Minimum Insertion Steps to Make a String Palindrome
A hard-tier problem at 72% community acceptance, tagged with String, Dynamic Programming. Reported in interviews at Arcesium and 1 others.
You're staring at a string and need to figure out the minimum number of character insertions to make it a palindrome. Arcesium and Squarepoint Capital have asked this. It's a hard-difficulty problem with a 72% acceptance rate, but that number lies. Most people who attempt it either brute-force badly or miss the connection to a classical DP pattern. The trick isn't insertion logic at all. It's recognizing that this problem is really asking you to find the longest palindromic subsequence hiding inside the string. Once you see that, the answer falls out cleanly. If you blank on the pattern during the live OA, StealthCoder surfaces the solution in seconds, invisible to the proctor.
Companies that ask "Minimum Insertion Steps to Make a String Palindrome"
Minimum Insertion Steps to Make a String Palindrome is the kind of problem that decides whether you pass. StealthCoder reads the problem on screen and surfaces a working solution in under 2 seconds. Invisible to screen share. The proctor sees nothing. Built by a senior engineer who knows the OA is theater. This is the script.
Get StealthCoderThe insight that kills this problem: the minimum insertions needed equals the string length minus the longest palindromic subsequence (LPS). Why? Because every character not in the LPS must be inserted as its mirror on the opposite side. Building LPS requires dynamic programming. You construct a table where dp[i][j] tracks the longest palindromic subsequence in substring s[i:j+1]. The recurrence checks if s[i] equals s[j], and if so, adds 2 to the inner result. If not, you take the max of excluding either endpoint. The table fills in diagonal order, growing outward from single characters. Most candidates either try greedy insertion strategies (wrong) or attempt memoized recursion without the table structure (slow and error-prone). When the test case has length 500 and you're running out of time during the OA, StealthCoder hands you the DP template and the final subtraction in one go.
Pattern tags
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Make sure you actually pass it.
Minimum Insertion Steps to Make a String Palindrome recycles across companies for a reason. It's hard-tier, and most candidates blank under the timer. StealthCoder is the hedge: an AI overlay invisible during screen share. It reads the problem and surfaces a working solution in under 2 seconds. Built by a senior engineer who knows the OA is theater. This is the script. Works on HackerRank, CodeSignal, CoderPad, and Karat.
Minimum Insertion Steps to Make a String Palindrome interview FAQ
Is this really about inserting characters, or is there a hidden pattern?+
Hidden pattern. The problem reduces to finding the longest palindromic subsequence. Once you have that length, subtract it from the total string length. That's your answer. No greedy insertion needed. The DP table for LPS is the entire solution.
Do Arcesium and Squarepoint Capital still ask this in 2024?+
Yes. Only 2 companies are named in the public record for this problem, but a 72% acceptance rate suggests it appears more broadly than the data shows. Hard problems with that high an acceptance tend to stay in rotation because they test pattern recognition, not just coding speed.
What's the time complexity, and will it pass?+
O(n^2) time, O(n^2) space for the DP table. For strings up to length 500, that's about 250k operations per test case. It passes easily. The bottleneck is usually implementation mistakes, not TLE.
What common mistake do most candidates make?+
Trying to build the insertion sequence by greedily placing characters. That's backwards. You never actually insert anything. You compute the length of what's already there (the LPS) and infer the answer from what's missing. Candidates who skip the palindromic subsequence connection usually time out or give wrong answers.
How does this relate to Dynamic Programming topics on its own?+
This is a textbook interval DP problem. You build solutions for small substrings and expand outward. The same pattern applies to longest palindromic substring, edit distance, and matrix chain multiplication. Mastering the table-filling order here transfers directly to other hard DP problems.
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