C Recursion

Recursion in C programming language refers to the technique of a function calling itself to perform a specific task. It is a powerful programming concept that can help solve complex problems in a concise and elegant way. Recursion can be used to solve problems that involve repetitive sub-tasks, such as searching or sorting algorithms, tree and graph traversal, and many more. Recursion offers several advantages over iterative approaches, such as simplicity, elegance, and modularity.

To implement recursion in C, we need to define a function that calls itself with modified arguments until a base condition is met, which terminates the recursion. In the process, the function builds up a call stack, which contains the current state of the function for each recursive call, until the base case is reached and the function starts to return values back to the previous calls in the call stack.

How recursion works in C?

Recursion in C works by a function calling itself to perform a specific task. When a function is called recursively, it builds up a call stack, which contains the current state of the function for each recursive call.

Here’s how recursion works in C:

1. A function is called with an argument.
2. The function checks if the argument satisfies a base case, which is a condition that terminates the recursion. If the argument satisfies the base case, the function returns a value.
3. If the argument does not satisfy the base case, the function modifies the argument and calls itself recursively with the modified argument.
4. The recursive call pushes the current state of the function onto the call stack and starts a new instance of the function with the modified argument.
5. Steps 2-4 are repeated until the base case is reached, at which point the function starts to return values back to the previous calls in the call stack.
6. As the function returns values, the call stack is gradually unwound, and the function states are restored to their previous values.

For example, consider the following recursive function to calculate the factorial of a positive integer:

```int factorial(int n) {
if (n == 1) {
return 1;
} else {
return n * factorial(n - 1);
}
}```

If we call the function with an argument of 5, the function will be called recursively as follows:

```factorial(5)
return 5 * factorial(4)
return 4 * factorial(3)
return 3 * factorial(2)
return 2 * factorial(1)
return 1```

At this point, the base case is reached, and the function starts to return values back to the previous calls in the call stack:

```factorial(5)
return 5 * factorial(4)
return 4 * factorial(3)
return 3 * factorial(2)
return 2 * 1```
```factorial(5)
return 5 * factorial(4)
return 4 * factorial(3)
return 3 * 2```
```factorial(5)
return 5 * factorial(4)
return 4 * 6```
```factorial(5)
return 5 * 24```
```factorial(5)
return 120```

Thus, the function returns the factorial of 5, which is 120.

Note that recursion can lead to stack overflow if the number of recursive calls is too large, as each call consumes some memory on the call stack. Therefore, it is important to define a base case that terminates the recursion and to use tail recursion optimization whenever possible.