Hard · Algorithms · Topics: dynamic programming, mcm, partition, string
The problem
You're building a DNA sequence compression tool for a genomics startup. A key preprocessing step requires splitting a genetic sequence into the fewest possible palindromic segments — palindromic substrings are special because they compress extremely efficiently using a symmetry-based encoding scheme. Your task: given a string s, partition it into substrings such that every substring is a palindrome, and find the minimum number of cuts needed to achieve this.
Example: "aab" can be partitioned as ["aa", "b"] — just 1 cut needed.
Function signature
int minCut(string s);
Test cases
Input s
Output
Explanation
"aab"
1
Partition: "aa" | "b" — 1 cut, both parts are palindromes
"a"
0
Already a palindrome, no cuts needed
"ab"
1
Partition: "a" | "b" — 1 cut needed
"aabb"
1
Partition: "aa" | "bb" — 1 cut
"aabbaa"
0
Whole string is itself a palindrome
"abcde"
4
No palindromic substrings longer than 1 char — must cut between every char
""
0
Empty string trivially needs 0 cuts
(Constraints typically: 1 <= s.length <= 2000, s consists of lowercase English letters)
How interviewers phrase it
"Given a string, partition it into the minimum number of pieces such that each piece is a palindrome. Return the minimum number of cuts."
Sometimes phrased as a follow-up to "Palindrome Partitioning I" (LeetCode 131), where I gives all partitions and II asks just for the minimum cut count — a strong signal this is LeetCode 132.
They may first ask you to solve it generating all partitions (backtracking), then pivot: "Now I just want the minimum cuts, can you do better than backtracking?"
Clarifying questions to ask
Is the string guaranteed non-empty? What about a single character — is that always considered a palindrome (0 cuts)?
Are we counting "cuts" or "number of partitions"? (Important distinction: cuts = partitions - 1, easy to mix up under pressure — confirm explicitly.)
What's the expected string length — is O(n²) acceptable, or do we need to push for the optimized O(n) palindrome-check-via-Manacher's approach within an O(n²) DP?
Is the string limited to lowercase letters, or could it contain uppercase/special characters/spaces? (Usually doesn't change the algorithm, but good practice to ask.)
Follow-ups to expect
"Can you also return the actual partitions, not just the count?"
"What's the difference between this and Palindrome Partitioning I?"
"Can you optimize the palindrome-check precomputation?"
"What if you wanted minimum cuts such that each partition's length is also at most k?"
"Can you do this in O(n) extra space instead of O(n²)?"
"Is this related to Matrix Chain Multiplication (MCM)?"
Practise questions like this with a real engineer
On Practick another engineer interviews you live for 60 minutes on a question from this bank. They have the full interviewer guide beside the call: the expected answer to every follow-up, hints to give if you stall, and a scoring rubric. You get the model solution once the session settles. It is free: interview someone for an hour and you have earned your own.