Given a string S. The task is to count the non-overlapping pairs of palindromic sub-strings S1 and S2 such that the strings should be S1[L1…R1] and S2[L2…R2] where 0 ≤ L1 ≤ R1 < L2 ≤ R2 < N. The task is to count the number of pairs of the non-overlapping palindromic sub-strings.
Input: s = “aaa”
All possible pairs are (s, s), (s, s),
(s, s[1, 2]), (s, s) and (s[0, 1], s)
Input: s = “abacaba”
Approach: We can use Dynamic Programming to solve the above problem. We can initially create the DP table which stores if substring[i….j] is palindrome or not. We maintain a boolean dp[n][n] that is filled in a bottom-up manner. The value of dp[i][j] is true if the substring is a palindrome, otherwise false. To calculate dp[i][j], we first check the value of dp[i+1][j-1], if the value is true and s[i] is same as s[j], then we make dp[i][j] true. Otherwise, the value of dp[i][j] is made false. The following steps can be followed thereafter to get the number of pairs.
- Create a left array, where left[i] stores the count of the number of palindromes to the left on the index i including i.
- Create a right array, where right[i] stores the count of the number of palindromes to the right on the index i including i.
- Iterate from 0 to length-1 and add left[i]*right[i+1]. The summation of it for every index will be the required number of pairs.
Below is the implementation of the above approach:
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