Question

Consider the following recursive function: void recFun(int x) { if (x > 10) { recFun(x / 10); cout << x % 10 << endl; } else cout << x << endl; } What is the output of the following statements? a. recFun(258); b. recFun(7); c. recFun(36); d. recFun(-85);

Short answer

a. 2, 5, 8; b. 7; c. 3, 6; d. -85

Step-by-step solution

Understanding the Base Case

In the function `recFun`, the base case is when the input `x` is less than or equal to 10. In this case, the output will be the entire number `x`. For any `x > 10`, the recursion will continue.

Handling Recursive Case

When `x` is greater than 10, `recFun` continues to call itself with the argument `x/10`. This means the function effectively breaks down the number `x` until each digit can be processed individually.

Output for recFun(258)

For `recFun(258)`, the function first calls itself with `258/10=25`, which then calls itself with `25/10=2`. `2` is output (base case), then the digits are output in reverse: - Base Case (x ≤ 10): Print `2` - Calculate `25 % 10 = 5`, then print `5` - Calculate `258 % 10 = 8`, then print `8`. The output sequence is `2, 5, 8`.

Output for recFun(7)

Since `7` is less than or equal to 10, `7` is printed immediately as it satisfies the base case condition.

Output for recFun(36)

For `recFun(36)`, the function calls itself with `36/10=3`. Since `3` is the base case, it prints `3`, - Then, calculate `36 % 10 = 6`, which is printed. The output is `3, 6`.

Output for recFun(-85)

For `recFun(-85)`, negative numbers are not directly considered in the function. Since `-85` is less than 10, it is printed directly as `-85` in line with the base case.

Key concepts

Recursive Function

A recursive function is a type of function that calls itself in order to solve a problem. This technique is like a chain reaction, with each function call stacked on the previous one until a specific condition is met, which stops the recursion.
Recursive functions are useful for problems that can be broken down into smaller, simpler sub-problems. For instance, tasks like calculating factorials, solving puzzles, or traversing data structures such as trees or graphs can often be tackled effectively with recursion.
In our exercise example, the function `recFun` is designed to print the digits of a number starting from the least significant to the most, using recursion to drill down into each digit.
Understanding the flow of recursive functions is key. Each call to the function processes a smaller part of the problem until it reaches a point where the answer is straightforward, known as the base case. Then, the function "unwinds" to reveal the complete solution step by step.

Base Case

The base case is a critical concept in recursion, providing the condition or conditions that determine when the recursive calls should stop.
In the `recFun` function, the base case occurs when the input number `x` is less than or equal to 10. At this point, the function outputs the number directly and doesn't call itself anymore.
Without a base case, a recursive function would continue to call itself indefinitely, leading to a stack overflow error. Thus, having a clear and well-defined base case ensures that the recursive process concludes effectively.
For various inputs in our function, such as `7`, the base case is reached immediately because `7` is less than or equal to 10, allowing it to be printed right away without further recursive calls.

Recursive Case

The recursive case deals with the situation where the function must continue breaking down the problem because it hasn't reached the base case yet.
In the `recFun` example, whenever `x` is greater than 10, the function calls itself with the argument `x/10`. This operation takes the number `x` and reduces it in size, one digit at a time, eventually reaching a point where the base case condition is satisfied.
This is akin to peeling layers off an onion—you remove the outer layers one by one until you reach the core. For example, with `recFun(258)`, the function calls itself with `25` and then `2` before reaching the base case. Each level of the function waits for its successor to complete before continuing operations, such as calculating remainders using the modulo operator. This ensures that each digit of the number `258` is processed and printed correctly.

Function Output Analysis

Analyzing the output of a recursive function involves understanding both the base case and the recursive nature of the function.
For `recFun(258)`, the output sequence is `2, 5, 8`. This is derived through recursive division and the use of the modulus operation. The function first breaks the number down to `2`, printing each resulting digit after reaching the base or completing the calculations for each division level.
Similarly, `recFun(36)` outputs `3, 6`, as `36` is broken to `3`, and then the remainder of `36 % 10` gives `6`. Lastly, with an input like `-85`, although a negative number isn't conventionally handled in stepwise recursion, our current function logic prints `-85` directly due to the base case being satisfied.
Understanding how these outputs are generated provides insight into the step-by-step operations of recursive functions. It demonstrates how each function call organizes data, processes it, and ultimately produces the desired result.