Tail recursion is a special form of recursion in which the recursive call is the last operation performed within a function. In tail recursion, the result of the recursive call is immediately returned without any further calculations or processing. This allows the compiler or interpreter to optimize the recursive function by reusing the same stack frame for each recursive call, rather than creating new stack frames.

Tail recursion has the following characteristics:

1. Recursive call as the last operation: In a tail-recursive function, the recursive call is the final operation performed in the function before returning. There are no pending calculations or operations after the recursive call.
2. Accumulator pattern: Tail-recursive functions often employ an accumulator parameter that accumulates the partial results during the recursive calls. The accumulated value is updated and passed as a parameter in each recursive call, eliminating the need for repeated calculations or storing intermediate results.
3. Constant stack space: Since tail recursion optimizes the function to reuse the same stack frame for each recursive call, it ensures that the space complexity remains constant, regardless of the input size. This makes tail-recursive functions more memory-efficient and avoids stack overflow errors for large input sizes.

Example of a tail-recursive function to calculate the factorial of a number (in C++):

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unsigned int factorial(int n, unsigned int accumulator = 1) {    if (n == 0) {        return accumulator;    }    return factorial(n - 1, n * accumulator);  // Tail recursive call with updated accumulator }

In this example, the factorial function uses tail recursion and employs the accumulator pattern. The recursive call passes the updated accumulator (n * accumulator) as a parameter, avoiding repeated multiplication operations and allowing the compiler to optimize the recursion.

Tail recursion is particularly useful when dealing with large input sizes or optimizing memory usage. By using tail recursion, the recursive function can be transformed into an iterative-like loop structure, reducing stack space and potentially improving performance.

However, it's important to note that not all recursive functions can be easily transformed into tail-recursive form. Some recursive algorithms require backtracking or processing after the recursive call, making it challenging to apply the tail recursion optimization.

To benefit from tail recursion optimization, it's essential to ensure that the recursive function follows the tail-recursive pattern with the recursive call as the last operation.