: 15

std::reduce() Initial Value and Operators

std::reduce() also has an overload that accepts an additional two arguments, so four in total:

  1. An iterator pointing at the beginning of the input
  2. An iterator pointing at the end of the input
  3. An initial value to use for the algorithm (we cover this in more detail later)
  4. A function / callable that determines how our objects are combined. It accepts two objects from our input as arguments and returns a single value

We can recreate the default behavior of adding everything in the range by passing 0 as the third argument, and a function that implements the addition operator as the fourth argument.

The standard library includes the std::plus helper, which returns a template functor that simply implements the binary + operator:

#include <numeric>
#include <iostream>
#include <vector>

int main(){
  std::vector Numbers{1, 2, 3, 4, 5};

  int Result{
    std::reduce(Numbers.begin(),
                Numbers.end(), 0, 
                std::plus{} 
    )
  };

  std::cout << "Result: " << Result;
}
Result: 15

Below, we change the behavior of std::reduce() to multiply the values in our input, rather than add them:

#include <numeric>
#include <iostream>
#include <vector>

int main(){
  std::vector Numbers{1, 2, 3, 4, 5};

  int Result{
    std::reduce(Numbers.begin(),
                Numbers.end(), 1,
                std::multiplies{} 
  )};

  std::cout << "Result: " << Result;
}
Result: 120

With multiplication, we set the initial value to 1, as that is the identity value for multiplication.

Identity Values of Operations

With algorithms like reduce(), the value we tend to pass as the initial value tends to be the identity of that operation. The identity is the value that causes the operator to return an object that is equal to the other operand.

For example, the identity of addition is 00, as n+0=nn + 0 = n. The multiplication identity is 11, as n√ó1=nn \times 1 = n.

Other, more complex operators may or may not have their own identity values.

If the operator we’re using with reduce() doesn’t have an identity or we don’t know what it is, we have a way to get around that. We can set our initial value to the first object of our input, and then exclude it from the rest of the algorithm.

It could look something like the below, where our initial value is the first number in our std::vector, and our first argument to std::reduce() excludes that value, by advancing the iterator past it:

#include <numeric>
#include <iostream>
#include <vector>

int main(){
  std::vector Numbers{1, 2, 3, 4, 5};

  int Result{
    std::reduce(Numbers.begin() + 1, 
                Numbers.end(),
                Numbers[0], 
                std::plus{}
  )};

  std::cout << "Result: " << Result;
}
Result: 15

This approach assumes our input has at least one value. If our input could have a size of 0, we can check for that before running the algorithm, and handle it in whatever way makes sense for our program.

C++23 added some alternatives to std::reduce which can take care of this edge case for us. These are called fold algorithms, and we introduce them in the next lesson.

User-Defined Operators with std::reduce()

Of course, for the operator argument of std::reduce(), we’re not just limited to what is in the standard library. We can write our own custom callable (eg, a function, lambda, or functor) and pass it as the fourth argument.

Below, we pass an operator that will add the absolute values of the objects in our input:

#include <iostream>
#include <numeric>
#include <vector>

int main(){
  std::vector Nums{1, -2, 3, -4, 5};

  int Result{
    std::reduce(
      Nums.begin(), Nums.end(), 0,
      [](int x, int y){ 
        return std::abs(x) + std::abs(y); 
      } 
    )
  };

  std::cout << "Result: " << Result;
}
Result: 15

std::reduce() Multithreading and Non-Deterministic Results

The std::reduce() algorithm is designed to be usable in multi-threaded environments. We cover multi-threading in detail later in the course, but for now, there is an implication we should be aware of.

Specifically, we cannot assume the objects in our input are always combined in the same order.

For example, if our operator function is func and our input is a collection comprising of a, b and c, the std::reduce() algorithm might return the result of:

  • func(a, func(b, c))
  • func(b, func(a, c))
  • func(func(c, a), b)
  • or any other permutation

As such, std::reduce() is most commonly used with an operator that will return the same result, regardless of how its operands are combined or grouped. The words commutative and associative are sometimes used to describe these operators.

Commutative Operations

An operation that is commutative gives the same result, regardless of which operand is on the left and which is on the right.

Addition is an example of a commutative operation because A+BA + B is equivalent to B+AB + A.

Subtraction is not commutative, because A‚ąíBA - B is not necessarily equivalent to B‚ąíAB - A.

Associative Operations

An operation that is associative gives the same result, regardless of how individual operations are grouped within a larger expression.

Addition is an example of an associative operation because (A+B)+C(A + B) + C is equivalent to A+(B+C)A + (B + C).

Subtraction is not associative, because (A‚ąíB)‚ąíC(A - B) - C is not necessarily equivalent to A‚ąí(B‚ąíC)A - (B - C).

For example: (1‚ąí2)‚ąí3=‚ąí4(1 - 2) - 3 = -4 but 1‚ąí(2‚ąí3)=21 - (2 - 3) = 2

If the operator we use with std::reduce() is not commutative or not associative, the algorithm will be non-deterministic. That is, it may give a different return value each time it is run, even though the inputs were the same.

The std::accumulate() Algorithm

std::accumulate() is also available within <numeric>, and has a very similar use case as std::reduce(). The key difference is that std::accumulate() guarantees that the operands in our input range are combined in a consistent order - left to right.

This means its output will be deterministic, even if the operator isn’t commutative or associative.

The trade-off is this guaranteed sequencing is that std::accumulate() is single-threaded so, for larger tasks, it can be slower than std::reduce()

Similar to std::reduce(), the std::accumulate algorithm implements the uses the + operator. The only difference is that the initial value isn’t optional:

#include <iostream>
#include <numeric> 
#include <vector>

int main(){
  std::vector Numbers{1, 2, 3, 4, 5};

  int Result{
    std::accumulate(Numbers.begin(), 
                    Numbers.end(), 0)}; 

  std::cout << "Result: " << Result;
}
Result: 15

We can change the operator in the usual way, by providing a 4th argument, and updating the initial value (the third argument) if needed:

#include <iostream>
#include <numeric>
#include <vector>

int main(){
  std::vector Numbers{1, 2, 3, 4, 5};

  int Result{
    std::accumulate(Numbers.begin(),
                    Numbers.end(), 1,
                    std::multiplies{})};

  std::cout << "Result: " << Result;
}
120

Accumulating to a Different Type

Because of the guaranteed sequencing, std::accumulate() makes it easy to return a type that is different from the types of our input.

The type that will be returned is the type of our initial value - the third argument.

Below, we accumulate our integers to a float:

#include <iostream>
#include <numeric>
#include <vector>

int main(){
  std::vector Nums{1, 2, 3};

  std::cout << std::accumulate(
    Nums.begin(), Nums.end(), 0.5f);
};
6.5

When providing a custom operator for a scenario where the input and output types are different, it’s worth reviewing what its signature will be:

  • Its first parameter will have the type of the initial value - what we passed as the third argument to std::accumulate()
  • Its second parameter will have the type of our input objects
  • Its return type will be the same as the initial value

The following example includes a lambda that implements the correct signature where we’re accumulating int objects to a float:

#include <iostream>
#include <numeric>
#include <vector>

int main(){
  std::vector Nums{1, -2, 3};

  auto Fun{
    [](float f, int i) -> float{
      return std::abs(f) + std::abs(i);
    }};

  std::cout << std::accumulate(
    Nums.begin(), Nums.end(), 0.5f, Fun);
};
6.5

In this more complex example, we accumulate our integers into a custom Accumulator type:

#include <iostream>
#include <numeric>
#include <vector>

struct Accumulator {
  int Total{0};
  int Count{0};

  static Accumulator Add(Accumulator A, int V){
    return {A.Total + V, A.Count + 1};
  }

  void Log(){
    std::cout
      << "Count: " << Count
      << "\nSum: " << Total;
    if (Count > 0) {
      std::cout
        << "\nAverage: "
        << static_cast<float>(Total) / Count;
    }
  }
};

int main(){
  std::vector Nums{99, 65, 26, 72, 17};

  std::accumulate(
    Nums.begin(), Nums.end(),
    Accumulator{}, Accumulator::Add
  ).Log();
};
Count: 5
Sum: 279
Average: 55.8

The std::reduce() algorithm can also reduce objects to a different type, including a custom type. However, it can involve a bit more effort to ensure everything is set up to work deterministically in a multi-threaded environment.

We cover those considerations in a dedicated section later in the course.

Changing the Accumulation Order

The std::accumulate() algorithm will always process elements in the input range from left to right. Many sequential containers over reverse iterators - rbegin() and rend() which allows std::accumulate() (and any other iterator-based algorithm) to proceed in reverse order:

#include <iostream>
#include <numeric>
#include <vector>

int main(){
  std::vector Numbers{1, 2, 3};

  auto Log{
    [](int x, int y){
      std::cout << y << ", ";
      return 0;
    }};

  std::cout << "Forward: ";
  std::accumulate(
    Numbers.begin(), Numbers.end(), 0, Log);

  std::cout << "\nReverse: ";
  std::accumulate(
    Numbers.rbegin(), Numbers.rend(), 0, Log);
}
Forward: 1, 2, 3, 
Reverse: 3, 2, 1, 

If reverse iterators are not available, we can also prepare our input using one of the other algorithms we covered earlier. For example, we can reverse our input using std::ranges::reverse(), or randomize it using std::ranges::shuffle(). We covered both of these in our earlier lesson on movement algorithms:

Range-Based Techniques with std::reduce() and std::accumulate()

C++23 includes std::ranges::fold_left(), which is effectively equivalent to std::accumulate(). We cover this and other fold algorithms in the next lesson.

A range-based variation of std::reduce() is likely to come in a future C++ version.

But for now, std::reduce() and std::accumulate() are iterator-based algorithms and are not directly compatible with ranges.

However, even though they don’t work with ranges directly, we can still use range-based techniques in the surrounding code to accomplish more complex tasks.

For example, below, we use a view to create a range that only includes the even numbers of our input. We then use the iterators the view provides to accumulate() only those even numbers:

#include <iostream>
#include <numeric>
#include <vector>
#include <ranges>

int main(){
  std::vector Numbers{1, 2, 3};

  auto V{
    std::views::filter(Numbers, [](int i){
      return i % 2 == 1;
    })};

  std::cout << "Result: "
    << std::accumulate(V.begin(), V.end(), 0);
}
Result: 4

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Ryan McCombe
Ryan McCombe
Posted
This lesson is part of the course:

Professional C++

Comprehensive course covering advanced concepts, and how to use them on large-scale projects.

Standard Library Algorithms
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Fold Algorithms

An introduction to the 6 new folding algorithms added in C++23, providing alternatives to std::reduce and std::accumulate
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