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 solve this problem, we need to compute the Levenshtein distance between two numpy integer arrays using Numba in nopython mode, where character substitutions cost 2 instead of the usual 1. The Levenshtein distance is a measure of the difference between two sequences, calculated as the minimum number of single-element edits (insertions, deletions, or substitutions) required to change one sequence into the other. ### Approach The approach uses dynamic programming (DP) to efficiently compute the Levenshtein distance. We create a 2D DP table where each cell `dp[i][j]` represents the minimum edit distance between the first `i` elements of the first array and the first `j` elements of the second array. The key operations considered are: 1. **Insertion** (cost 1) 2. **Deletion** (cost 1) 3. **Substitution** (cost 2 if elements differ, 0 if they are the same) The DP table is initialized such that the first row and column represent the cumulative cost of inserting or deleting elements. The rest of the table is filled by considering the minimum cost of each possible operation at each step. ### Solution Code 

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import numba
import numpy as np

@numba.njit(nogil=True, cache=True)
def levenshtein(a, b):
    len_a = len(a)
    len_b = len(b)
    
    # Initialize a DP table with dimensions (len_a + 1) x (len_b + 1)
    dp = np.zeros((len_a + 1, len_b + 1), dtype=np.int64)
    
    # Base cases: transforming an empty string to a[0..i]
    for i in range(len_a + 1):
        dp[i, 0] = i
    # Base cases: transforming an empty string to b[0..j]
    for j in range(len_b + 1):
        dp[0, j] = j
    
    # Fill the DP table
    for i in range(1, len_a + 1):
        for j in range(1, len_b + 1):
            if a[i-1] == b[j-1]:
                substitution_cost = 0
            else:
                substitution_cost = 2
            # Compute the minimum of deletion, insertion, and substitution
            dp[i, j] = min(
                dp[i-1, j] + 1,          # Deletion
                dp[i, j-1] + 1,          # Insertion
                dp[i-1, j-1] + substitution_cost  # Substitution
            )
    
    return dp[len_a, len_b]
### Explanation 1. **Initialization**: The DP table `dp` is initialized with dimensions `(len_a + 1) x (len_b + 1)`. The first row and column are filled with values representing the cumulative cost of deletions and insertions, respectively. 2. **Filling the DP Table**: For each element in the two arrays, we determine the cost of substitution (0 if the elements are the same, 2 if they differ). The value of each cell `dp[i][j]` is computed as the minimum cost of: - Deleting an element from the first array (`dp[i-1][j] + 1`) - Inserting an element into the first array (`dp[i][j-1] + 1`) - Substituting an element (cost depends on whether elements match) 3. **Result**: The value at `dp[len_a][len_b]` gives the Levenshtein distance between the two arrays, considering the specified costs for each operation. This approach efficiently computes the edit distance using dynamic programming, optimized with Numba for performance in nopython mode.

Extract Code

I extracted the following code from that output: 

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import numba
import numpy as np

@numba.njit(nogil=True, cache=True)
def levenshtein(a, b):
    len_a = len(a)
    len_b = len(b)
    
    # Initialize a DP table with dimensions (len_a + 1) x (len_b + 1)
    dp = np.zeros((len_a + 1, len_b + 1), dtype=np.int64)
    
    # Base cases: transforming an empty string to a[0..i]
    for i in range(len_a + 1):
        dp[i, 0] = i
    # Base cases: transforming an empty string to b[0..j]
    for j in range(len_b + 1):
        dp[0, j] = j
    
    # Fill the DP table
    for i in range(1, len_a + 1):
        for j in range(1, len_b + 1):
            if a[i-1] == b[j-1]:
                substitution_cost = 0
            else:
                substitution_cost = 2
            # Compute the minimum of deletion, insertion, and substitution
            dp[i, j] = min(
                dp[i-1, j] + 1,          # Deletion
                dp[i, j-1] + 1,          # Insertion
                dp[i-1, j-1] + substitution_cost  # Substitution
            )
    
    return dp[len_a, len_b]

Check if all of the following conditions are true:

Run Code Interpreter

Running the following program: 

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import numba
import numpy as np

@numba.njit(nogil=True, cache=True)
def levenshtein(a, b):
    len_a = len(a)
    len_b = len(b)
    
    # Initialize a DP table with dimensions (len_a + 1) x (len_b + 1)
    dp = np.zeros((len_a + 1, len_b + 1), dtype=np.int64)
    
    # Base cases: transforming an empty string to a[0..i]
    for i in range(len_a + 1):
        dp[i, 0] = i
    # Base cases: transforming an empty string to b[0..j]
    for j in range(len_b + 1):
        dp[0, j] = j
    
    # Fill the DP table
    for i in range(1, len_a + 1):
        for j in range(1, len_b + 1):
            if a[i-1] == b[j-1]:
                substitution_cost = 0
            else:
                substitution_cost = 2
            # Compute the minimum of deletion, insertion, and substitution
            dp[i, j] = min(
                dp[i-1, j] + 1,          # Deletion
                dp[i, j-1] + 1,          # Insertion
                dp[i-1, j-1] + substitution_cost  # Substitution
            )
    
    return dp[len_a, len_b]





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: True

Substring Evaluation

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

Final Answer: True

Final Answer: True