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 a Numba-optimized implementation of the Levenshtein distance algorithm tailored for two NumPy integer arrays. This implementation operates in **nopython** mode for maximum performance. Additionally, it considers character swaps (transpositions) with a cost of 2, effectively implementing the Damerau-Levenshtein distance. 

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import numpy as np
from numba import njit

@njit
def levenshtein(a, b):
    """
    Compute the Damerau-Levenshtein distance between two integer arrays.
    Operations:
        - Insertion: 1
        - Deletion: 1
        - Substitution: 1
        - Transposition (swap): 2
    Parameters:
        a (np.ndarray): 1D array of integers.
        b (np.ndarray): 1D array of integers.
    Returns:
        int: The Damerau-Levenshtein distance between `a` and `b`.
    """
    len_a = a.shape[0]
    len_b = b.shape[0]
    
    # Initialize the distance matrix
    dp = np.zeros((len_a + 1, len_b + 1), dtype=np.int32)
    
    for i in range(len_a + 1):
        dp[i, 0] = i
    for j in range(len_b + 1):
        dp[0, j] = j
        
    for i in range(1, len_a + 1):
        for j in range(1, len_b + 1):
            cost = 0 if a[i-1] == b[j-1] else 1
            # Compute minimum of deletion, insertion, substitution
            min_cost = dp[i-1, j] + 1            # Deletion
            if dp[i, j-1] + 1 < min_cost:
                min_cost = dp[i, j-1] + 1        # Insertion
            if dp[i-1, j-1] + cost < min_cost:
                min_cost = dp[i-1, j-1] + cost  # Substitution
            
            # Check for transposition
            if i > 1 and j > 1 and a[i-1] == b[j-2] and a[i-2] == b[j-1]:
                trans_cost = dp[i-2, j-2] + 2  # Transposition cost
                if trans_cost < min_cost:
                    min_cost = trans_cost
            dp[i, j] = min_cost
    return dp[len_a, len_b]

# Example usage:
if __name__ == "__main__":
    # Example integer arrays
    a = np.array([1, 2, 3, 4], dtype=np.int32)
    b = np.array([1, 3, 2, 4], dtype=np.int32)
    
    distance = levenshtein(a, b)
    print(f"Levenshtein distance: {distance}")
### Explanation: 1. **Imports:** - `numpy` for handling integer arrays. - `njit` from `numba` to compile the function in nopython mode for optimal performance. 2. **Function `levenshtein`:** - **Parameters:** - `a`: First input NumPy integer array. - `b`: Second input NumPy integer array. - **Initialization:** - The distance matrix `dp` of size `(len(a)+1) x (len(b)+1)` is initialized. - The first row and first column are populated to represent the base cases of transforming empty strings. - **Dynamic Programming:** - Iterates through each character of both arrays. - Calculates the cost for deletion, insertion, and substitution. - Additionally checks for possible transpositions (swaps) and applies the specified cost. - **Return:** - The final cell `dp[len_a, len_b]` contains the Damerau-Levenshtein distance. 3. **Example Usage:** - Demonstrates how to use the `levenshtein` function with example integer arrays. - Outputs the computed distance. ### Notes: - **Performance:** - This implementation is optimized using Numba's `njit` decorator, which compiles the function to machine code, resulting in significant speedups, especially for large arrays. - **Transposition Handling:** - The function checks for adjacent character swaps (transpositions) and applies a cost of 2 when such an operation can reduce the overall distance. - **Data Types:** - It's important that the input arrays `a` and `b` are one-dimensional NumPy arrays of integers (`dtype=np.int32` or similar). Feel free to integrate this function into your codebase. If you encounter any issues or have further customization needs, let me know!

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(a, b):
    """
    Compute the Damerau-Levenshtein distance between two integer arrays.
    Operations:
        - Insertion: 1
        - Deletion: 1
        - Substitution: 1
        - Transposition (swap): 2
    Parameters:
        a (np.ndarray): 1D array of integers.
        b (np.ndarray): 1D array of integers.
    Returns:
        int: The Damerau-Levenshtein distance between `a` and `b`.
    """
    len_a = a.shape[0]
    len_b = b.shape[0]
    
    # Initialize the distance matrix
    dp = np.zeros((len_a + 1, len_b + 1), dtype=np.int32)
    
    for i in range(len_a + 1):
        dp[i, 0] = i
    for j in range(len_b + 1):
        dp[0, j] = j
        
    for i in range(1, len_a + 1):
        for j in range(1, len_b + 1):
            cost = 0 if a[i-1] == b[j-1] else 1
            # Compute minimum of deletion, insertion, substitution
            min_cost = dp[i-1, j] + 1            # Deletion
            if dp[i, j-1] + 1 < min_cost:
                min_cost = dp[i, j-1] + 1        # Insertion
            if dp[i-1, j-1] + cost < min_cost:
                min_cost = dp[i-1, j-1] + cost  # Substitution
            
            # Check for transposition
            if i > 1 and j > 1 and a[i-1] == b[j-2] and a[i-2] == b[j-1]:
                trans_cost = dp[i-2, j-2] + 2  # Transposition cost
                if trans_cost < min_cost:
                    min_cost = trans_cost
            dp[i, j] = min_cost
    return dp[len_a, len_b]

# Example usage:
if __name__ == "__main__":
    # Example integer arrays
    a = np.array([1, 2, 3, 4], dtype=np.int32)
    b = np.array([1, 3, 2, 4], dtype=np.int32)
    
    distance = levenshtein(a, b)
    print(f"Levenshtein distance: {distance}")

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(a, b):
    """
    Compute the Damerau-Levenshtein distance between two integer arrays.
    Operations:
        - Insertion: 1
        - Deletion: 1
        - Substitution: 1
        - Transposition (swap): 2
    Parameters:
        a (np.ndarray): 1D array of integers.
        b (np.ndarray): 1D array of integers.
    Returns:
        int: The Damerau-Levenshtein distance between `a` and `b`.
    """
    len_a = a.shape[0]
    len_b = b.shape[0]
    
    # Initialize the distance matrix
    dp = np.zeros((len_a + 1, len_b + 1), dtype=np.int32)
    
    for i in range(len_a + 1):
        dp[i, 0] = i
    for j in range(len_b + 1):
        dp[0, j] = j
        
    for i in range(1, len_a + 1):
        for j in range(1, len_b + 1):
            cost = 0 if a[i-1] == b[j-1] else 1
            # Compute minimum of deletion, insertion, substitution
            min_cost = dp[i-1, j] + 1            # Deletion
            if dp[i, j-1] + 1 < min_cost:
                min_cost = dp[i, j-1] + 1        # Insertion
            if dp[i-1, j-1] + cost < min_cost:
                min_cost = dp[i-1, j-1] + cost  # Substitution
            
            # Check for transposition
            if i > 1 and j > 1 and a[i-1] == b[j-2] and a[i-2] == b[j-1]:
                trans_cost = dp[i-2, j-2] + 2  # Transposition cost
                if trans_cost < min_cost:
                    min_cost = trans_cost
            dp[i, j] = min_cost
    return dp[len_a, len_b]

# Example usage:
if __name__ == "__main__":
    # Example integer arrays
    a = np.array([1, 2, 3, 4], dtype=np.int32)
    b = np.array([1, 3, 2, 4], dtype=np.int32)
    
    distance = levenshtein(a, b)
    print(f"Levenshtein distance: {distance}")





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: Levenshtein distance: 2 Traceback (most recent call last): File "/usr/src/app/main.py", line 64, in <module> assert answer == expected, f'Wrong answer; got {answer} instead of {expected}' AssertionError: Wrong answer; got 2 instead of 3

Substring Evaluation

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

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: False

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 a Numba-optimized implementation of the Levenshtein distance tailored to work with two NumPy integer arrays. This implementation operates in **nopython mode** for maximum performance and assigns a cost of **2** for character swaps (transpositions). ### Overview - **Function Name**: `levenshtein` - **Inputs**: - `a`: NumPy integer array representing the first sequence. - `b`: NumPy integer array representing the second sequence. - **Output**: An integer representing the Levenshtein distance between the two input arrays. - **Operation Costs**: - **Insertion**: 1 - **Deletion**: 1 - **Substitution**: 1 - **Swap (Transposition)**: 2 ### Implementation Details 1. **Initialization**: - The algorithm initializes two 1D arrays: `previous` and `current` to store distance computations for the previous and current rows of the dynamic programming matrix. - The `previous` array is initialized to represent the distance from an empty sequence to the first sequence. 2. **Dynamic Programming Loop**: - Iterates through each character in both input arrays. - Computes the cost of insertion, deletion, and substitution. - Additionally checks for possible transpositions (swaps) and updates the distance accordingly if a swap is detected. 3. **Swap Detection**: - A swap is considered only if the current and previous characters in both sequences are transposed. - If a swap is possible, it updates the distance by considering the swap cost. 4. **Final Distance**: - After processing all characters, the final distance is obtained from the `previous` array. ### Complete Code 

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import numpy as np
from numba import njit

@njit
def levenshtein(a: np.ndarray, b: np.ndarray) -> int:
    """
    Compute the Levenshtein distance between two integer arrays with
    insertion, deletion, substitution costs of 1 and swap (transposition) cost of 2.

    Parameters:
    a (np.ndarray): First integer array.
    b (np.ndarray): Second integer array.

    Returns:
    int: The Levenshtein distance.
    """
    m = a.shape[0]
    n = b.shape[0]

    # Handle empty strings
    if m == 0:
        return n
    if n == 0:
        return m

    # Initialize two work vectors
    previous = np.empty(n + 1, dtype=np.int32)
    current = np.empty(n + 1, dtype=np.int32)

    # Initialize the previous row
    for j in range(n + 1):
        previous[j] = j

    # Iterate over each character in a
    for i in range(1, m + 1):
        current[0] = i
        for j in range(1, n + 1):
            if a[i - 1] == b[j - 1]:
                cost = 0
            else:
                cost = 1

            # Calculate minimum cost among insertion, deletion, and substitution
            insertion = current[j - 1] + 1
            deletion = previous[j] + 1
            substitution = previous[j - 1] + cost

            min_cost = insertion
            if deletion < min_cost:
                min_cost = deletion
            if substitution < min_cost:
                min_cost = substitution

            # Check for possible swap (transposition)
            if i > 1 and j > 1 and a[i - 1] == b[j - 2] and a[i - 2] == b[j - 1]:
                swap = previous[j - 2] + 2  # Cost of swapping is 2
                if swap < min_cost:
                    min_cost = swap

            current[j] = min_cost

        # Swap the current and previous rows for next iteration
        temp = previous
        previous = current
        current = temp

    return previous[n]

# Example Usage
if __name__ == "__main__":
    # Example integer arrays representing sequences
    a = np.array([1, 2, 3, 4], dtype=np.int32)
    b = np.array([1, 3, 2, 4], dtype=np.int32)

    distance = levenshtein(a, b)
    print(f"Levenshtein distance: {distance}")
### Explanation of the Example In the provided example: - **Sequence `a`**: `[1, 2, 3, 4]` - **Sequence `b`**: `[1, 3, 2, 4]` Here, the sequences `a` and `b` can be transformed into each other by swapping the `2` and `3`. Since the cost of a swap is `2`, the Levenshtein distance computed will be `2`. ### Notes - **Numba's `njit` Decorator**: The `@njit` decorator compiles the function in nopython mode, ensuring high performance by avoiding Python interpreter overhead. - **Data Types**: It's essential to use fixed-size NumPy data types (e.g., `np.int32`) to ensure compatibility with Numba's nopython mode. - **Performance**: This implementation is optimized for performance with large sequences, leveraging Numba's just-in-time compilation. Feel free to integrate this function into your projects where you need an efficient computation of the Levenshtein distance between two integer sequences with specified operation costs.

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(a: np.ndarray, b: np.ndarray) -> int:
    """
    Compute the Levenshtein distance between two integer arrays with
    insertion, deletion, substitution costs of 1 and swap (transposition) cost of 2.

    Parameters:
    a (np.ndarray): First integer array.
    b (np.ndarray): Second integer array.

    Returns:
    int: The Levenshtein distance.
    """
    m = a.shape[0]
    n = b.shape[0]

    # Handle empty strings
    if m == 0:
        return n
    if n == 0:
        return m

    # Initialize two work vectors
    previous = np.empty(n + 1, dtype=np.int32)
    current = np.empty(n + 1, dtype=np.int32)

    # Initialize the previous row
    for j in range(n + 1):
        previous[j] = j

    # Iterate over each character in a
    for i in range(1, m + 1):
        current[0] = i
        for j in range(1, n + 1):
            if a[i - 1] == b[j - 1]:
                cost = 0
            else:
                cost = 1

            # Calculate minimum cost among insertion, deletion, and substitution
            insertion = current[j - 1] + 1
            deletion = previous[j] + 1
            substitution = previous[j - 1] + cost

            min_cost = insertion
            if deletion < min_cost:
                min_cost = deletion
            if substitution < min_cost:
                min_cost = substitution

            # Check for possible swap (transposition)
            if i > 1 and j > 1 and a[i - 1] == b[j - 2] and a[i - 2] == b[j - 1]:
                swap = previous[j - 2] + 2  # Cost of swapping is 2
                if swap < min_cost:
                    min_cost = swap

            current[j] = min_cost

        # Swap the current and previous rows for next iteration
        temp = previous
        previous = current
        current = temp

    return previous[n]

# Example Usage
if __name__ == "__main__":
    # Example integer arrays representing sequences
    a = np.array([1, 2, 3, 4], dtype=np.int32)
    b = np.array([1, 3, 2, 4], dtype=np.int32)

    distance = levenshtein(a, b)
    print(f"Levenshtein distance: {distance}")

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(a: np.ndarray, b: np.ndarray) -> int:
    """
    Compute the Levenshtein distance between two integer arrays with
    insertion, deletion, substitution costs of 1 and swap (transposition) cost of 2.

    Parameters:
    a (np.ndarray): First integer array.
    b (np.ndarray): Second integer array.

    Returns:
    int: The Levenshtein distance.
    """
    m = a.shape[0]
    n = b.shape[0]

    # Handle empty strings
    if m == 0:
        return n
    if n == 0:
        return m

    # Initialize two work vectors
    previous = np.empty(n + 1, dtype=np.int32)
    current = np.empty(n + 1, dtype=np.int32)

    # Initialize the previous row
    for j in range(n + 1):
        previous[j] = j

    # Iterate over each character in a
    for i in range(1, m + 1):
        current[0] = i
        for j in range(1, n + 1):
            if a[i - 1] == b[j - 1]:
                cost = 0
            else:
                cost = 1

            # Calculate minimum cost among insertion, deletion, and substitution
            insertion = current[j - 1] + 1
            deletion = previous[j] + 1
            substitution = previous[j - 1] + cost

            min_cost = insertion
            if deletion < min_cost:
                min_cost = deletion
            if substitution < min_cost:
                min_cost = substitution

            # Check for possible swap (transposition)
            if i > 1 and j > 1 and a[i - 1] == b[j - 2] and a[i - 2] == b[j - 1]:
                swap = previous[j - 2] + 2  # Cost of swapping is 2
                if swap < min_cost:
                    min_cost = swap

            current[j] = min_cost

        # Swap the current and previous rows for next iteration
        temp = previous
        previous = current
        current = temp

    return previous[n]

# Example Usage
if __name__ == "__main__":
    # Example integer arrays representing sequences
    a = np.array([1, 2, 3, 4], dtype=np.int32)
    b = np.array([1, 3, 2, 4], dtype=np.int32)

    distance = levenshtein(a, b)
    print(f"Levenshtein distance: {distance}")





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: Levenshtein distance: 2 Traceback (most recent call last): File "/usr/src/app/main.py", line 85, in <module> assert answer == expected, f'Wrong answer; got {answer} instead of {expected}' AssertionError: Wrong answer; got 2 instead of 3

Substring Evaluation

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

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: False