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What would the output to mystery(3) be, given the following function definition: def mystery(n): if n< e: return 2 * n else: return mystery(n - 1) + n

What would the output to mystery(3) be, given the following function definition: def mystery(n): if n< e: return 2 * n else: return mystery(n - 1) + n

Database System Concepts
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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need help with this python recursion question. why is 4? please explain clear on each steps , please show steps with graph or drawing thanks

### Exploring Recursive Functions: Understanding `mystery(3)` In this lesson, we'll explore the behavior of a recursive function named `mystery`. Here is the function's definition: ```python def mystery(n): if n < 0: return 2 * n else: return mystery(n - 1) + n ``` **Function Definition Overview:** - The function `mystery` takes a single integer parameter `n`. - It includes a conditional statement: - **Base Case**: If `n` is less than 0, the function returns `2 * n`. - **Recursive Case**: If `n` is 0 or greater, the function calls itself with the argument `n - 1` and adds `n` to the result. **Understanding the Recursive Call with `mystery(3)`** To determine the output of `mystery(3)`, we need to trace the function calls: 1. `mystery(3)`: Since `3 >= 0`, it leads to `mystery(2) + 3`. 2. `mystery(2)`: Since `2 >= 0`, it leads to `mystery(1) + 2`. 3. `mystery(1)`: Since `1 >= 0`, it leads to `mystery(0) + 1`. 4. `mystery(0)`: Since `0 >= 0`, it leads to `mystery(-1) + 0`. 5. `mystery(-1)`: Since `-1 < 0`, it returns `2 * (-1) = -2`. Now, let's compute the final result by substituting back up through the recursive calls: - `mystery(-1)` returns `-2`. - `mystery(0)` is `-2 + 0 = -2`. - `mystery(1)` is `-2 + 1 = -1`. - `mystery(2)` is `-1 + 2 = 1`. - `mystery(3)` is `1 + 3 = 4`. Therefore, the output of `mystery(3)` is `4`. This exercise demonstrates the mechanics of recursion, where the function continues to call itself with a reduced argument until the
Transcribed Image Text:### Exploring Recursive Functions: Understanding `mystery(3)` In this lesson, we'll explore the behavior of a recursive function named `mystery`. Here is the function's definition: ```python def mystery(n): if n < 0: return 2 * n else: return mystery(n - 1) + n ``` **Function Definition Overview:** - The function `mystery` takes a single integer parameter `n`. - It includes a conditional statement: - **Base Case**: If `n` is less than 0, the function returns `2 * n`. - **Recursive Case**: If `n` is 0 or greater, the function calls itself with the argument `n - 1` and adds `n` to the result. **Understanding the Recursive Call with `mystery(3)`** To determine the output of `mystery(3)`, we need to trace the function calls: 1. `mystery(3)`: Since `3 >= 0`, it leads to `mystery(2) + 3`. 2. `mystery(2)`: Since `2 >= 0`, it leads to `mystery(1) + 2`. 3. `mystery(1)`: Since `1 >= 0`, it leads to `mystery(0) + 1`. 4. `mystery(0)`: Since `0 >= 0`, it leads to `mystery(-1) + 0`. 5. `mystery(-1)`: Since `-1 < 0`, it returns `2 * (-1) = -2`. Now, let's compute the final result by substituting back up through the recursive calls: - `mystery(-1)` returns `-2`. - `mystery(0)` is `-2 + 0 = -2`. - `mystery(1)` is `-2 + 1 = -1`. - `mystery(2)` is `-1 + 2 = 1`. - `mystery(3)` is `1 + 3 = 4`. Therefore, the output of `mystery(3)` is `4`. This exercise demonstrates the mechanics of recursion, where the function continues to call itself with a reduced argument until the
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