Types of Recursion in C++

Recursion is a process where a function calls itself, either directly or indirectly to repeat the same task for smaller data. In C++, recursion occurs by writing a function that includes a call to itself within its body.

Based on how and where this function calls are present, recursion in C++ can be classified into the following types:

Let’s look at each type one by one.

1. Direct Recursion

Direct recursion occurs when a function calls itself directly from within its body. This is the most common and straightforward form of recursion.

Example:

#include <iostream>
using namespace std;

void show(int n) {
    if (n == 0)
        return;
    cout << n << " ";

    // Direct recursive call
    show(n - 1);
}

int main() {
    show(5);
    return 0;
}

5 4 3 2 1 

In this example, the show() function calls itself directly with a reduced value of n.

Direct recursion can be divided into:

A. Head Recursion

In head recursion, the recursive call happens before any processing in the function. The function calls itself first and processes later.

#include <iostream>
using namespace std;

void head(int n) {
    if (n != 0) {
        // Recursive call before processing
        head(n - 1);
    }
    cout << n << " ";
}

int main() {
    head(5);
    return 0;
}

0 1 2 3 4 5 

Here, the function goes deep into recursion first and processes while returning.

B. Tail Recursion

In tail recursion, the function processes first and the recursive call is the last operation.

#include <iostream>
using namespace std;

void tail(int n) {
    if (n == 0)
        return;
    cout << n << " ";

    // Recursive call after processing
    tail(n - 1);
}

int main() {
    tail(5);
    return 0;
}

5 4 3 2 1 

Tail recursion can be more memory-efficient and may benefit from compiler optimizations.

C. Tree Recursion

Tree recursion happens when a function calls itself more than once within its body, forming a tree-like structure.

#include <iostream>
using namespace std;

void tree(int n) {
    if (n == 0)
        return;
    cout << n << " ";

    // Two recursive calls
    tree(n - 1);
    tree(n - 1);
}

int main() {
    tree(3);
    return 0;
}

3 2 1 1 2 1 1 

The function calls itself twice for each value, branching like a tree.

D. Nested Recursion

Nested recursion means the argument to a function is itself a recursive call.

#include <iostream>
using namespace std;

int nested(int n) {
    if (n > 100)
        return n - 10;

    // Recursive call inside another recursive call
    return nested(nested(n + 11));
}

int main() {
    cout << nested(95);
    return 0;
}

This type of recursion is complex and used only when necessary.

2. Indirect Recursion

In indirect recursion, a function does not call itself directly. Instead, it calls another function that eventually calls the first one, creating a chain of calls.

#include <iostream>
using namespace std;

void funcA(int);
void funcB(int);

void funcA(int n) {
    if (n > 0) {
        cout << n << " ";
        funcB(n - 1);
    }
}

void funcB(int n) {
    if (n > 0) {
        cout << n << " ";
        funcA(n / 2);
    }
}

int main() {
    funcA(10);
    return 0;
}

10 9 4 3 1 

Here, funcA() calls funcB(), which calls funcA() again, forming indirect recursion.