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, here's a Numba implementation of the Levenshtein distance function that takes two NumPy integer arrays as input. It also includes the cost of character swaps, which is set to 2. 

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import numpy as np
from numba import njit

@njit(nopython=True)
def levenshtein(str1, str2):
    n, m = len(str1), len(str2)
    dp = np.zeros((n + 1, m + 1), dtype=np.int64)

    for i in range(n + 1):
        dp[i, 0] = i
    for j in range(m + 1):
        dp[0, j] = j

    for i in range(1, n + 1):
        for j in range(1, m + 1):
            if str1[i - 1] == str2[j - 1]:
                cost = 0
            else:
                cost = 1

            dp[i, j] = min(
                dp[i - 1, j] + 1,
                dp[i, j - 1] + 1,
                dp[i - 1, j - 1] + cost
            )

            # Check for swaps
            if i > 1 and j > 1 and str1[i - 1] == str2[j - 2] and str1[i - 2] == str2[j - 1]:
                dp[i, j] = min(dp[i, j], dp[i - 2, j - 2] + 2)

    return dp[n, m]
Here's how you can use this function: 
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str1 = np.array([1, 2, 3, 4], dtype=np.int64)
str2 = np.array([1, 2, 4], dtype=np.int64)

distance = levenshtein(str1, str2)
print(f"The Levenshtein distance between {str1} and {str2} is {distance}")
This will output: 
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The Levenshtein distance between [1 2 3 4] and [1 2 4] is 2
Explanation: 1. The `levenshtein` function takes two NumPy integer arrays `str1` and `str2` as input. 2. The function initializes a 2D NumPy array `dp` to store the Levenshtein distances for subproblems. 3. The base cases are set, where the Levenshtein distance between an empty string and a string of length `n` is `n`. 4. The function iterates over the characters of `str1` and `str2` and computes the Levenshtein distance using dynamic programming. 5. If the current characters match, the cost is 0; otherwise, the cost is 1. 6. The Levenshtein distance at `dp[i, j]` is the minimum of three cases: - Deleting a character from `str1`: `dp[i - 1, j] + 1` - Deleting a character from `str2`: `dp[i, j - 1] + 1` - Replacing a character in `str1` with the corresponding character in `str2`: `dp[i - 1, j - 1] + cost` 7. Additionally, the function checks for swaps by looking at the previous two characters in both strings. If a swap is possible, it updates the Levenshtein distance at `dp[i, j]` with the minimum of the current distance and the distance from the subproblem `dp[i - 2, j - 2]` plus 2 (the cost of a swap). 8. Finally, the function returns the Levenshtein distance stored in `dp[n, m]`, where `n` and `m` are the lengths of `str1` and `str2`, respectively. Note that the `@njit(nopython=True)` decorator from Numba is used to compile the function to machine code, enabling faster execution.

Extract Code

I extracted the following code from that output: 

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import numpy as np
from numba import njit

@njit(nopython=True)
def levenshtein(str1, str2):
    n, m = len(str1), len(str2)
    dp = np.zeros((n + 1, m + 1), dtype=np.int64)

    for i in range(n + 1):
        dp[i, 0] = i
    for j in range(m + 1):
        dp[0, j] = j

    for i in range(1, n + 1):
        for j in range(1, m + 1):
            if str1[i - 1] == str2[j - 1]:
                cost = 0
            else:
                cost = 1

            dp[i, j] = min(
                dp[i - 1, j] + 1,
                dp[i, j - 1] + 1,
                dp[i - 1, j - 1] + cost
            )

            if i > 1 and j > 1 and str1[i - 1] == str2[j - 2] and str1[i - 2] == str2[j - 1]:
                dp[i, j] = min(dp[i, j], dp[i - 2, j - 2] + 2)

    return dp[n, m]

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(nopython=True)
def levenshtein(str1, str2):
    n, m = len(str1), len(str2)
    dp = np.zeros((n + 1, m + 1), dtype=np.int64)

    for i in range(n + 1):
        dp[i, 0] = i
    for j in range(m + 1):
        dp[0, j] = j

    for i in range(1, n + 1):
        for j in range(1, m + 1):
            if str1[i - 1] == str2[j - 1]:
                cost = 0
            else:
                cost = 1

            dp[i, j] = min(
                dp[i - 1, j] + 1,
                dp[i, j - 1] + 1,
                dp[i - 1, j - 1] + cost
            )

            if i > 1 and j > 1 and str1[i - 1] == str2[j - 2] and str1[i - 2] == str2[j - 1]:
                dp[i, j] = min(dp[i, j], dp[i - 2, j - 2] + 2)

    return dp[n, m]





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: /usr/local/lib/python3.11/dist-packages/numba/core/decorators.py:250: RuntimeWarning: nopython is set for njit and is ignored warnings.warn('nopython is set for njit and is ignored', RuntimeWarning) Traceback (most recent call last): File "/usr/src/app/main.py", line 39, 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: 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: 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

Here's a Numba implementation of the Levenshtein distance function that takes two NumPy integer arrays as input. This implementation considers the cost of character swaps as 2. 

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import numpy as np
from numba import jit

@jit(nopython=True)
def levenshtein(s1, s2):
    m, n = len(s1), len(s2)
    dp = np.zeros((m + 1, n + 1), dtype=np.int64)

    # Initialize the base cases
    for i in range(m + 1):
        dp[i, 0] = i
    for j in range(n + 1):
        dp[0, j] = j

    # Fill the dp table
    for i in range(1, m + 1):
        for j in range(1, n + 1):
            if s1[i - 1] == s2[j - 1]:
                dp[i, j] = dp[i - 1, j - 1]
            else:
                dp[i, j] = min(
                    dp[i - 1, j] + 1,  # Deletion
                    dp[i, j - 1] + 1,  # Insertion
                    dp[i - 1, j - 1] + 2  # Substitution (or swap)
                )

    return dp[m, n]

# Example usage
s1 = np.array([1, 2, 3, 4], dtype=np.int64)
s2 = np.array([2, 3, 4, 5], dtype=np.int64)

distance = levenshtein(s1, s2)
print(f"The Levenshtein distance between {s1} and {s2} is {distance}")
In this implementation, the `levenshtein` function takes two NumPy integer arrays `s1` and `s2` as input and computes the Levenshtein distance between them. The cost of a character swap is set to 2. The function uses dynamic programming to fill a 2D table `dp` of size `(m + 1) x (n + 1)`, where `m` and `n` are the lengths of `s1` and `s2`, respectively. The base cases are initialized with the respective lengths of the strings, as the cost of transforming an empty string to another string is equal to the length of the target string. The main loop fills the `dp` table by considering three operations: deletion, insertion, and substitution (or swap). The minimum cost among these three operations is stored in the corresponding cell in the `dp` table. Finally, the function returns the value stored in `dp[m, n]`, which represents the Levenshtein distance between `s1` and `s2`. Note that the `@jit(nopython=True)` decorator is used to enable Numba's just-in-time compilation, which can significantly improve the performance of the function for large inputs. In the example usage, two NumPy integer arrays `s1` and `s2` are created, and the `levenshtein` function is called with these arrays as input. The resulting Levenshtein distance is printed to the console.

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(s1, s2):
    m, n = len(s1), len(s2)
    dp = np.zeros((m + 1, n + 1), dtype=np.int64)

    # Initialize the base cases
    for i in range(m + 1):
        dp[i, 0] = i
    for j in range(n + 1):
        dp[0, j] = j

    # Fill the dp table
    for i in range(1, m + 1):
        for j in range(1, n + 1):
            if s1[i - 1] == s2[j - 1]:
                dp[i, j] = dp[i - 1, j - 1]
            else:
                dp[i, j] = min(
                    dp[i - 1, j] + 1,  # Deletion
                    dp[i, j - 1] + 1,  # Insertion
                    dp[i - 1, j - 1] + 2  # Substitution (or swap)
                )

    return dp[m, n]

# Example usage
s1 = np.array([1, 2, 3, 4], dtype=np.int64)
s2 = np.array([2, 3, 4, 5], dtype=np.int64)

distance = levenshtein(s1, s2)
print(f"The Levenshtein distance between {s1} and {s2} is {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 jit

@jit(nopython=True)
def levenshtein(s1, s2):
    m, n = len(s1), len(s2)
    dp = np.zeros((m + 1, n + 1), dtype=np.int64)

    # Initialize the base cases
    for i in range(m + 1):
        dp[i, 0] = i
    for j in range(n + 1):
        dp[0, j] = j

    # Fill the dp table
    for i in range(1, m + 1):
        for j in range(1, n + 1):
            if s1[i - 1] == s2[j - 1]:
                dp[i, j] = dp[i - 1, j - 1]
            else:
                dp[i, j] = min(
                    dp[i - 1, j] + 1,  # Deletion
                    dp[i, j - 1] + 1,  # Insertion
                    dp[i - 1, j - 1] + 2  # Substitution (or swap)
                )

    return dp[m, n]

# Example usage
s1 = np.array([1, 2, 3, 4], dtype=np.int64)
s2 = np.array([2, 3, 4, 5], dtype=np.int64)

distance = levenshtein(s1, s2)
print(f"The Levenshtein distance between {s1} and {s2} is {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: The Levenshtein distance between [1 2 3 4] and [2 3 4 5] is 2 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, here's a Numba implementation of the Levenshtein distance that takes two NumPy integer arrays and considers character swaps as a cost of 2. This implementation will run in `nopython` mode: 

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import numpy as np
from numba import jit, int64

@jit(nopython=True)
def levenshtein(a, b):
    """
    Compute the Levenshtein distance between two NumPy integer arrays.
    Character swaps have a cost of 2.
    """
    m, n = len(a), len(b)
    dp = np.zeros((m + 1, n + 1), dtype=np.int64)

    for i in range(m + 1):
        dp[i, 0] = i
    for j in range(n + 1):
        dp[0, j] = j

    for i in range(1, m + 1):
        for j in range(1, n + 1):
            if a[i - 1] == b[j - 1]:
                cost = 0
            else:
                cost = 1

            dp[i, j] = min(
                dp[i - 1, j] + 1,  # Deletion
                dp[i, j - 1] + 1,  # Insertion
                dp[i - 1, j - 1] + cost,  # Substitution
            )

            # Check for a swap
            if i > 1 and j > 1 and a[i - 1] == b[j - 2] and a[i - 2] == b[j - 1]:
                dp[i, j] = min(dp[i, j], dp[i - 2, j - 2] + 2)

    return int64(dp[m, n])
Here's how you can use this function: 
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a = np.array([1, 2, 3], dtype=np.int64)
b = np.array([2, 3, 1], dtype=np.int64)

distance = levenshtein(a, b)
print(distance)  # Output: 2
In this example, the Levenshtein distance between `[1, 2, 3]` and `[2, 3, 1]` is 2 (one swap operation is required). Here's a breakdown of the `levenshtein` function: 1. The function takes two NumPy integer arrays `a` and `b`. 2. It initializes a 2D NumPy array `dp` of dimensions `(m + 1, n + 1)`, where `m` and `n` are the lengths of `a` and `b`, respectively. This array will store the intermediate values for computing the Levenshtein distance. 3. It initializes the base cases by setting the first row and column of `dp` with the corresponding indices. 4. It iterates over the remaining cells of `dp` and computes the minimum cost of reaching that cell from its neighbors (deletion, insertion, or substitution). 5. It checks for a possible swap operation and updates the cost if a swap is possible. 6. Finally, it returns the value stored in the bottom-right cell of `dp`, which represents the Levenshtein distance between `a` and `b`. By using the `@jit(nopython=True)` decorator from Numba, this function will be compiled to efficient machine code and run in `nopython` mode, avoiding the overhead of the Python interpreter.

Extract Code

I extracted the following code from that output: 

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import numpy as np
from numba import jit, int64

@jit(nopython=True)
def levenshtein(a, b):
    m, n = len(a), len(b)
    dp = np.zeros((m + 1, n + 1), dtype=np.int64)

    for i in range(m + 1):
        dp[i, 0] = i
    for j in range(n + 1):
        dp[0, j] = j

    for i in range(1, m + 1):
        for j in range(1, n + 1):
            if a[i - 1] == b[j - 1]:
                cost = 0
            else:
                cost = 1

            dp[i, j] = min(
                dp[i - 1, j] + 1,
                dp[i, j - 1] + 1,
                dp[i - 1, j - 1] + cost,
            )

            if i > 1 and j > 1 and a[i - 1] == b[j - 2] and a[i - 2] == b[j - 1]:
                dp[i, j] = min(dp[i, j], dp[i - 2, j - 2] + 2)

    return int64(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 jit, int64

@jit(nopython=True)
def levenshtein(a, b):
    m, n = len(a), len(b)
    dp = np.zeros((m + 1, n + 1), dtype=np.int64)

    for i in range(m + 1):
        dp[i, 0] = i
    for j in range(n + 1):
        dp[0, j] = j

    for i in range(1, m + 1):
        for j in range(1, n + 1):
            if a[i - 1] == b[j - 1]:
                cost = 0
            else:
                cost = 1

            dp[i, j] = min(
                dp[i - 1, j] + 1,
                dp[i, j - 1] + 1,
                dp[i - 1, j - 1] + cost,
            )

            if i > 1 and j > 1 and a[i - 1] == b[j - 2] and a[i - 2] == b[j - 1]:
                dp[i, j] = min(dp[i, j], dp[i - 2, j - 2] + 2)

    return int64(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: Traceback (most recent call last): File "/usr/src/app/main.py", line 39, 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: 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: 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

Sure, here's a Numba implementation of the Levenshtein distance algorithm that takes two NumPy integer arrays as input. This implementation assumes that character swaps have a cost of 2. 

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import numpy as np
from numba import jit

@jit(nopython=True)
def levenshtein(a, b):
    """
    Compute the Levenshtein distance between two NumPy integer arrays.
    Character swaps are considered with a cost of 2.
    """
    m, n = len(a), len(b)
    dp = np.zeros((m + 1, n + 1), dtype=np.int64)

    # Initialize the first row and column
    for i in range(m + 1):
        dp[i, 0] = i
    for j in range(n + 1):
        dp[0, j] = j

    # Fill the dp table
    for i in range(1, m + 1):
        for j in range(1, n + 1):
            if a[i - 1] == b[j - 1]:
                dp[i, j] = dp[i - 1, j - 1]
            else:
                dp[i, j] = min(dp[i - 1, j], dp[i, j - 1], dp[i - 1, j - 1]) + 1
                # Check for swaps
                if i > 1 and j > 1 and a[i - 1] == b[j - 2] and a[i - 2] == b[j - 1]:
                    dp[i, j] = min(dp[i, j], dp[i - 2, j - 2] + 2)

    return dp[m, n]
Here's how you can use the `levenshtein` function: 
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# Example usage
a = np.array([1, 2, 3, 4, 5], dtype=np.int64)
b = np.array([2, 3, 4, 5, 6], dtype=np.int64)

distance = levenshtein(a, b)
print(f"The Levenshtein distance between {a} and {b} (with swaps cost 2) is: {distance}")
This will output: 
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The Levenshtein distance between [1 2 3 4 5] and [2 3 4 5 6] (with swaps cost 2) is: 3
Explanation: 1. The `levenshtein` function takes two NumPy integer arrays `a` and `b` as input. 2. It initializes a 2D NumPy array `dp` with zeros, where `dp[i, j]` will store the Levenshtein distance between the first `i` characters of `a` and the first `j` characters of `b`. 3. The first row and column of `dp` are initialized with the corresponding indices, as the distance between an empty string and a string of length `i` (or `j`) is simply `i` (or `j`). 4. The function then fills the `dp` table using dynamic programming. For each pair of characters `a[i - 1]` and `b[j - 1]`, it computes the minimum cost of the following operations: - Delete `a[i - 1]` and move to `dp[i - 1, j]` - Delete `b[j - 1]` and move to `dp[i, j - 1]` - Replace `a[i - 1]` with `b[j - 1]` (or vice versa) and move to `dp[i - 1, j - 1]` 5. Additionally, the function checks for potential character swaps by looking at the characters `a[i - 2]`, `a[i - 1]`, `b[j - 2]`, and `b[j - 1]`. If swapping these characters results in a lower cost, it updates `dp[i, j]` accordingly. 6. Finally, the function returns the value stored in `dp[m, n]`, which represents the Levenshtein distance between the entire strings `a` and `b`. Note that the `@jit(nopython=True)` decorator from Numba is used to enable ahead-of-time compilation and optimization of the `levenshtein` function, which can significantly improve its performance for numeric computations.

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(a, b):
    """
    Compute the Levenshtein distance between two NumPy integer arrays.
    Character swaps are considered with a cost of 2.
    """
    m, n = len(a), len(b)
    dp = np.zeros((m + 1, n + 1), dtype=np.int64)

    # Initialize the first row and column
    for i in range(m + 1):
        dp[i, 0] = i
    for j in range(n + 1):
        dp[0, j] = j

    # Fill the dp table
    for i in range(1, m + 1):
        for j in range(1, n + 1):
            if a[i - 1] == b[j - 1]:
                dp[i, j] = dp[i - 1, j - 1]
            else:
                dp[i, j] = min(dp[i - 1, j], dp[i, j - 1], dp[i - 1, j - 1]) + 1
                # Check for swaps
                if i > 1 and j > 1 and a[i - 1] == b[j - 2] and a[i - 2] == b[j - 1]:
                    dp[i, j] = min(dp[i, j], dp[i - 2, j - 2] + 2)

    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 jit

@jit(nopython=True)
def levenshtein(a, b):
    """
    Compute the Levenshtein distance between two NumPy integer arrays.
    Character swaps are considered with a cost of 2.
    """
    m, n = len(a), len(b)
    dp = np.zeros((m + 1, n + 1), dtype=np.int64)

    # Initialize the first row and column
    for i in range(m + 1):
        dp[i, 0] = i
    for j in range(n + 1):
        dp[0, j] = j

    # Fill the dp table
    for i in range(1, m + 1):
        for j in range(1, n + 1):
            if a[i - 1] == b[j - 1]:
                dp[i, j] = dp[i - 1, j - 1]
            else:
                dp[i, j] = min(dp[i - 1, j], dp[i, j - 1], dp[i - 1, j - 1]) + 1
                # Check for swaps
                if i > 1 and j > 1 and a[i - 1] == b[j - 2] and a[i - 2] == b[j - 1]:
                    dp[i, j] = min(dp[i, j], dp[i - 2, j - 2] + 2)

    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: Traceback (most recent call last): File "/usr/src/app/main.py", line 39, 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: 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: 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

Sure, here's a Numba implementation of the Levenshtein distance, taking two NumPy integer arrays. Character swaps are considered to have a cost of 2. 

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import numpy as np
from numba import njit

@njit(nopython=True)
def levenshtein(s1, s2):
    m, n = len(s1), len(s2)
    dp = np.zeros((m + 1, n + 1), dtype=np.int64)

    # Initialize the first row and column
    for i in range(m + 1):
        dp[i, 0] = i
    for j in range(n + 1):
        dp[0, j] = j

    # Fill the dp table
    for i in range(1, m + 1):
        for j in range(1, n + 1):
            if s1[i - 1] == s2[j - 1]:
                dp[i, j] = dp[i - 1, j - 1]
            else:
                dp[i, j] = min(
                    dp[i - 1, j] + 1,     # Deletion
                    dp[i, j - 1] + 1,     # Insertion
                    dp[i - 1, j - 1] + 2  # Substitution (considering swap as cost 2)
                )

    return dp[m, n]
This implementation uses dynamic programming to calculate the Levenshtein distance between two NumPy integer arrays, `s1` and `s2`. The `@njit(nopython=True)` decorator from Numba is used to compile the function to machine instructions, which can significantly improve performance for numerical computations. Here's how the `levenshtein` function works: 1. The function first initializes a 2D NumPy array `dp` with dimensions `(m + 1, n + 1)`, where `m` and `n` are the lengths of `s1` and `s2`, respectively. This array will store the intermediate results of the dynamic programming algorithm. 2. The first row and column of `dp` are initialized with the corresponding indices, representing the cost of deleting or inserting characters to transform an empty string to the other string. 3. The function then fills the `dp` table using dynamic programming. For each pair of characters `s1[i - 1]` and `s2[j - 1]`, it computes the minimum cost among the following three cases: - Deletion: The cost is `dp[i - 1, j] + 1`, as the previous character in `s1` is deleted. - Insertion: The cost is `dp[i, j - 1] + 1`, as a character from `s2` is inserted. - Substitution (or swap): The cost is `dp[i - 1, j - 1] + 2`, as the current characters are swapped (with a cost of 2). 4. Finally, the function returns the value stored in `dp[m, n]`, which represents the minimum cost (i.e., the Levenshtein distance) to transform `s1` into `s2`. You can use this function as follows: 
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s1 = np.array([1, 2, 3, 4])
s2 = np.array([2, 3, 4, 5])
distance = levenshtein(s1, s2)
print(distance)  # Output: 3
In this example, the Levenshtein distance between the arrays `[1, 2, 3, 4]` and `[2, 3, 4, 5]` is 3, as it requires one deletion (removing the 1) and one insertion (adding the 5) to transform `s1` into `s2`.

Extract Code

I extracted the following code from that output: 

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import numpy as np
from numba import njit

@njit(nopython=True)
def levenshtein(s1, s2):
    m, n = len(s1), len(s2)
    dp = np.zeros((m + 1, n + 1), dtype=np.int64)

    for i in range(m + 1):
        dp[i, 0] = i
    for j in range(n + 1):
        dp[0, j] = j

    for i in range(1, m + 1):
        for j in range(1, n + 1):
            if s1[i - 1] == s2[j - 1]:
                dp[i, j] = dp[i - 1, j - 1]
            else:
                dp[i, j] = min(
                    dp[i - 1, j] + 1,
                    dp[i, j - 1] + 1,
                    dp[i - 1, j - 1] + 2
                )

    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(nopython=True)
def levenshtein(s1, s2):
    m, n = len(s1), len(s2)
    dp = np.zeros((m + 1, n + 1), dtype=np.int64)

    for i in range(m + 1):
        dp[i, 0] = i
    for j in range(n + 1):
        dp[0, j] = j

    for i in range(1, m + 1):
        for j in range(1, n + 1):
            if s1[i - 1] == s2[j - 1]:
                dp[i, j] = dp[i - 1, j - 1]
            else:
                dp[i, j] = min(
                    dp[i - 1, j] + 1,
                    dp[i, j - 1] + 1,
                    dp[i - 1, j - 1] + 2
                )

    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 /usr/local/lib/python3.11/dist-packages/numba/core/decorators.py:250: RuntimeWarning: nopython is set for njit and is ignored warnings.warn('nopython is set for njit and is ignored', RuntimeWarning)

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: 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