Identifying the palindrome DP pattern
The palindrome DP pattern solves problems where the input is a single sequence and the subproblems are contiguous ranges where the solution is decided by comparing the two endpoint characters. These are generally medium problems where the state carries two indices instead of one, so the subproblems lay out as a 2D table of ranges.
When a problem statement, or its natural recursive solution, fits the template below, it is a palindrome DP problem.
Given a sequence of length
n, compute dp(i, j) for each contiguous range s[i..j] from the shorter ranges created by removing its two endpoint characters and combining the subproblems with the operator pair (opt and ⊕).How to identify the palindrome DP pattern
There are two signals that tell us a problem fits the palindrome DP pattern.
The subproblem is a contiguous range treated as a palindrome
If the input is a single array or string, and the goal is to reduce the whole sequence to a single value, like an optimum, a count, or a yes or no, where the question to answer at each subproblem is about a contiguous range that reads the same forwards and backwards, the problem is generally a palindrome DP problem. Words like palindrome or symmetric point to this signal.
A single sequence, its contiguous ranges, and a symmetry to check
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