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

Okay, here is a Numba implementation of the Levenshtein distance (specifically, the Damerau-Levenshtein distance variant where only *adjacent* transpositions are considered) for NumPy integer arrays, running in `nopython` mode, with a swap cost of 2. 

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import numpy as np
import numba

@numba.njit # Equivalent to @numba.jit(nopython=True)
def levenshtein(a: np.ndarray, b: np.ndarray) -> int:
    """
    Calculates the Levenshtein distance between two NumPy integer arrays.

    This implementation includes adjacent transpositions (swaps) with a cost of 2.
    Standard insertions, deletions, and substitutions have a cost of 1.

    Args:
        a: The first NumPy integer array.
        b: The second NumPy integer array.

    Returns:
        The Levenshtein distance between a and b.
    """
    n = len(a)
    m = len(b)

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

    # Initialize DP matrix (distance matrix)
    # Use np.int64 for potentially large distances and compatibility
    dp = np.zeros((n + 1, m + 1), dtype=np.int64)

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

    # Fill the DP matrix
    for i in range(1, n + 1):
        for j in range(1, m + 1):
            # Cost of substitution (0 if characters match, 1 otherwise)
            # Remember arrays are 0-indexed, dp matrix is 1-indexed conceptually
            cost = 0 if a[i - 1] == b[j - 1] else 1

            # Calculate cost based on deletion, insertion, substitution
            dp[i, j] = min(dp[i - 1, j] + 1,        # Deletion from a
                           dp[i, j - 1] + 1,        # Insertion into a
                           dp[i - 1, j - 1] + cost) # Substitution/Match

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

    # The final distance is in the bottom-right corner
    return dp[n, m]

# --- Example Usage ---
if __name__ == "__main__":
    # Example 1: Simple case
    arr1 = np.array([10, 20, 30], dtype=np.int64)
    arr2 = np.array([10, 50, 30], dtype=np.int64)
    # Expected: 1 (substitute 20 for 50)
    dist1 = levenshtein(arr1, arr2)
    print(f"Array 1: {arr1}")
    print(f"Array 2: {arr2}")
    print(f"Levenshtein distance: {dist1}\n")

    # Example 2: Swap case
    arr3 = np.array([1, 2, 3, 4], dtype=np.int64)
    arr4 = np.array([1, 3, 2, 4], dtype=np.int64)
    # Expected: 2 (swap 2 and 3)
    dist2 = levenshtein(arr3, arr4)
    print(f"Array 3: {arr3}")
    print(f"Array 4: {arr4}")
    print(f"Levenshtein distance: {dist2}\n")

    # Example 3: Swap vs Substitution/Insertion/Deletion
    arr5 = np.array([5, 6], dtype=np.int64)
    arr6 = np.array([6, 5], dtype=np.int64)
    # Expected: 2 (swap 5 and 6)
    # Without swap cost 2, it would be 2 (sub 5->6, sub 6->5)
    dist3 = levenshtein(arr5, arr6)
    print(f"Array 5: {arr5}")
    print(f"Array 6: {arr6}")
    print(f"Levenshtein distance: {dist3}\n")

    # Example 4: Longer sequences
    arr7 = np.array([1, 2, 3, 4, 5, 6, 7], dtype=np.int64)
    arr8 = np.array([1, 3, 2, 4, 5, 8, 7], dtype=np.int64)
    # Expected: 1 (swap 2,3 cost 2) + 1 (sub 6->8 cost 1) = 3
    # Let's trace:
    # 1 == 1 (cost 0)
    # 2,3 vs 3,2 -> swap (cost 2) -> state is now 1,3,2
    # 4 == 4 (cost 0) -> state is 1,3,2,4
    # 5 == 5 (cost 0) -> state is 1,3,2,4,5
    # 6 vs 8 -> sub (cost 1) -> state is 1,3,2,4,5,8
    # 7 == 7 (cost 0) -> state is 1,3,2,4,5,8,7
    # Total cost = 2 + 1 = 3
    dist4 = levenshtein(arr7, arr8)
    print(f"Array 7: {arr7}")
    print(f"Array 8: {arr8}")
    print(f"Levenshtein distance: {dist4}\n")

    # Example 5: Empty array
    arr9 = np.array([1, 2, 3], dtype=np.int64)
    arr10 = np.array([], dtype=np.int64)
    # Expected: 3 (delete 1, 2, 3)
    dist5 = levenshtein(arr9, arr10)
    print(f"Array 9: {arr9}")
    print(f"Array 10: {arr10}")
    print(f"Levenshtein distance: {dist5}\n")

    # Example 6: Identical arrays
    arr11 = np.array([9, 8, 7], dtype=np.int64)
    arr12 = np.array([9, 8, 7], dtype=np.int64)
    # Expected: 0
    dist6 = levenshtein(arr11, arr12)
    print(f"Array 11: {arr11}")
    print(f"Array 12: {arr12}")
    print(f"Levenshtein distance: {dist6}\n")

    # --- Performance check (optional) ---
    # Numba compiles on first call, subsequent calls are fast
    # print("Timing...")
    # large_arr1 = np.random.randint(0, 100, size=500, dtype=np.int64)
    # large_arr2 = np.random.randint(0, 100, size=550, dtype=np.int64)
    # %timeit levenshtein(large_arr1, large_arr2) # Use in Jupyter/IPython
    # Or use timeit module for standard Python script
    # import timeit
    # setup = """
    # import numpy as np
    # from __main__ import levenshtein
    # large_arr1 = np.random.randint(0, 100, size=500, dtype=np.int64)
    # large_arr2 = np.random.randint(0, 100, size=550, dtype=np.int64)
    # levenshtein(large_arr1, large_arr2) # Run once for compilation
    # """
    # n_runs = 10
    # t = timeit.timeit("levenshtein(large_arr1, large_arr2)", setup=setup, number=n_runs)
    # print(f"Average time over {n_runs} runs: {t/n_runs:.6f} seconds")
**Explanation:** 1. **Imports:** Import `numpy` for array creation and `numba`. 2. **Decorator:** `@numba.njit` is used to compile the function in `nopython` mode. This means Numba will try to compile the function without falling back to slower object mode. If it can't, it will raise an error. Type hints (`a: np.ndarray`, `-> int`) are good practice but not strictly required for Numba inference here. 3. **Initialization:** * Get lengths `n` and `m`. * Handle the base cases where one or both arrays are empty. * Create the dynamic programming table `dp` of size `(n+1) x (m+1)`. Using `np.int64` is generally safe for the distances. * Initialize the first row and column: `dp[i, 0] = i` and `dp[0, j] = j`, representing the cost of deleting all characters from one array or inserting all characters into the other. 4. **DP Calculation:** * Iterate through the `dp` table starting from `(1, 1)`. * `cost`: Calculate the substitution cost. It's 0 if the corresponding elements `a[i-1]` and `b[j-1]` are equal, and 1 otherwise. (Remember the `i-1`/`j-1` indexing because `dp` is offset by 1 compared to the arrays). * `dp[i, j]`: Calculate the minimum cost to reach `dp[i, j]` using one of the standard operations: * `dp[i-1, j] + 1`: Deleting `a[i-1]`. * `dp[i, j-1] + 1`: Inserting `b[j-1]`. * `dp[i-1, j-1] + cost`: Substituting `a[i-1]` with `b[j-1]` (or matching if `cost` is 0). * **Transposition Check:** * If `i > 1` and `j > 1` (meaning we have at least two characters from both arrays to compare), check if the last two characters are swapped: `a[i-1] == b[j-2]` and `a[i-2] == b[j-1]`. * If they are swapped, consider the cost of reaching this state via a transposition: `dp[i-2, j-2] + 2`. The `+ 2` is the specified cost for a swap. * Update `dp[i, j]` to be the minimum of its current value and the transposition cost. 5. **Return Value:** The final distance is stored in the bottom-right cell `dp[n, m]`. 6. **Example Usage (`if __name__ == "__main__":`)**: Demonstrates how to call the function with different NumPy integer arrays and prints the results. Includes cases for substitution, swap, mixed operations, empty arrays, and identical arrays.

Extract Code

I extracted the following code from that output: 

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import numpy as np
import numba

@numba.njit # Equivalent to @numba.jit(nopython=True)
def levenshtein(a: np.ndarray, b: np.ndarray) -> int:
    """
    Calculates the Levenshtein distance between two NumPy integer arrays.

    This implementation includes adjacent transpositions (swaps) with a cost of 2.
    Standard insertions, deletions, and substitutions have a cost of 1.

    Args:
        a: The first NumPy integer array.
        b: The second NumPy integer array.

    Returns:
        The Levenshtein distance between a and b.
    """
    n = len(a)
    m = len(b)

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

    # Initialize DP matrix (distance matrix)
    # Use np.int64 for potentially large distances and compatibility
    dp = np.zeros((n + 1, m + 1), dtype=np.int64)

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

    # Fill the DP matrix
    for i in range(1, n + 1):
        for j in range(1, m + 1):
            # Cost of substitution (0 if characters match, 1 otherwise)
            # Remember arrays are 0-indexed, dp matrix is 1-indexed conceptually
            cost = 0 if a[i - 1] == b[j - 1] else 1

            # Calculate cost based on deletion, insertion, substitution
            dp[i, j] = min(dp[i - 1, j] + 1,        # Deletion from a
                           dp[i, j - 1] + 1,        # Insertion into a
                           dp[i - 1, j - 1] + cost) # Substitution/Match

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

    # The final distance is in the bottom-right corner
    return dp[n, m]

# --- Example Usage ---
if __name__ == "__main__":
    # Example 1: Simple case
    arr1 = np.array([10, 20, 30], dtype=np.int64)
    arr2 = np.array([10, 50, 30], dtype=np.int64)
    # Expected: 1 (substitute 20 for 50)
    dist1 = levenshtein(arr1, arr2)
    print(f"Array 1: {arr1}")
    print(f"Array 2: {arr2}")
    print(f"Levenshtein distance: {dist1}\n")

    # Example 2: Swap case
    arr3 = np.array([1, 2, 3, 4], dtype=np.int64)
    arr4 = np.array([1, 3, 2, 4], dtype=np.int64)
    # Expected: 2 (swap 2 and 3)
    dist2 = levenshtein(arr3, arr4)
    print(f"Array 3: {arr3}")
    print(f"Array 4: {arr4}")
    print(f"Levenshtein distance: {dist2}\n")

    # Example 3: Swap vs Substitution/Insertion/Deletion
    arr5 = np.array([5, 6], dtype=np.int64)
    arr6 = np.array([6, 5], dtype=np.int64)
    # Expected: 2 (swap 5 and 6)
    # Without swap cost 2, it would be 2 (sub 5->6, sub 6->5)
    dist3 = levenshtein(arr5, arr6)
    print(f"Array 5: {arr5}")
    print(f"Array 6: {arr6}")
    print(f"Levenshtein distance: {dist3}\n")

    # Example 4: Longer sequences
    arr7 = np.array([1, 2, 3, 4, 5, 6, 7], dtype=np.int64)
    arr8 = np.array([1, 3, 2, 4, 5, 8, 7], dtype=np.int64)
    # Expected: 1 (swap 2,3 cost 2) + 1 (sub 6->8 cost 1) = 3
    # Let's trace:
    # 1 == 1 (cost 0)
    # 2,3 vs 3,2 -> swap (cost 2) -> state is now 1,3,2
    # 4 == 4 (cost 0) -> state is 1,3,2,4
    # 5 == 5 (cost 0) -> state is 1,3,2,4,5
    # 6 vs 8 -> sub (cost 1) -> state is 1,3,2,4,5,8
    # 7 == 7 (cost 0) -> state is 1,3,2,4,5,8,7
    # Total cost = 2 + 1 = 3
    dist4 = levenshtein(arr7, arr8)
    print(f"Array 7: {arr7}")
    print(f"Array 8: {arr8}")
    print(f"Levenshtein distance: {dist4}\n")

    # Example 5: Empty array
    arr9 = np.array([1, 2, 3], dtype=np.int64)
    arr10 = np.array([], dtype=np.int64)
    # Expected: 3 (delete 1, 2, 3)
    dist5 = levenshtein(arr9, arr10)
    print(f"Array 9: {arr9}")
    print(f"Array 10: {arr10}")
    print(f"Levenshtein distance: {dist5}\n")

    # Example 6: Identical arrays
    arr11 = np.array([9, 8, 7], dtype=np.int64)
    arr12 = np.array([9, 8, 7], dtype=np.int64)
    # Expected: 0
    dist6 = levenshtein(arr11, arr12)
    print(f"Array 11: {arr11}")
    print(f"Array 12: {arr12}")
    print(f"Levenshtein distance: {dist6}\n")

    # --- Performance check (optional) ---
    # Numba compiles on first call, subsequent calls are fast
    # print("Timing...")
    # large_arr1 = np.random.randint(0, 100, size=500, dtype=np.int64)
    # large_arr2 = np.random.randint(0, 100, size=550, dtype=np.int64)
    # %timeit levenshtein(large_arr1, large_arr2) # Use in Jupyter/IPython
    # Or use timeit module for standard Python script
    # import timeit
    # setup = """
    # import numpy as np
    # from __main__ import levenshtein
    # large_arr1 = np.random.randint(0, 100, size=500, dtype=np.int64)
    # large_arr2 = np.random.randint(0, 100, size=550, dtype=np.int64)
    # levenshtein(large_arr1, large_arr2) # Run once for compilation
    # """
    # n_runs = 10
    # t = timeit.timeit("levenshtein(large_arr1, large_arr2)", setup=setup, number=n_runs)
    # print(f"Average time over {n_runs} runs: {t/n_runs:.6f} seconds")

Check if all of the following conditions are true:

Run Code Interpreter

Running the following program: 

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import numpy as np
import numba

@numba.njit # Equivalent to @numba.jit(nopython=True)
def levenshtein(a: np.ndarray, b: np.ndarray) -> int:
    """
    Calculates the Levenshtein distance between two NumPy integer arrays.

    This implementation includes adjacent transpositions (swaps) with a cost of 2.
    Standard insertions, deletions, and substitutions have a cost of 1.

    Args:
        a: The first NumPy integer array.
        b: The second NumPy integer array.

    Returns:
        The Levenshtein distance between a and b.
    """
    n = len(a)
    m = len(b)

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

    # Initialize DP matrix (distance matrix)
    # Use np.int64 for potentially large distances and compatibility
    dp = np.zeros((n + 1, m + 1), dtype=np.int64)

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

    # Fill the DP matrix
    for i in range(1, n + 1):
        for j in range(1, m + 1):
            # Cost of substitution (0 if characters match, 1 otherwise)
            # Remember arrays are 0-indexed, dp matrix is 1-indexed conceptually
            cost = 0 if a[i - 1] == b[j - 1] else 1

            # Calculate cost based on deletion, insertion, substitution
            dp[i, j] = min(dp[i - 1, j] + 1,        # Deletion from a
                           dp[i, j - 1] + 1,        # Insertion into a
                           dp[i - 1, j - 1] + cost) # Substitution/Match

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

    # The final distance is in the bottom-right corner
    return dp[n, m]

# --- Example Usage ---
if __name__ == "__main__":
    # Example 1: Simple case
    arr1 = np.array([10, 20, 30], dtype=np.int64)
    arr2 = np.array([10, 50, 30], dtype=np.int64)
    # Expected: 1 (substitute 20 for 50)
    dist1 = levenshtein(arr1, arr2)
    print(f"Array 1: {arr1}")
    print(f"Array 2: {arr2}")
    print(f"Levenshtein distance: {dist1}\n")

    # Example 2: Swap case
    arr3 = np.array([1, 2, 3, 4], dtype=np.int64)
    arr4 = np.array([1, 3, 2, 4], dtype=np.int64)
    # Expected: 2 (swap 2 and 3)
    dist2 = levenshtein(arr3, arr4)
    print(f"Array 3: {arr3}")
    print(f"Array 4: {arr4}")
    print(f"Levenshtein distance: {dist2}\n")

    # Example 3: Swap vs Substitution/Insertion/Deletion
    arr5 = np.array([5, 6], dtype=np.int64)
    arr6 = np.array([6, 5], dtype=np.int64)
    # Expected: 2 (swap 5 and 6)
    # Without swap cost 2, it would be 2 (sub 5->6, sub 6->5)
    dist3 = levenshtein(arr5, arr6)
    print(f"Array 5: {arr5}")
    print(f"Array 6: {arr6}")
    print(f"Levenshtein distance: {dist3}\n")

    # Example 4: Longer sequences
    arr7 = np.array([1, 2, 3, 4, 5, 6, 7], dtype=np.int64)
    arr8 = np.array([1, 3, 2, 4, 5, 8, 7], dtype=np.int64)
    # Expected: 1 (swap 2,3 cost 2) + 1 (sub 6->8 cost 1) = 3
    # Let's trace:
    # 1 == 1 (cost 0)
    # 2,3 vs 3,2 -> swap (cost 2) -> state is now 1,3,2
    # 4 == 4 (cost 0) -> state is 1,3,2,4
    # 5 == 5 (cost 0) -> state is 1,3,2,4,5
    # 6 vs 8 -> sub (cost 1) -> state is 1,3,2,4,5,8
    # 7 == 7 (cost 0) -> state is 1,3,2,4,5,8,7
    # Total cost = 2 + 1 = 3
    dist4 = levenshtein(arr7, arr8)
    print(f"Array 7: {arr7}")
    print(f"Array 8: {arr8}")
    print(f"Levenshtein distance: {dist4}\n")

    # Example 5: Empty array
    arr9 = np.array([1, 2, 3], dtype=np.int64)
    arr10 = np.array([], dtype=np.int64)
    # Expected: 3 (delete 1, 2, 3)
    dist5 = levenshtein(arr9, arr10)
    print(f"Array 9: {arr9}")
    print(f"Array 10: {arr10}")
    print(f"Levenshtein distance: {dist5}\n")

    # Example 6: Identical arrays
    arr11 = np.array([9, 8, 7], dtype=np.int64)
    arr12 = np.array([9, 8, 7], dtype=np.int64)
    # Expected: 0
    dist6 = levenshtein(arr11, arr12)
    print(f"Array 11: {arr11}")
    print(f"Array 12: {arr12}")
    print(f"Levenshtein distance: {dist6}\n")

    # --- Performance check (optional) ---
    # Numba compiles on first call, subsequent calls are fast
    # print("Timing...")
    # large_arr1 = np.random.randint(0, 100, size=500, dtype=np.int64)
    # large_arr2 = np.random.randint(0, 100, size=550, dtype=np.int64)
    # %timeit levenshtein(large_arr1, large_arr2) # Use in Jupyter/IPython
    # Or use timeit module for standard Python script
    # import timeit
    # setup = """
    # import numpy as np
    # from __main__ import levenshtein
    # large_arr1 = np.random.randint(0, 100, size=500, dtype=np.int64)
    # large_arr2 = np.random.randint(0, 100, size=550, dtype=np.int64)
    # levenshtein(large_arr1, large_arr2) # Run once for compilation
    # """
    # n_runs = 10
    # t = timeit.timeit("levenshtein(large_arr1, large_arr2)", setup=setup, number=n_runs)
    # print(f"Average time over {n_runs} runs: {t/n_runs:.6f} seconds")






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: Array 1: [10 20 30] Array 2: [10 50 30] Levenshtein distance: 1 Array 3: [1 2 3 4] Array 4: [1 3 2 4] Levenshtein distance: 2 Array 5: [5 6] Array 6: [6 5] Levenshtein distance: 2 Array 7: [1 2 3 4 5 6 7] Array 8: [1 3 2 4 5 8 7] Levenshtein distance: 3 Array 9: [1 2 3] Array 10: [] Levenshtein distance: 3 Array 11: [9 8 7] Array 12: [9 8 7] Levenshtein distance: 0 Traceback (most recent call last): File "/usr/src/app/main.py", line 150, 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: True

Substring Evaluation

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

Final Answer: True

Final Answer: False