Given a string containing characters as integers only. We need to delete all character of this string in a minimum number of steps where in one step we can delete the substring which is a palindrome. After deleting a substring remaining parts are concatenated.
Input : s = “2553432” Output : 2 We can delete all character of above string in 2 steps, first deleting the substring s[3, 5] “343” and then remaining string completely s[0, 3] “2552” Input : s = “1234” Output : 4 We can delete all character of above string in 4 steps only because each character need to be deleted separately. No substring of length 2 is a palindrome in above string.
We can solve this problem using Dynamic programming. Let dp[i][j] denotes the number of steps it takes to delete the substring s[i, j]. Each character will be deleted alone or as part of some substring so in the first case we will delete the character itself and call subproblem (i+1, j). In the second case we will iterate over all occurrence of the current character in right side, if K is the index of one such occurrence then the problem will reduce to two subproblems (i+1, K – 1) and (K+1, j). We can reach to this subproblem (i+1, K-1) because we can just delete the same character and call for mid substring. We need to take care of a case when first two characters are same in that case we can directly reduce to the subproblem (i+2, j)
So after above discussion of relation among subproblems, we can write dp relation as follows,
dp[i][j] = min(1 + dp[i+1][j], dp[i+1][K-1] + dp[K+1][j], where s[i] == s[K] 1 + dp[i+2][j] )
Total time complexity of above solution is O(n^3)
This article is contributed by Utkarsh Trivedi. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to firstname.lastname@example.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.
Don’t stop now and take your learning to the next level. Learn all the important concepts of Data Structures and Algorithms with the help of the most trusted course: DSA Self Paced. Become industry ready at a student-friendly price.
- Minimum steps to delete a string by deleting substring comprising of same characters
- Size of array after repeated deletion of LIS
- Minimum changes to a string to make all substrings distinct
- Minimum steps to remove substring 010 from a binary string
- Minimum steps to convert one binary string to other only using negation
- Find minimum number of steps to reach the end of String
- Remove minimum characters from string to split it into three substrings under given constraints
- Minimum number of substrings the given string can be splitted into that satisfy the given conditions
- Minimum number of steps needed to remove the substring K from given string
- Minimum cost to convert string into palindrome
- Count minimum swap to make string palindrome
- Minimum number of deletions to make a string palindrome | Set 2
- Minimum reduce operations to convert a given string into a palindrome
- Minimum number of deletions to make a string palindrome
- Minimum characters to be added at front to make string palindrome
- Minimum number of Appends needed to make a string palindrome
- Minimum number of characters to be replaced to make a given string Palindrome
- Construct binary palindrome by repeated appending and trimming
- Count pair of strings whose concatenation of substrings form a palindrome
- String slicing in Python to check if a string can become empty by recursive deletion