问题
Here is the problem states to convert a string into a palindrome with minimum number of operations. I know it is similar to the Levenshtein distance but I can't solve it yet
For example, for input mohammadsajjadhossain, the output is 8.
回答1:
Perform Levenshtein distance on the string and its reverse. The solution will be the minimum of the operations in the diagonal of the DP array going from bottom-left to top-right, as well as each entry just above and just below the diagonal.
This works because the entries along the diagonal represent the minimum edits required to make the first i and last N-i characters of the string equal and the entries just above and just below represent the minimum for strings ending up with odd-length where the middle (left-over) character doesn't match against anything.
回答2:
You just need to compute a limited number of Levenshtein distances, one for each possible palindrome pivot point. A pivot point can be a letter or it can be between two letters, so a string of length n has 2n-1 pivot points. For each pivot point, you calculate the Levenshtein distance of the characters before the pivot point and the reverse of the characters after it:
(m)ohammadsajjadhossain: Levensthein("", "niassohdajjasdammaho")m ohammadsajjadhossain: Levensthein("m", "niassohdajjasdammaho")m(o)hammadsajjadhossain: Levensthein("m", "niassohdajjasdammah")mo hammadsajjadhossain: Levensthein("mo", "niassohdajjasdammah")mo(h)ammadsajjadhossain: Levensthein("mo", "niassohdajjasdamma")moh ammadsajjadhossain: Levensthein("moh", "niassohdajjasdamma")
etc.
Now just take the minimum of these distances. If speed is important, you can optimise away many of these calls.
来源：https://stackoverflow.com/questions/4737791/how-to-convert-a-string-into-a-palindrome-with-minimum-number-of-operations