This is a DP problem but it's easy to go down the wrong path if you start thinking about it greedily.
Recognize that the minimum insertions equal the string length minus the length of the longest palindromic subsequence (LPS). Compute LPS using dynamic programming (or by finding the longest common subsequence between the string and its reverse). Then return n - LPS length.
Pro tip: After presenting the DP solution, mention that the problem can also be solved with a 2D DP where dp[i][j] = min insertions for substring s[i..j], and that this approach directly yields the answer without the LPS detour. This shows deeper understanding and flexibility.
Confirm that insertions can be at any position and that we want the minimum number. Restate the problem in your own words to ensure alignment.
Explain that the minimum insertions equal the number of characters not part of the longest palindromic subsequence. Thus, answer = n - LPS length.
Describe how to compute LPS: either via DP on the string or by finding LCS between the string and its reverse. Mention time and space complexity (O(n^2)).
Pick a short example (e.g., 'ab') and show step-by-step how the LPS is found and the insertions calculated.
Mention space optimization (e.g., using 1D DP for LCS) and handle edge cases like empty string or already palindrome.
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