Initial Query

Write me a numba implementation of levensthin distance, taking two numpy int arrays. Call it levenshtein. Run it in nopython mode. Character swaps are cost 2.

LLM Generation

Query

Write me a numba implementation of levensthin distance, taking two numpy int arrays. Call it levenshtein. Run it in nopython mode. Character swaps are cost 2.

Output

Certainly! Below is an implementation of the Levenshtein distance algorithm using Numba, a just-in-time compiler for Python that can greatly speed up the execution of code that uses NumPy arrays. This implementation specifically takes two 1D NumPy arrays of integers as input. The cost of an insertion or deletion is 1, and the cost of a substitution (character swap) is set to 2, as per your request. To use this code, you need to have both Numba and NumPy installed in your Python environment. You can install these packages using pip if you haven't done so already: 

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pip install numba numpy
Here's the Numba-accelerated Levenshtein distance function: 
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from numba import jit
import numpy as np

@jit(nopython=True)
def levenshtein(arr1, arr2):
    len_arr1 = len(arr1)
    len_arr2 = len(arr2)
    
    # Initialize the distance matrix
    dist = np.zeros((len_arr1 + 1, len_arr2 + 1), dtype=np.int32)
    
    for i in range(len_arr1 + 1):
        dist[i, 0] = i
        
    for j in range(len_arr2 + 1):
        dist[0, j] = j
        
    for i in range(1, len_arr1 + 1):
        for j in range(1, len_arr2 + 1):
            cost = 0 if arr1[i-1] == arr2[j-1] else 2  # Substitution cost is 2
            
            dist[i, j] = min(dist[i-1, j] + 1,        # Deletion
                             dist[i, j-1] + 1,        # Insertion
                             dist[i-1, j-1] + cost)   # Substitution
            
    return dist[len_arr1, len_arr2]

# Example usage:
arr1 = np.array([1, 2, 3, 4])
arr2 = np.array([1, 2, 4, 3])

print(levenshtein(arr1, arr2))
This function computes the Levenshtein distance between two arrays `arr1` and `arr2`. It initializes a matrix `dist` to keep track of the distances, then iterates over the arrays to fill in the matrix based on the costs of insertions, deletions, and substitutions. Finally, it returns the value at the bottom right of the matrix, which represents the Levenshtein distance between the two arrays.

Extract Code

I extracted the following code from that output: 

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from numba import jit
import numpy as np

@jit(nopython=True)
def levenshtein(arr1, arr2):
    len_arr1 = len(arr1)
    len_arr2 = len(arr2)
    
    # Initialize the distance matrix
    dist = np.zeros((len_arr1 + 1, len_arr2 + 1), dtype=np.int32)
    
    for i in range(len_arr1 + 1):
        dist[i, 0] = i
        
    for j in range(len_arr2 + 1):
        dist[0, j] = j
        
    for i in range(1, len_arr1 + 1):
        for j in range(1, len_arr2 + 1):
            cost = 0 if arr1[i-1] == arr2[j-1] else 2  # Substitution cost is 2
            
            dist[i, j] = min(dist[i-1, j] + 1,        # Deletion
                             dist[i, j-1] + 1,        # Insertion
                             dist[i-1, j-1] + cost)   # Substitution
            
    return dist[len_arr1, len_arr2]

Check if all of the following conditions are true:

Run Code Interpreter

Running the following program: 

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from numba import jit
import numpy as np

@jit(nopython=True)
def levenshtein(arr1, arr2):
    len_arr1 = len(arr1)
    len_arr2 = len(arr2)
    
    # Initialize the distance matrix
    dist = np.zeros((len_arr1 + 1, len_arr2 + 1), dtype=np.int32)
    
    for i in range(len_arr1 + 1):
        dist[i, 0] = i
        
    for j in range(len_arr2 + 1):
        dist[0, j] = j
        
    for i in range(1, len_arr1 + 1):
        for j in range(1, len_arr2 + 1):
            cost = 0 if arr1[i-1] == arr2[j-1] else 2  # Substitution cost is 2
            
            dist[i, j] = min(dist[i-1, j] + 1,        # Deletion
                             dist[i, j-1] + 1,        # Insertion
                             dist[i-1, j-1] + cost)   # Substitution
            
    return dist[len_arr1, len_arr2]





answer = levenshtein(np.array([3, 5, 2, 4, 8, 7]), np.array([3, 4, 2, 4, 8, 7, 9]))
expected = 3
assert answer == expected, f'Wrong answer; got {answer} instead of {expected}'
print('All tests passed')
And got the output: All tests passed

Substring Evaluation

Testing if the previous output contains the string All tests passed: True

Check if any of the following conditions are true:

Substring Evaluation

Testing if the previous output contains the string njit: False

Substring Evaluation

Testing if the previous output contains the string nopython: True

Final Answer: True

Check if any of the following conditions are true:

Substring Evaluation

Testing if the previous output contains the string import numba: False

Substring Evaluation

Testing if the previous output contains the string from numba: True

Final Answer: True

Final Answer: True

Initial Query

Write me a numba implementation of levensthin distance, taking two numpy int arrays. Call it levenshtein. Run it in nopython mode. Character swaps are cost 2.

LLM Generation

Query

Write me a numba implementation of levensthin distance, taking two numpy int arrays. Call it levenshtein. Run it in nopython mode. Character swaps are cost 2.

Output

To create a Numba implementation of the Levenshtein distance that works with two NumPy arrays of integers and considers character swaps to have a cost of 2, you can follow the approach outlined below. This implementation will be designed to run in Nopython mode for efficiency. Numba is a Just-In-Time (JIT) compiler that translates a subset of Python and NumPy code into fast machine code. The following code example uses Numba's JIT decorator to compile the Python function into machine code when it's called with the specific argument types (in this case, NumPy arrays of integers) for the first time. The Levenshtein distance is a measure of the difference between two sequences. It is calculated as the minimum number of single-character edits (insertions, deletions, or substitutions) required to change one word into the other. In this implementation, we will modify the cost of substitutions (swaps) to be 2, as per your request. 

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import numpy as np
from numba import jit

@jit(nopython=True)
def levenshtein(arr1, arr2):
    len_arr1 = len(arr1)
    len_arr2 = len(arr2)
    if len_arr1 == 0:
        return len_arr2
    if len_arr2 == 0:
        return len_arr1

    d = np.zeros((len_arr1 + 1, len_arr2 + 1), dtype=np.int32)

    for i in range(len_arr1 + 1):
        d[i, 0] = i
    for j in range(len_arr2 + 1):
        d[0, j] = j

    for i in range(1, len_arr1 + 1):
        for j in range(1, len_arr2 + 1):
            cost = 0 if arr1[i - 1] == arr2[j - 1] else 2
            d[i, j] = min(
                d[i - 1, j] + 1,     # deletion
                d[i, j - 1] + 1,     # insertion
                d[i - 1, j - 1] + cost  # substitution
            )

    return d[len_arr1, len_arr2]

# Example usage
if __name__ == "__main__":
    arr1 = np.array([1, 2, 3, 4])
    arr2 = np.array([1, 2, 4, 5])
    print("Levenshtein distance:", levenshtein(arr1, arr2))
This script defines a `levenshtein` function that computes the Levenshtein distance between two NumPy arrays of integers. Note that we've explicitly imported `jit` from `numba` and used the `nopython=True` argument to ensure that the function is compiled in Nopython mode, which requires that the function be fully compiled (without using the Python object mode) for performance reasons. Remember to install Numba and NumPy in your environment if you haven't already: 
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pip install numba numpy
The example at the bottom shows how to use this function with two NumPy arrays.

Extract Code

I extracted the following code from that output: 

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import numpy as np
from numba import jit

@jit(nopython=True)
def levenshtein(arr1, arr2):
    len_arr1 = len(arr1)
    len_arr2 = len(arr2)
    if len_arr1 == 0:
        return len_arr2
    if len_arr2 == 0:
        return len_arr1

    d = np.zeros((len_arr1 + 1, len_arr2 + 1), dtype=np.int32)

    for i in range(len_arr1 + 1):
        d[i, 0] = i
    for j in range(len_arr2 + 1):
        d[0, j] = j

    for i in range(1, len_arr1 + 1):
        for j in range(1, len_arr2 + 1):
            cost = 0 if arr1[i - 1] == arr2[j - 1] else 2
            d[i, j] = min(
                d[i - 1, j] + 1,     # deletion
                d[i, j - 1] + 1,     # insertion
                d[i - 1, j - 1] + cost  # substitution
            )

    return d[len_arr1, len_arr2]

Check if all of the following conditions are true:

Run Code Interpreter

Running the following program: 

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import numpy as np
from numba import jit

@jit(nopython=True)
def levenshtein(arr1, arr2):
    len_arr1 = len(arr1)
    len_arr2 = len(arr2)
    if len_arr1 == 0:
        return len_arr2
    if len_arr2 == 0:
        return len_arr1

    d = np.zeros((len_arr1 + 1, len_arr2 + 1), dtype=np.int32)

    for i in range(len_arr1 + 1):
        d[i, 0] = i
    for j in range(len_arr2 + 1):
        d[0, j] = j

    for i in range(1, len_arr1 + 1):
        for j in range(1, len_arr2 + 1):
            cost = 0 if arr1[i - 1] == arr2[j - 1] else 2
            d[i, j] = min(
                d[i - 1, j] + 1,     # deletion
                d[i, j - 1] + 1,     # insertion
                d[i - 1, j - 1] + cost  # substitution
            )

    return d[len_arr1, len_arr2]





answer = levenshtein(np.array([3, 5, 2, 4, 8, 7]), np.array([3, 4, 2, 4, 8, 7, 9]))
expected = 3
assert answer == expected, f'Wrong answer; got {answer} instead of {expected}'
print('All tests passed')
And got the output: All tests passed

Substring Evaluation

Testing if the previous output contains the string All tests passed: True

Check if any of the following conditions are true:

Substring Evaluation

Testing if the previous output contains the string njit: False

Substring Evaluation

Testing if the previous output contains the string nopython: True

Final Answer: True

Check if any of the following conditions are true:

Substring Evaluation

Testing if the previous output contains the string import numba: False

Substring Evaluation

Testing if the previous output contains the string from numba: True

Final Answer: True

Final Answer: True

Initial Query

Write me a numba implementation of levensthin distance, taking two numpy int arrays. Call it levenshtein. Run it in nopython mode. Character swaps are cost 2.

LLM Generation

Query

Write me a numba implementation of levensthin distance, taking two numpy int arrays. Call it levenshtein. Run it in nopython mode. Character swaps are cost 2.

Output

Sure, I'll provide you with a Numba implementation of the Levenshtein distance, designed to work with two NumPy arrays of integers. The Levenshtein distance is a measure of the difference between two sequences. In its most simple form, it calculates the minimum number of single-character edits (insertions, deletions, or substitutions) required to change one word into the other. In this implementation, a character swap will be considered as two operations (delete and insert, or two substitutions), since Numba's `@njit` decorator (nopython mode) will be used for performance, and direct swapping is not inherently part of the standard Levenshtein algorithm. First, ensure you have Numba and NumPy installed in your environment: 

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pip install numba numpy
Then, use the following Python code with Numba to calculate the Levenshtein distance: 
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import numpy as np
from numba import njit

@njit
def levenshtein(arr1, arr2):
    """
    Compute the Levenshtein distance between two NumPy arrays of integers.
    """
    m, n = len(arr1), len(arr2)
    # Initialize the matrix
    dp = np.zeros((m + 1, n + 1), dtype=np.int32)
    
    # Initialize source prefixes to transform into empty string by deletions:
    for i in range(1, m + 1):
        dp[i, 0] = i
    
    # Initialize target prefixes to be transformed from empty string by inserting:
    for j in range(1, n + 1):
        dp[0, j] = j

    # Compute Levenshtein distance
    for i in range(1, m + 1):
        for j in range(1, n + 1):
            deletion = dp[i - 1, j] + 1
            insertion = dp[i, j - 1] + 1
            substitution = dp[i - 1, j - 1] + (0 if arr1[i - 1] == arr2[j - 1] else 2)
            dp[i, j] = min(deletion, insertion, substitution)
    
    return dp[m, n]

# Example usage:

# Convert the sequences or strings to numpy arrays of integers, if not already
arr1 = np.array([1, 2, 3, 4])
arr2 = np.array([1, 3, 4, 2])

distance = levenshtein(arr1, arr2)
print("Levenshtein Distance:", distance)
This implementation is a straightforward adaptation of the classic Levenshtein algorithm, adjusted for integer arrays and considering substitutions as having a cost of 2, as per your requirement. Note that this is a basic version and might need adjustments based on specific needs or optimizations for larger datasets.

Extract Code

I extracted the following code from that output: 

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import numpy as np
from numba import njit

@njit
def levenshtein(arr1, arr2):
    """
    Compute the Levenshtein distance between two NumPy arrays of integers.
    """
    m, n = len(arr1), len(arr2)
    # Initialize the matrix
    dp = np.zeros((m + 1, n + 1), dtype=np.int32)
    
    # Initialize source prefixes to transform into empty string by deletions:
    for i in range(1, m + 1):
        dp[i, 0] = i
    
    # Initialize target prefixes to be transformed from empty string by inserting:
    for j in range(1, n + 1):
        dp[0, j] = j

    # Compute Levenshtein distance
    for i in range(1, m + 1):
        for j in range(1, n + 1):
            deletion = dp[i - 1, j] + 1
            insertion = dp[i, j - 1] + 1
            substitution = dp[i - 1, j - 1] + (0 if arr1[i - 1] == arr2[j - 1] else 2)
            dp[i, j] = min(deletion, insertion, substitution)
    
    return dp[m, n]

Check if all of the following conditions are true:

Run Code Interpreter

Running the following program: 

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import numpy as np
from numba import njit

@njit
def levenshtein(arr1, arr2):
    """
    Compute the Levenshtein distance between two NumPy arrays of integers.
    """
    m, n = len(arr1), len(arr2)
    # Initialize the matrix
    dp = np.zeros((m + 1, n + 1), dtype=np.int32)
    
    # Initialize source prefixes to transform into empty string by deletions:
    for i in range(1, m + 1):
        dp[i, 0] = i
    
    # Initialize target prefixes to be transformed from empty string by inserting:
    for j in range(1, n + 1):
        dp[0, j] = j

    # Compute Levenshtein distance
    for i in range(1, m + 1):
        for j in range(1, n + 1):
            deletion = dp[i - 1, j] + 1
            insertion = dp[i, j - 1] + 1
            substitution = dp[i - 1, j - 1] + (0 if arr1[i - 1] == arr2[j - 1] else 2)
            dp[i, j] = min(deletion, insertion, substitution)
    
    return dp[m, n]





answer = levenshtein(np.array([3, 5, 2, 4, 8, 7]), np.array([3, 4, 2, 4, 8, 7, 9]))
expected = 3
assert answer == expected, f'Wrong answer; got {answer} instead of {expected}'
print('All tests passed')
And got the output: All tests passed

Substring Evaluation

Testing if the previous output contains the string All tests passed: True

Check if any of the following conditions are true:

Substring Evaluation

Testing if the previous output contains the string njit: True

Substring Evaluation

Testing if the previous output contains the string nopython: False

Final Answer: True

Check if any of the following conditions are true:

Substring Evaluation

Testing if the previous output contains the string import numba: False

Substring Evaluation

Testing if the previous output contains the string from numba: True

Final Answer: True

Final Answer: True

Initial Query

Write me a numba implementation of levensthin distance, taking two numpy int arrays. Call it levenshtein. Run it in nopython mode. Character swaps are cost 2.

LLM Generation

Query

Write me a numba implementation of levensthin distance, taking two numpy int arrays. Call it levenshtein. Run it in nopython mode. Character swaps are cost 2.

Output

Certainly! Below is an implementation of the Levenshtein distance algorithm, specifically tailored for dealing with numpy arrays of integers. The implementation is designed to work in nopython mode with Numba, a high-performance Just-In-Time compiler for Python. This version of the Levenshtein distance takes into account substitutions with a cost of 2, in line with your request. Insertions and deletions still have a cost of 1. First, ensure you have Numba and numpy installed in your environment: 

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pip install numba numpy
Then, you can use the following Python code: 
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import numpy as np
from numba import njit

@njit
def levenshtein(arr1, arr2):
    """
    Compute the Levenshtein distance between two numpy arrays of integers.
    In this implementation, character swaps (substitutions) have a cost of 2.
    Insertions and deletions have a cost of 1.
    """
    len_arr1 = len(arr1)
    len_arr2 = len(arr2)
    
    # Initialize the matrix
    dp = np.zeros((len_arr1 + 1, len_arr2 + 1), dtype=np.int32)
    
    for i in range(len_arr1 + 1):
        for j in range(len_arr2 + 1):
            if i == 0:
                dp[i][j] = j  # Deletion
            elif j == 0:
                dp[i][j] = i  # Insertion
            else:
                cost = 0 if arr1[i-1] == arr2[j-1] else 2
                dp[i][j] = min(dp[i-1][j] + 1,  # Insertion
                               dp[i][j-1] + 1,  # Deletion
                               dp[i-1][j-1] + cost)  # Substitution
    
    return dp[len_arr1][len_arr2]

# Example usage
if __name__ == "__main__":
    arr1 = np.array([1, 2, 3], dtype=np.int32)
    arr2 = np.array([1, 3, 2], dtype=np.int32)
    
    distance = levenshtein(arr1, arr2)
    print(f"Levenshtein distance: {distance}")
This code defines a function `levenshtein` that calculates the Levenshtein distance between two numpy arrays of integers, adjusting the cost of substitutions to 2 as per your request. You can test this function with any pair of integer arrays by following the example provided in the `if __name__ == "__main__"` block.

Extract Code

I extracted the following code from that output: 

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import numpy as np
from numba import njit

@njit
def levenshtein(arr1, arr2):
    """
    Compute the Levenshtein distance between two numpy arrays of integers.
    In this implementation, character swaps (substitutions) have a cost of 2.
    Insertions and deletions have a cost of 1.
    """
    len_arr1 = len(arr1)
    len_arr2 = len(arr2)
    
    # Initialize the matrix
    dp = np.zeros((len_arr1 + 1, len_arr2 + 1), dtype=np.int32)
    
    for i in range(len_arr1 + 1):
        for j in range(len_arr2 + 1):
            if i == 0:
                dp[i][j] = j  # Deletion
            elif j == 0:
                dp[i][j] = i  # Insertion
            else:
                cost = 0 if arr1[i-1] == arr2[j-1] else 2
                dp[i][j] = min(dp[i-1][j] + 1,  # Insertion
                               dp[i][j-1] + 1,  # Deletion
                               dp[i-1][j-1] + cost)  # Substitution
    
    return dp[len_arr1][len_arr2]

Check if all of the following conditions are true:

Run Code Interpreter

Running the following program: 

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import numpy as np
from numba import njit

@njit
def levenshtein(arr1, arr2):
    """
    Compute the Levenshtein distance between two numpy arrays of integers.
    In this implementation, character swaps (substitutions) have a cost of 2.
    Insertions and deletions have a cost of 1.
    """
    len_arr1 = len(arr1)
    len_arr2 = len(arr2)
    
    # Initialize the matrix
    dp = np.zeros((len_arr1 + 1, len_arr2 + 1), dtype=np.int32)
    
    for i in range(len_arr1 + 1):
        for j in range(len_arr2 + 1):
            if i == 0:
                dp[i][j] = j  # Deletion
            elif j == 0:
                dp[i][j] = i  # Insertion
            else:
                cost = 0 if arr1[i-1] == arr2[j-1] else 2
                dp[i][j] = min(dp[i-1][j] + 1,  # Insertion
                               dp[i][j-1] + 1,  # Deletion
                               dp[i-1][j-1] + cost)  # Substitution
    
    return dp[len_arr1][len_arr2]





answer = levenshtein(np.array([3, 5, 2, 4, 8, 7]), np.array([3, 4, 2, 4, 8, 7, 9]))
expected = 3
assert answer == expected, f'Wrong answer; got {answer} instead of {expected}'
print('All tests passed')
And got the output: All tests passed

Substring Evaluation

Testing if the previous output contains the string All tests passed: True

Check if any of the following conditions are true:

Substring Evaluation

Testing if the previous output contains the string njit: True

Substring Evaluation

Testing if the previous output contains the string nopython: False

Final Answer: True

Check if any of the following conditions are true:

Substring Evaluation

Testing if the previous output contains the string import numba: False

Substring Evaluation

Testing if the previous output contains the string from numba: True

Final Answer: True

Final Answer: True

Initial Query

Write me a numba implementation of levensthin distance, taking two numpy int arrays. Call it levenshtein. Run it in nopython mode. Character swaps are cost 2.

LLM Generation

Query

Write me a numba implementation of levensthin distance, taking two numpy int arrays. Call it levenshtein. Run it in nopython mode. Character swaps are cost 2.

Output

To create a Numba implementation of the Levenshtein distance algorithm that operates on two numpy arrays of integers and runs in nopython mode, you can follow the structure below. This version of the Levenshtein distance algorithm includes a cost of 2 for character swaps, instead of the more traditional cost of 1. This means that substitution operations are penalized more heavily compared to insertions or deletions. First, ensure you have Numba and NumPy installed in your environment. You can install them using pip if you haven't already: 

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pip install numba numpy
Here's the Python code with Numba's JIT decorator to compile the function in nopython mode: 
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from numba import jit
import numpy as np

@jit(nopython=True)
def levenshtein(arr1, arr2):
    len_arr1 = len(arr1) + 1
    len_arr2 = len(arr2) + 1
    d = np.zeros((len_arr1, len_arr2), dtype=np.int32)
    
    for i in range(len_arr1):
        d[i, 0] = i
    for j in range(len_arr2):
        d[0, j] = j
    
    for i in range(1, len_arr1):
        for j in range(1, len_arr2):
            cost = 0 if arr1[i - 1] == arr2[j - 1] else 2
            d[i, j] = min(d[i - 1, j] + 1,        # deletion
                          d[i, j - 1] + 1,        # insertion
                          d[i - 1, j - 1] + cost) # substitution
            
    return d[len_arr1 - 1, len_arr2 - 1]

# Example usage:
arr1 = np.array([1, 2, 3, 4])
arr2 = np.array([1, 3, 4, 2])

distance = levenshtein(arr1, arr2)
print(f"Levenshtein distance: {distance}")
This code defines a function `levenshtein` that calculates the Levenshtein distance between two numpy arrays of integers. The distance calculation incorporates a substitution cost of 2. You can replace `arr1` and `arr2` in the example usage with any two numpy arrays of integers you wish to compare. Remember that the Levenshtein distance measures the minimum number of single-character edits (insertions, deletions, or substitutions) required to change one word into the other. Since this implementation uses numpy arrays of integers, you can think of each integer as a "character" in this context.

Extract Code

I extracted the following code from that output: 

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from numba import jit
import numpy as np

@jit(nopython=True)
def levenshtein(arr1, arr2):
    len_arr1 = len(arr1) + 1
    len_arr2 = len(arr2) + 1
    d = np.zeros((len_arr1, len_arr2), dtype=np.int32)
    
    for i in range(len_arr1):
        d[i, 0] = i
    for j in range(len_arr2):
        d[0, j] = j
    
    for i in range(1, len_arr1):
        for j in range(1, len_arr2):
            cost = 0 if arr1[i - 1] == arr2[j - 1] else 2
            d[i, j] = min(d[i - 1, j] + 1,        # deletion
                          d[i, j - 1] + 1,        # insertion
                          d[i - 1, j - 1] + cost) # substitution
            
    return d[len_arr1 - 1, len_arr2 - 1]

Check if all of the following conditions are true:

Run Code Interpreter

Running the following program: 

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from numba import jit
import numpy as np

@jit(nopython=True)
def levenshtein(arr1, arr2):
    len_arr1 = len(arr1) + 1
    len_arr2 = len(arr2) + 1
    d = np.zeros((len_arr1, len_arr2), dtype=np.int32)
    
    for i in range(len_arr1):
        d[i, 0] = i
    for j in range(len_arr2):
        d[0, j] = j
    
    for i in range(1, len_arr1):
        for j in range(1, len_arr2):
            cost = 0 if arr1[i - 1] == arr2[j - 1] else 2
            d[i, j] = min(d[i - 1, j] + 1,        # deletion
                          d[i, j - 1] + 1,        # insertion
                          d[i - 1, j - 1] + cost) # substitution
            
    return d[len_arr1 - 1, len_arr2 - 1]





answer = levenshtein(np.array([3, 5, 2, 4, 8, 7]), np.array([3, 4, 2, 4, 8, 7, 9]))
expected = 3
assert answer == expected, f'Wrong answer; got {answer} instead of {expected}'
print('All tests passed')
And got the output: All tests passed

Substring Evaluation

Testing if the previous output contains the string All tests passed: True

Check if any of the following conditions are true:

Substring Evaluation

Testing if the previous output contains the string njit: False

Substring Evaluation

Testing if the previous output contains the string nopython: True

Final Answer: True

Check if any of the following conditions are true:

Substring Evaluation

Testing if the previous output contains the string import numba: False

Substring Evaluation

Testing if the previous output contains the string from numba: True

Final Answer: True

Final Answer: True