The edit distance is the minimum number of character insertions and character deletions required to turn one string into another. Compute the edit distance between each pair of the strings he, she, his, and hers. Then, identify which of the following is a true statement about the number of pairs at a certain edit distance.
There are 3 pairs at distance 4.
There is 1 pair at distance 1.
There is 1 pair at distance 3.
There are 4 pairs at distance 2.
There are 4 pairs at distance 2.
There is 1 pair at distance 3
There is 1 pair at distance 1.
There are 4 pairs at distance 2.
To compute the edit distance between two strings, you can use the Levenshtein distance algorithm. This algorithm calculates the minimum number of insertions, deletions, and substitutions required to transform one string into another.
Let's apply the algorithm to the given strings: he, she, his, and hers.
1. Edit distance between "he" and "she":
- Start with an empty matrix of size (len("he")+1) x (len("she")+1).
- Fill the first row and first column with values from 0 to the length of the corresponding string.
- Iterate through each element of the matrix (excluding the first row and column), comparing characters:
- If the characters are the same, assign the diagonal element's value to the current element.
- If they are different, assign the minimum value from the left, above, and diagonal elements plus 1 to the current element.
- The value at the bottom right corner of the matrix will be the edit distance between "he" and "she". In this case, it is 1.
2. Edit distance between "he" and "his":
- Using the same process as above, the edit distance is 2.
3. Edit distance between "he" and "hers":
- The edit distance is 2, following the same process.
4. Edit distance between "she" and "his":
- The edit distance is 2.
5. Edit distance between "she" and "hers":
- The edit distance is 1.
6. Edit distance between "his" and "hers":
- The edit distance is 2.
Now, let's evaluate the statements:
- "There are 3 pairs at distance 4." False. None of the pairs have a distance of 4.
- "There is 1 pair at distance 1." True. The pair "she" and "hers" have a distance of 1.
- "There is 1 pair at distance 3." False. None of the pairs have a distance of 3.
- "There are 4 pairs at distance 2." False. Only three pairs (he and his, he and hers, she and his) have a distance of 2.
Therefore, the correct statement is "There is 1 pair at distance 1."