Paint House IV
Time O(n * l^4) · Space O(l^2) · Official statement on LeetCode
Solutions
// Time: O(n * l^4)
// Space: O(l^2)
// dp
class Solution {
public:
long long minCost(int n, vector<vector<int>>& cost) {
const int l = size(cost[0]);
vector<vector<int64_t>> dp(l, vector<int64_t>(l));
for (int k = 0; k * 2 < n; ++k) {
vector<vector<int64_t>> new_dp(l, vector<int64_t>(l, numeric_limits<int64_t>::max()));
for (int i = 0; i < l; ++i) {
for (int j = 0; j < l; ++j) {
if (j == i) {
continue;
}
for (int ni = 0; ni < l; ++ni) {
if (ni == i) {
continue;
}
for (int nj = 0; nj < l; ++nj) {
if (nj == j || ni == nj) {
continue;
}
new_dp[ni][nj] = min(new_dp[ni][nj], dp[i][j] + cost[k][ni] + cost[n - 1 - k][nj]);
}
}
}
}
dp = move(new_dp);
}
int64_t result = numeric_limits<int64_t>::max();
for (int i = 0; i < l; ++i) {
for (int j = 0; j < l; ++j) {
if (i != j) {
result = min(result, dp[i][j]);
}
}
}
return result;
}
};
Beginner Explanation
What is Paint House IV?
Paint House IV (LeetCode #3429) is a Medium 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.
- Only then translate the idea into code.
Why this problem matters
It sits in the sweet spot of interview difficulty: multiple valid approaches, clear trade-offs. Official solution notes mention: DP.
AlgoForge explanations are original teaching notes. Always open the official problem statement on LeetCode for constraints and examples.
Interview Walkthrough
Interview approach for Paint House 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.
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 * l^4)) and space (O(l^2)) 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 * l^4) time and O(l^2) space.
Pattern focus: dynamic programming
Use the pattern as a checklist:
- dynamic programming — confirm the invariant holds after each step
Start from the primary solution, then rewrite from memory to lock it in.
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 * l^4) |
| Space | O(l^2) |
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 Paint House IV
- Skipping edge cases — empty collections, single-element inputs, max constraints.
- Wrong invariant for dynamic programming — 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
AI expand laterAlternatives
Placeholder for multi-approach comparison. Future AI content generation can expand:
- Brute force baseline
- Optimal dynamic programming solution
- Space-optimized rewrite
Prompt slot: expand alternatives for paint-house-iv.
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:
- 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 Paint House 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 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
Paint House IV (#3429) — Medium. Pattern: dynamic programming. Complexity: O(n * l^4) time / O(l^2) space. Re-derive the invariant before coding.
FAQs
What is the time complexity of Paint House IV?+
The reference solutions aim for O(n * l^4) time and O(l^2) space. Always re-derive complexity from the code you write in the interview.
What pattern does Paint House IV use?+
It primarily maps to dynamic programming, within the broader topic of dynamic programming.
Is Paint House IV good for interviews?+
Yes — as a Medium 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/paint-house-iv/