C++ Tail Recursion

Tail recursion is a special case of recursion where the recursive call is the last operation performed in a function. In other words, the recursive call is in the tail position, meaning there are no pending operations or computations after the recursive call.

Tail call optimization: Some programming languages and compilers can optimize tail recursive functions by replacing the recursive call with a loop-like structure, eliminating the need for additional stack frames. This optimization avoids stack overflow errors and improves the efficiency of the recursive algorithm.

Constant stack space: Tail recursion allows recursive functions to be executed using a constant amount of stack space regardless of the input size. Each recursive call replaces the current stack frame as it is not used anymore in the recursive call. This prevents stack space from growing with each recursive step.

Improved performance: By eliminating the overhead of maintaining multiple stack frames, tail recursion can lead to faster execution and improved performance compared to non-tail recursive functions.

Simplified code: Tail recursion can often result in simpler and more readable code. Since there are no pending operations after the recursive call, the control flow is straightforward and easier to understand.

Use of accumulator variables: Tail-recursive functions often employ an accumulator variable to accumulate the intermediate results during the recursion. The base case should return the accumulator, as it now holds the result of the computation. This approach avoids the need to create multiple intermediate stack frames and allows for efficient computation of the final result.

It’s important to note that not all programming languages or compilers perform tail call optimization. Therefore, the benefits of tail recursion may vary depending on the language and the implementation. Additionally, tail recursion requires careful design and adherence to the tail call position to ensure proper optimization.

Here’s an example of a tail-recursive function that calculates the factorial of a number in C++:

int factorial(int n, int acc = 1) {
    if (n == 0) {
        return acc;
    }
    else {
        return factorial(n - 1, acc * n);
    }
}

In this example, the recursive call factorial(n – 1, n * acc) is in the tail position since it is the last operation performed before returning the result. The intermediate results are accumulated in the acc variable, and the function uses constant stack space regardless of the input size.

Other problems

Write a tail recursive function to sum the integers from 1 to n

int summation(int n, int acc = 0) {
    if (n == 0) {
        return acc; // Base case: return accumulated sum
    } else {
        return summation(n - 1, acc + n); // Recursive case: update accumulator with current number
    }
}



Write a tail recursive function to compute:
f(n) = 1 x 2 + 2 x 3 + 3 x 4 + … + (n-1) x n

int addition(int n, int acc = 2) {
    if (n == 2) {
        return acc; //Base case: return accumulated sum
    } else {
        return addition(n-1, acc + (n-1)*n);  //recursive case
    }
}



Write a tail recursive function that implements x^n  (i.e. 2^3 = 2 * 2 * 2), where x is any real number and n is a non-negative integer

int power(int x, int n, int acc = 1) {
    if (n == 0) {
        return acc; //Base case: return accumulated product
    } else {
        return power(x, n-1, acc * x);  //recursive case
    }
}



Write a tail recursive function to reverse a string

string reverseString(string characters, string acc =""){
    if (characters.length() == 0) {
        return acc; // Base case: accumulated reversed string
    } else {
        char lastChar = characters.back();
        string remainingChars = characters.substr(0, characters.length() - 1);
        return reverseString(remainingChars, lastChar + acc);
    }
}