a - recursion Recursion is a programming technique where a function calls itself directly or indirectly to solve smaller instances of the same problem. It's important to include a base case in recursive functions to prevent infinite recursion This can lead to stack overflow error Basic Structure of a Recursive Function: 1. Base Case → A condition that stops the recursion. 2. Recursive Case → The function calls itself with a modified argument to solve a smaller problem. Advantages of Recursion: 1. Simplicity → Recursive solutions can be more concise and easier to understand for problems that naturally fit a recursive pattern. 2. Readability → For certain problems, recursion makes the code more readable by directly mirroring the problem's structure. Disadvantages of Recursion: 1. Performance Overhead → Each function call adds a new layer to the call stack, which can lead to increased memory usage and slower performance for deep recursions. 2. Stack Overflow → Excessive recursion can cause a stack overflow error if the maximum call stack size is exceeded. 3. Debugging Difficulty → Debugging recursive functions can be more challenging due to the multiple layers of function calls.
b - recursion examples common use cases: 1. Tree Traversal → Recursion is often used to traverse tree-like data structures. 2. Dynamic Programming → Recursive solutions can be optimized using memoization or tabulation. 3. Fractals and Graphics → Recursion can generate complex patterns and shapes. 4. Sorting Algorithms → Some sorting algorithms like quicksort and mergesort use recursion. Tail recursion is a special case of recursion where the recursive call is the last operation in the function. While recursion can be elegant, iterative solutions are often more efficient in terms of memory usage. It's important to use recursion judiciously, considering its potential performance overhead and stack overflow risks