Given a string, find the minimum number of characters to be inserted to convert it to a palindrome.Examples :Input: str = "abcd"Output: 3Explanation: Inserted character marked with bold characters in dcbabcd, here we need minimum three characters to make it palindrome.
Question
Given a string, find the minimum number of characters to be inserted to convert it to a palindrome.Examples :Input: str = "abcd"Output: 3Explanation: Inserted character marked with bold characters in dcbabcd, here we need minimum three characters to make it palindrome.
Solution
To solve this problem, we can use dynamic programming. Here are the steps:
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Create a 2D array dp[][] of size (n x n) where n is the length of the string. dp[i][j] will store the minimum number of insertions needed to convert str[i..j] to a palindrome.
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Initialize all the diagonal elements as 0. This is because a single character is always a palindrome, so no insertions are needed.
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For strings of length greater than 1, fill up the dp[][] table in a bottom-up manner. For any string of length l, we compare the outermost characters (str[i] and str[j]) and then recursively consider the remaining substring str[i+1, j-1].
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If outermost characters are same, then we recur for remaining substring. i.e., dp[i][j] = dp[i+1][j-1]
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Else (If outermost characters are not same), we take minimum of two values:
- When we insert a character at the beginning of string, recur for the remaining substring. i.e., dp[i][j] = min (dp[i][j], 1 + dp[i+1][j])
- When we insert a character at the end of string, recur for the remaining substring. i.e., dp[i][j] = min (dp[i][j], 1 + dp[i][j-1])
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The minimum number of insertions needed to make the string a palindrome is stored in dp[0][n-1].
For example, if the input string is "abcd", the output will be 3. We can insert 3 characters to make it a palindrome: "dcbabcd".
Similar Questions
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