All questions of Recursion for Software Development Exam

Characteristics of Recursive Functions

Base Case:
- Recursive functions must have a base case, which is a condition that stops the recursion and prevents infinite loops.
- The base case defines the simplest scenario where the function does not call itself again.

Recursive Case:
- Recursive functions must also have a recursive case, where the function calls itself with modified input parameters.
- This allows the function to break down complex problems into smaller, more manageable subproblems.

Complex Problem Solving:
- Recursive functions are often used to solve complex problems by breaking them down into simpler subproblems.
- This divide-and-conquer approach can be more intuitive and easier to implement for certain types of problems.

Not Involving Loops:
- Contrary to common belief, recursive functions do not always involve the use of loops.
- Recursive functions achieve iteration through repeated function calls instead of explicit loops.
In conclusion, while recursive functions must have a base case, a recursive case, and can be used to solve complex problems, they do not necessarily involve the use of loops.

Introduction:
In computer programming, a recursive function is a function that calls itself within its own definition. It is a powerful technique used to solve complex problems by breaking them down into smaller subproblems. However, when implementing a recursive function, it is crucial to include a base case, which is a condition that terminates the recursion. Without a base case, the recursive function will continue to call itself indefinitely, resulting in an infinite loop.

Explanation:
When a recursive function does not have a base case, the following consequences occur:

1. The program goes into an infinite loop:
Without a base case, the recursive function will continue to call itself repeatedly. Each recursive call creates a new instance of the function on the call stack, consuming memory. As a result, the program will eventually run out of available stack memory, causing a stack overflow error. This error occurs when the call stack exceeds its maximum size, leading to the termination of the program.

Example:
Consider the following example of a recursive function without a base case:

```
void infiniteLoop() {
infiniteLoop(); // Recursive call without base case
}

int main() {
infiniteLoop();
return 0;
}
```

In this example, the `infiniteLoop()` function calls itself indefinitely without any condition to terminate the recursion. As a result, the program will go into an infinite loop, continuously creating new instances of the function until the stack overflows.

Conclusion:
In summary, when a recursive function lacks a base case, it results in an infinite loop. This infinite loop consumes memory and can eventually lead to a stack overflow error, causing the program to crash. Therefore, it is crucial to include a base case in recursive functions to ensure termination and prevent unintended consequences.