General Steps to solve recursion problems | DSA in C++ - Software Development PDF Download

Solving Recursion Problems in C++

Recursion is a powerful technique used in programming to solve complex problems by breaking them down into simpler, self-referential subproblems. It involves solving a problem by repeatedly applying the same algorithm to a smaller subset of the problem until a base case is reached. In this article, we will explore the general steps to solve recursion problems in C++.

Step 1: Identify the Base Case

The base case is the simplest form of the problem that can be solved directly without recursion. It serves as the stopping condition for the recursive function. When the base case is reached, the recursion stops, and the function starts unwinding the stack.

Example:

int factorial(int n) {

    // Base case: factorial of 0 is 1

    if (n == 0) {

        return 1;

    }

    // Recursive case: multiply n by factorial of (n - 1)

    else {

        return n * factorial(n - 1);

    }

}

Step 2: Define the Recursive Function

The recursive function is responsible for breaking down the original problem into smaller subproblems and making recursive calls to solve them. It typically follows a similar structure:

• Check if the base case is reached. If so, return the base case value.
• Otherwise, break down the problem into smaller subproblems.
• Make recursive calls to solve the subproblems.
• Combine the results of the subproblems to obtain the final result.

Example:

// Recursive function to compute the factorial of a number

int factorial(int n) {

    // Base case: factorial of 0 is 1

    if (n == 0) {

        return 1;

    }

    // Recursive case: multiply n by factorial of (n - 1)

    else {

        return n * factorial(n - 1);

    }

}

Step 3: Determine the Recursive Case

The recursive case defines how the original problem is broken down into smaller subproblems. It involves identifying the relationship between the current problem and the subproblem(s) to be solved.

Example:

In the factorial example, the recursive case multiplies the current number 'n' with the factorial of '(n - 1)'.

Step 4: Ensure Progress Toward the Base Case

To avoid infinite recursion, it's crucial to ensure that each recursive call brings us closer to the base case. If the recursive function fails to make progress, it can lead to an infinite loop and stack overflow.

Example:

In the factorial example, each recursive call reduces the value of 'n' by 1, eventually reaching the base case of 'n == 0'.

Step 5: Handle the Recursive Results

Once the base case is reached and the recursion starts unwinding, each recursive call returns a result. These results need to be combined to obtain the final result of the original problem.

Example:

In the factorial example, each recursive call returns the factorial of '(n - 1)'. The results are multiplied together to obtain the factorial of 'n'.

Step 6: Test the Recursive Function

Before using the recursive function in production or for larger inputs, it's essential to test it with various inputs to ensure correctness and efficiency. It helps identify any potential issues, such as incorrect base case handling or excessive recursion depth.

Example:

int main() {

    // Test the factorial function

    int n = 5;

    int result = factorial(n);

    cout << "Factorial of " << n << " is: " << result << endl;

    return 0;

}

Output:

Factorial of 5 is: 120

Conclusion

Recursion is a valuable technique in solving complex problems by breaking them down into simpler subproblems. By following the general steps outlined in this article, you can approach recursion problems in C++ with confidence. Remember to identify the base case, define the recursive function, determine the recursive case, ensure progress toward the base case, handle the recursive results, and thoroughly test your solution.