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Base cases in Recursion:

A base case, also known as the stopping condition, is essential in any recursive function. It ensures that the recursion eventually terminates. Without a base case, the function would keep calling itself indefinitely, consuming stack memory until a stack overflow error occurs, which leads to memory wastage. Therefore, base cases play a crucial role in preventing infinite recursion and ensuring efficient program execution.

Defining base cases:

The base case refers to the simplest possible solution for a given problem, which acts as the stopping condition in recursion. For example, if you are writing a program to calculate the factorial of a number, the smallest possible answers are 0! and 1!, both of which equal 1. Therefore, the base case is written as: if the given number becomes 0 or 1, return 1.

Once the base case is reached, the recursive calls stop, and the results start returning back up the call stack. Usually, base cases are defined at the beginning of the code and should be carefully chosen based on the problem.

If a base case is not defined, the recursive function will keep calling itself indefinitely, eventually causing a stack overflow error.

Output resulted in stack overflow error because of not defining a base case.

In recursion, each function call is placed on the call stack, and execution pauses until the next call is completed. Once the base case is reached, the calls start returning one by one, unwinding the stack until the initial call is resolved.