Recursive templates

Learn compile-time loops with recursive templates.

Recursive templates

A recursive template is a compile-time loop where a template refers to itself. Factorial is written this way: the general case Factorial<N>::value = N * Factorial<N-1>::value, and the base case Factorial<0>::value = 1 is given as a specialization.

Example: template <int N> struct Factorial { static const int value = N * Factorial<N-1>::value; }; and template <> struct Factorial<0> { static const int value = 1; };. The compiler unfolds 3 * 2 * 1 * 1 for Factorial<3> at compile time.

Stopping with specialization

For recursion to stop, a specialization is needed. template <> struct Factorial<0> is a full specialization with an empty parameter list. When the compiler reaches Factorial<0> it takes value = 1 without using the general template.

So the chain for Factorial<3>::value ends as 3 * Factorial<2> → 2 * Factorial<1> → 1 * Factorial<0> → 1. The result is 6 and is used as a constant at run time.

Exercise Write the recursive Factorial

Write the general template <int N> struct Factorial with body static const int value = N * Factorial<N-1>::value;. Then add the template <> struct Factorial<0> specialization with value = 1. In main write std::cout << Factorial<5>::value;.

Show example solution

#include <iostream>

template <int N>
struct Factorial {
    static const int value = N * Factorial<N-1>::value;
};

template <>
struct Factorial<0> {
    static const int value = 1;
};

int main() {
    std::cout << Factorial<5>::value;
    return 0;
}

Test yourself

Complete the base case

template <> struct Factorial<0> { static const int value = ____; };

Show answer

template <> struct Factorial<0> { static const int value = 1; };

What is Factorial<3>::value?
```
template <int N> struct Factorial { static const int value = N * Factorial<N-1>::value; };
```
- 3
- 9
- 6
- 0
Show answer

6 — The right answer is: 6. 3! = 3 * 2 * 1 = 6.
Match each call to its result

Factorial<1>::value

returns 1
Factorial<3>::value

returns 6
Factorial<4>::value

returns 24
Factorial<5>::value

returns 120

Next lesson: Type lists

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