Palindrome Partitioning IV
Time O(n^2) · Space O(n) · Official statement on LeetCode
Solutions
// Time: O(n^2)
// Space: O(n)
class Solution {
public:
bool checkPartitioning(string s) {
const auto& P = manacher(s);
vector<int> prefix, suffix;
for (int i = 2; i < size(P) - 2; ++i) {
if (i - 1 - P[i] == 0) {
prefix.emplace_back(i);
}
if (i + 1 + P[i] == size(P) - 1) {
suffix.emplace_back(i);
}
}
for (const auto& i : prefix) {
for (const auto& j : suffix) {
int left = i + 1 + P[i], right = j - 1 - P[j];
if (left > right) {
continue;
}
int mid = left + (right - left) / 2;
if (P[mid] >= mid - left) {
return true;
}
}
}
return false;
}
private:
vector<int> manacher(const string& s) {
string T = preProcess(s);
const int n = size(T);
vector<int> P(n);
int C = 0, R = 0;
for (int i = 1; i < n - 1; ++i) {
int i_mirror = 2 * C - i;
P[i] = (R > i) ? min(R - i, P[i_mirror]) : 0;
while (T[i + 1 + P[i]] == T[i - 1 - P[i]]) {
++P[i];
}
if (i + P[i] > R) {
C = i;
R = i + P[i];
}
}
return P;
}
string preProcess(const string& s) {
if (empty(s)) {
return "^$";
}
string ret = "^";
for (int i = 0; i < size(s); ++i) {
ret += "#" + s.substr(i, 1);
}
ret += "#$";
return ret;
}
};
// Time: O(n^2)
// Space: O(n^2)
class Solution2 {
public:
bool checkPartitioning(string s) {
vector<vector<bool>> dp(size(s), vector<bool>(size(s)));
for (int i = size(s) - 1; i >= 0; --i) {
for (int j = i; j < size(s); ++j) {
if (s[i] == s[j] && (j - i < 2 || dp[i + 1][j - 1])) {
dp[i][j] = true;
}
}
}
for (int i = 1; i + 1 < size(s); ++i) {
if (!dp[0][i - 1]) {
continue;
}
for (int j = i + 1; j < size(s); ++j) {
if (!dp[j][size(s) - 1]) {
continue;
}
if (dp[i][j - 1]) {
return true;
}
}
}
return false;
}
};
Beginner Explanation
What is Palindrome Partitioning IV?
Palindrome Partitioning IV (LeetCode #1745) is a Hard problem that primarily trains dynamic programming.
How to think about it
- Restate the goal in your own words before coding.
- Work a tiny example by hand so the invariant becomes obvious.
- Identify the pattern — this problem aligns with dynamic programming and manachers algorithm.
- Only then translate the idea into code.
Why this problem matters
Hard problems force you to combine patterns and prove complexity carefully — interview gold. Official solution notes mention: DP, Manacher's Algorithm.
AlgoForge explanations are original teaching notes. Always open the official problem statement on LeetCode for constraints and examples.
Interview Walkthrough
Interview approach for Palindrome Partitioning IV
Opening (30–60 seconds)
- Clarify inputs/outputs and edge cases (empty input, single element, duplicates, overflow).
- State a brute force so the interviewer knows you can solve it naively.
- Propose the optimal direction tied to dynamic programming and manachers algorithm.
Core solution narrative
- Define the state you track (pointers, DP cell, set membership, stack top, etc.).
- Explain the transition when you process the next element.
- Call out time (O(n^2)) and space (O(n)) before coding.
- Code cleanly; narrate variable names.
What interviewers listen for
- Correctness on edge cases
- Complexity honesty
- Ability to discuss trade-offs (e.g., hash map space vs. sort + two pointers)
Follow-up questions they may ask
- Can you solve it with less memory?
- What if the input stream is infinite / doesn't fit in RAM?
- How would tests look for adversarial inputs?
Optimized Approach
Optimized solution notes
The reference solutions on AlgoForge target O(n^2) time and O(n) space.
Pattern focus: dynamic programming and manachers algorithm
Use the pattern as a checklist:
- dynamic programming — confirm the invariant holds after each step
- manachers algorithm — confirm the invariant holds after each step
Multiple methods appear in the source solutions — compare them and explain when each is preferable.
Implementation tips
- Prefer readable names over micro-optimizations in interviews.
- Extract helpers only when they clarify (e.g., expand-around-center, DFS visit).
- After AC-level logic, re-scan for off-by-one and null checks.
Complexity Analysis
Complexity
| Measure | Bound |
|---|---|
| Time | O(n^2) |
| Space | O(n) |
How to justify this in an interview
- Time: count loops, map/set operations, and recursive branching; state average vs worst case if relevant.
- Space: include hash maps, recursion stack, and output allocation when the problem asks for it.
If your implementation differs from the reference, re-derive big-O from your code — never memorize a complexity you cannot defend.
Common Mistakes
Common mistakes on Palindrome Partitioning IV
- Skipping edge cases — empty collections, single-element inputs, max constraints.
- Wrong invariant for dynamic programming and manachers algorithm — updating state too early or too late.
- Mutating input unexpectedly when the problem forbids it.
- Off-by-one in windows, ranges, or binary search bounds.
- Ignoring overflow / precision for integer arithmetic problems.
- Overengineering — jumping to an advanced structure when a simpler approach works.
Alternative Approaches
Alternatives
The source file includes more than one method. Compare:
- Primary optimized path — best complexity for typical interviews.
- Secondary approach — often brute force, sorting-based, or space-optimized variant.
Practice articulating when you would pick each (constraints, readability, follow-ups).
Edge Cases
Edge cases checklist
- Minimum input size
- Maximum input size / time limits
- Duplicates and already-sorted input
- Negative numbers / zeros (if applicable)
- Disconnected structures (graphs/trees)
- Single path vs branching recursion depth
Pattern Recognition
Spotting this pattern
Signal phrases that point to dynamic programming and manachers algorithm:
- Sorted input or ability to sort without changing the answer class
- Need for contiguous subarray / substring → consider sliding window
- Need for O(1) membership → hash set/map
- Optimal substructure + overlapping subproblems → DP
- Connectivity / components → graph DFS/BFS or Union-Find
Primary topics: dynamic programming.
Follow-up Interview Questions
Follow-ups
- How does the solution change if the input is a stream?
- Can you solve it in-place?
- What if duplicates must be handled differently?
- How would you parallelize the approach?
- Design tests that would break a buggy implementation.
Practice Recommendations
What to practice next
- Re-solve Palindrome Partitioning IV in a second language (cpp, python).
- Drill 3–5 more problems tagged dynamic programming.
- Teach the solution out loud in under 5 minutes.
- Add this problem to your revision calendar in 3 days and 14 days.
Visualization
Study checklist
- Read the official problem statement on LeetCode
- Solve on paper / whiteboard first
- Implement the dynamic programming and manachers algorithm approach
- Verify edge cases from the checklist
- State time and space complexity aloud
- Compare with the AlgoForge reference solution
- Schedule a revision session
Revision notes
Palindrome Partitioning IV (#1745) — Hard. Pattern: dynamic programming and manachers algorithm. Complexity: O(n^2) time / O(n) space. Re-derive the invariant before coding.
FAQs
What is the time complexity of Palindrome Partitioning IV?+
The reference solutions aim for O(n^2) time and O(n) space. Always re-derive complexity from the code you write in the interview.
What pattern does Palindrome Partitioning IV use?+
It primarily maps to dynamic programming and manachers algorithm, within the broader topic of dynamic programming.
Is Palindrome Partitioning IV good for interviews?+
Yes — as a Hard problem it is a solid practice target. Pair it with related problems in the same pattern family for spaced repetition.
Where can I read the official statement?+
Open the official LeetCode page for constraints and examples: https://leetcode.com/problems/palindrome-partitioning-iv/