Implement a function to calculate the edit distance between two strings:

Implement a function to calculate the edit distance between two strings:

The edit distance between two strings is the minimum number of operations (insertion, deletion, or substitution) needed to transform one string into the other. This problem can be solved using dynamic programming.

The basic idea is to build a table of size (m+1) x (n+1), where m and n are the lengths of the two strings, and fill in the table iteratively from top to bottom and from left to right.

The first row and first column of the table correspond to the empty string and the two strings being compared, respectively. The entries in the table represent the edit distance between the substrings formed by the corresponding rows and columns.

The algorithm can be implemented as follows:

1. Initialize the table with the appropriate values:

• The entry (0,0) is 0, since the edit distance between two empty strings is 0.
• The entries in the first row and first column are the indexes of the characters being compared, since the edit distance between a string and an empty string is the number of characters in the string.

2. For each position (i,j) in the table, compute the minimum of the following values:

• The entry (i-1,j) plus 1, representing the cost of deleting a character from the first string.
• The entry (i,j-1) plus 1, representing the cost of inserting a character into the first string.
• The entry (i-1,j-1) plus 0 or 1, depending on whether the characters at positions i and j are equal or not. If they are equal, the cost is 0, otherwise the cost is 1, representing the cost of substituting a character in the first string.

3. The final entry in the table, (m,n), contains the edit distance between the two strings.

Here is a Python implementation of this algorithm:

def edit_distance(s1, s2):

    m, n = len(s1), len(s2)

    table = [[0 for j in range(n+1)] for i in range(m+1)]

    # Initialize the table

    for i in range(m+1):

        table[i][0] = i

    for j in range(n+1):

        table[0][j] = j

    # Fill in the table

    for i in range(1, m+1):

        for j in range(1, n+1):

            delete = table[i-1][j] + 1

            insert = table[i][j-1] + 1

            substitute = table[i-1][j-1] + (s1[i-1] != s2[j-1])

            table[i][j] = min(delete, insert, substitute)

    return table[m][n]

 Here's how it works:

• Create a 2D array dp of size (m+1) x (n+1), where m and n are the lengths of s1 and s2, respectively. dp[i][j] represents the edit distance between the first i characters of s1 and the first j characters of s2.
• Initialize the first row and column of dp to be the edit distances between each prefix of one string and the empty string.
• For each position (i, j) in dp, calculate the edit distance between the prefixes s1[:i] and s2[:j]. There are three possible operations:
  • If the characters at positions i-1 and j-1 are equal, then no operation is needed. The edit distance is the same as the edit distance between the prefixes without these characters, i.e., dp[i][j] = dp[i-1][j-1].
  • If the characters are different, we can either insert a character into s1 (which corresponds to incrementing i), delete a character from s1 (which corresponds to incrementing j), or substitute a character in s1 (which corresponds to incrementing both i and j). We take the minimum of these three options and add one to get the edit distance, i.e., dp[i][j] = 1 + min(dp[i-1][j], dp[i][j-1], dp[i-1][j-1]).
• The final answer is dp[m][n], which is the edit distance between the entire strings.

Here's an example usage of the function:

s1 = "kitten"

s2 = "sitting"

print(edit_distance(s1, s2))  # Output: 3

In this case, the edit distance between "kitten" and "sitting" is 3, which corresponds to deleting the "k", substituting "i" for "e", and inserting "g".

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