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# C Programming Classic Exercise 28: Solving Age Relations Using Recursion In computer science and programming, recursion is a powerful technique where a function calls itself to solve a smaller instance of the same problem. This tutorial demonstrates how to use recursion in C to solve a classic word problem involving age relationships. --- ## 1. Problem Description Five people are sitting together. You want to find out the age of the fifth person. * The **fifth** person says they are 2 years older than the **fourth** person. * The **fourth** person says they are 2 years older than the **third** person. * The **third** person says they are 2 years older than the **second** person. * The **second** person says they are 2 years older than the **first** person. * Finally, you ask the **first** person, and they say they are **10** years old. **Question:** How old is the fifth person? --- ## 2. Problem Analysis & Mathematical Modeling To solve this problem programmatically, we can define a mathematical relationship for the age of the $n$-th person, denoted as $f(n)$: 1. **Base Case:** When $n = 1$, we know the exact age: $$f(1) = 10$$ 2. **Recursive Step:** For any person $n > 1$, their age is 2 years older than the $(n-1)$-th person: $$f(n) = f(n-1) + 2$$ ### The Two Phases of Recursion: * **Winding (Pushing/Going Down):** To find the age of the 5th person, the program requests the age of the 4th, which requests the 3rd, then the 2nd, and finally the 1st. * **Unwinding (Returning/Coming Up):** Once the base case ($n=1$, age is 10) is reached, the function returns the value back up the call stack. * $f(2) = 10 + 2 = 12$ * $f(3) = 12 + 2 = 14$ * $f(4) = 14 + 2 = 16$ * $f(5) = 16 + 2 = 18$ --- ## 3. C Source Code Implementation Below is the complete C program. > **Note on Code Style:** The original code used the legacy K&R C style for function parameter declarations. The code below has been updated to modern ANSI C standards for better compatibility with modern compilers, while preserving the core logic. ```c #include /** * Recursive function to calculate the age of the n-th person. * @param n The position of the person (1 to 5) * @return The age of the n-th person */ int get_age(int n) { int current_age; // Base Case: The first person is 10 years old if (n == 1) { current_age = 10; } // Recursive Case: n-th person is 2 years older than the (n-1)-th person else { current_age = get_age(n - 1) + 2; } return current_age; } int main() { int target_person = 5; int result_age = get_age(target_person); printf("The age of the 5th person is: %d\n", result_age); return 0; } ``` --- ## 4. Output and Execution When you compile and run the program, it produces the following output: ```text The age of the 5th person is: 18 ``` --- ## 5. Key Considerations and Best Practices When working with recursive functions in C, keep the following points in mind: * **Base Case is Mandatory:** Every recursive function must have a well-defined base case (in this example, `if (n == 1)`). Without a base case, the function will call itself infinitely, leading to a **Stack Overflow** error. * **Stack Overhead:** Each recursive call adds a new stack frame to the call stack. For very deep recursions, an iterative approach (using a `for` or `while` loop) is often more memory-efficient. * **Input Validation:** In production code, you should validate the input parameter `n`. If a user passes a value less than 1 (e.g., `0` or `-1`), the current recursive logic would result in infinite recursion. Adding a guard clause like `if (n < 1) return -1;` is highly recommended.