Minimum steps to delete a string after repeated deletion of palindrome substrings

Given a string containing characters as integers only. We need to delete all characters of this string in a minimum number of steps wherein one step we can delete the substring which is a palindrome. After deleting a substring remaining parts are concatenated. 
 

Examples:

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 the overall occurrence of the current character on the 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 this subproblem (i+1, K-1) because we can just delete the same character and call for the mid substring. We need to take care of a case when the first two characters are the same in that case we can directly reduce to the subproblem (i+2, j).
So after the above discussion of the 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] )

The total time complexity of the above solution is O(n^3) 
 

Output: 

2