Database System Concepts
7th Edition
ISBN: 9780078022159
Author: Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher: McGraw-Hill Education
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Returns True/False depending on the case (examples listed in the code). Write answers using one dimensional loops in Python.
![```python
def test1(arr):
"""
Return true if-and-only-if the sequence arr[0], * arr[arr[0]], arr[arr[arr[0]]], ... reaches 0 * after traversing all entries in arr.
Sample input/outputs:
* test1([3, 5, 7, 4, 1, 8, 0, 6, 2]) --> True
* test1([3, 5, 7, 4, 1, 8, 6, 0, 2]) --> False
* test1([3, 1, 0, 3, 0]) --> False
* test1([]) --> True
"""
pass
```
### Explanation
The function `test1` is designed to check if a sequence of indices in an array ultimately leads to a zero after traversing all entries. It evaluates the indices using the pattern `arr[0]`, `arr[arr[0]]`, `arr[arr[arr[0]]]`, and so on, returning `True` if this sequence results in reaching 0 and `False` otherwise.
#### Sample Inputs and Outputs
- `test1([3, 5, 7, 4, 1, 8, 0, 6, 2])` returns `True` because the sequence reaches 0 after the traversal.
- `test1([3, 5, 7, 4, 1, 8, 6, 0, 2])` returns `False` as the sequence does not end in a 0.
- `test1([3, 1, 0, 3, 0])` returns `False` indicating it doesn't resolve to 0.
- `test1([])` returns `True`, as an empty array trivially satisfies the condition without any elements.
This function could be used to solve problems related to array indexing and cyclical patterns in sequences.](https://content.bartleby.com/qna-images/question/cfa33f99-0a88-4c27-bdb9-7417e58c2439/579a2c34-394b-4c39-82a7-ce546e39b631/7qn7b5i_processed.png)
Transcribed Image Text:```python
def test1(arr):
"""
Return true if-and-only-if the sequence arr[0], * arr[arr[0]], arr[arr[arr[0]]], ... reaches 0 * after traversing all entries in arr.
Sample input/outputs:
* test1([3, 5, 7, 4, 1, 8, 0, 6, 2]) --> True
* test1([3, 5, 7, 4, 1, 8, 6, 0, 2]) --> False
* test1([3, 1, 0, 3, 0]) --> False
* test1([]) --> True
"""
pass
```
### Explanation
The function `test1` is designed to check if a sequence of indices in an array ultimately leads to a zero after traversing all entries. It evaluates the indices using the pattern `arr[0]`, `arr[arr[0]]`, `arr[arr[arr[0]]]`, and so on, returning `True` if this sequence results in reaching 0 and `False` otherwise.
#### Sample Inputs and Outputs
- `test1([3, 5, 7, 4, 1, 8, 0, 6, 2])` returns `True` because the sequence reaches 0 after the traversal.
- `test1([3, 5, 7, 4, 1, 8, 6, 0, 2])` returns `False` as the sequence does not end in a 0.
- `test1([3, 1, 0, 3, 0])` returns `False` indicating it doesn't resolve to 0.
- `test1([])` returns `True`, as an empty array trivially satisfies the condition without any elements.
This function could be used to solve problems related to array indexing and cyclical patterns in sequences.
![```python
def test2(arr, k):
"""
Return True if-and-only-if the entries in arr are sorted sloppily
"up to k", that is, every entry precedes at most k smaller values
and follows at most k larger values.
Sample input/outputs:
* test2([3, 2, 1, 0, 4, 8, 7, 6, 5], 3) --> True
* test2([3, 2, 1, 0, 4, 8, 7, 6, 5], 2) --> False
* test2([0, 1, 2, 3, 4, 5, 6, 7, 8], 1) --> True
* test2([], 3) --> True
"""
pass
```
### Explanation
This Python function, `test2`, is designed to determine if the elements in an array `arr` are sorted in a relaxed manner with respect to a parameter `k`. This "sloppily sorted" condition means that each element can be preceded by at most `k` smaller elements and followed by at most `k` larger elements.
#### Sample Inputs and Outputs
1. **`test2([3, 2, 1, 0, 4, 8, 7, 6, 5], 3) --> True`**
The array allows each element to have at most 3 smaller and larger elements in its preceding or following positions.
2. **`test2([3, 2, 1, 0, 4, 8, 7, 6, 5], 2) --> False`**
Here, the condition fails because more than 2 smaller or larger elements can follow or precede some numbers.
3. **`test2([0, 1, 2, 3, 4, 5, 6, 7, 8], 1) --> True`**
This represents a normally sorted array that trivially satisfies the condition for `k=1`.
4. **`test2([], 3) --> True`**
An empty array is trivially considered sorted for any `k` value.
The function](https://content.bartleby.com/qna-images/question/cfa33f99-0a88-4c27-bdb9-7417e58c2439/579a2c34-394b-4c39-82a7-ce546e39b631/merf8y_processed.png)
Transcribed Image Text:```python
def test2(arr, k):
"""
Return True if-and-only-if the entries in arr are sorted sloppily
"up to k", that is, every entry precedes at most k smaller values
and follows at most k larger values.
Sample input/outputs:
* test2([3, 2, 1, 0, 4, 8, 7, 6, 5], 3) --> True
* test2([3, 2, 1, 0, 4, 8, 7, 6, 5], 2) --> False
* test2([0, 1, 2, 3, 4, 5, 6, 7, 8], 1) --> True
* test2([], 3) --> True
"""
pass
```
### Explanation
This Python function, `test2`, is designed to determine if the elements in an array `arr` are sorted in a relaxed manner with respect to a parameter `k`. This "sloppily sorted" condition means that each element can be preceded by at most `k` smaller elements and followed by at most `k` larger elements.
#### Sample Inputs and Outputs
1. **`test2([3, 2, 1, 0, 4, 8, 7, 6, 5], 3) --> True`**
The array allows each element to have at most 3 smaller and larger elements in its preceding or following positions.
2. **`test2([3, 2, 1, 0, 4, 8, 7, 6, 5], 2) --> False`**
Here, the condition fails because more than 2 smaller or larger elements can follow or precede some numbers.
3. **`test2([0, 1, 2, 3, 4, 5, 6, 7, 8], 1) --> True`**
This represents a normally sorted array that trivially satisfies the condition for `k=1`.
4. **`test2([], 3) --> True`**
An empty array is trivially considered sorted for any `k` value.
The function
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