a. Given the following recursive mysterious method (in pseudocode), can you figure out what it computes? b. What is the time complexity? c. What would the following method return when the array is i. [38, 24, 10, 22, 6, 9, 5, 12] ii. [10, 14, 19, 26, 31, 42, 27, 44] [14, 16, 15, 17, 18, 20, 29, 10] nitially called as MysteryEven(array, size, 1) oolean MysteryEven(int array, int size, int element){ if (element > size/2) return true; one= 2*element; two= 2*element+1; if (two <= size) if (array[element] > array[one] || array[element]> array[two]) return false; return true && MysteryEven(array, size, element++); else

Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
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Chapter1: Introduction
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The image presents a pseudocode for a recursive method named `MysteryEven`. Let's break it down step by step:

### Pseudocode Explanation

- **Function Definition:**
  - The function `MysteryEven` takes three parameters:
    - `int array`: An array of integers.
    - `int size`: The size of the array.
    - `int element`: The current element index being processed.
  
- **Base Case:**
  - If the `element` is greater than `size/2`, the function returns `true`.

- **Recursive Case:**
  - `one` and `two` are calculated as twice the `element` and twice the `element` plus one, respectively.
  - If `two` is less than or equal to `size`:
    - It checks two conditions:
      - If the `array[element]` is greater than `array[one]`.
      - If the `array[element]` is greater than `array[two]`.
    - If any condition is false, it returns `false`. Otherwise, it continues recursively with the next `element`.
  - If `two` is greater than `size`, it compares the `array[element]` with `array[one]`.
    - If `array[element]` is greater than `array[one]`, it returns `false`.
    - Otherwise, it returns `true`.

### Questions and Analysis

**a. What does this method compute?**
- This function checks if the given array satisfies the heap property for a binary tree. Specifically, it checks if each parent node is greater than its child nodes.

**b. What is the time complexity?**
- The time complexity of this method is O(n), where n is the number of elements in the array. This is because each element is visited once in the recursion.

**c. Outputs for given arrays:**

i. `[38, 24, 10, 22, 6, 9, 5, 12]`
   - This array does not maintain the heap property; hence, the output would be `false`.

ii. `[10, 14, 9, 26, 31, 42, 27, 44]`
   - This array does not maintain the heap property; hence, the output would be `false`.

iii. `[14, 16, 15, 17, 18,
Transcribed Image Text:The image presents a pseudocode for a recursive method named `MysteryEven`. Let's break it down step by step: ### Pseudocode Explanation - **Function Definition:** - The function `MysteryEven` takes three parameters: - `int array`: An array of integers. - `int size`: The size of the array. - `int element`: The current element index being processed. - **Base Case:** - If the `element` is greater than `size/2`, the function returns `true`. - **Recursive Case:** - `one` and `two` are calculated as twice the `element` and twice the `element` plus one, respectively. - If `two` is less than or equal to `size`: - It checks two conditions: - If the `array[element]` is greater than `array[one]`. - If the `array[element]` is greater than `array[two]`. - If any condition is false, it returns `false`. Otherwise, it continues recursively with the next `element`. - If `two` is greater than `size`, it compares the `array[element]` with `array[one]`. - If `array[element]` is greater than `array[one]`, it returns `false`. - Otherwise, it returns `true`. ### Questions and Analysis **a. What does this method compute?** - This function checks if the given array satisfies the heap property for a binary tree. Specifically, it checks if each parent node is greater than its child nodes. **b. What is the time complexity?** - The time complexity of this method is O(n), where n is the number of elements in the array. This is because each element is visited once in the recursion. **c. Outputs for given arrays:** i. `[38, 24, 10, 22, 6, 9, 5, 12]` - This array does not maintain the heap property; hence, the output would be `false`. ii. `[10, 14, 9, 26, 31, 42, 27, 44]` - This array does not maintain the heap property; hence, the output would be `false`. iii. `[14, 16, 15, 17, 18,
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