Make Array Non-decreasing or Non-increasing
Time O(nlogn) · Space O(n) · Official statement on LeetCode
Solutions
// Time: O(nlogn)
// Space: O(n)
// greedy, heap
class Solution {
public:
int convertArray(vector<int>& nums) {
const auto& f = [](const auto& begin, const auto& end) {
int result = 0;
priority_queue<int> max_heap;
for (auto it = begin; it != end; ++it) {
if (!empty(max_heap) && *it < max_heap.top()) {
result += max_heap.top() - *it; max_heap.pop();
max_heap.emplace(*it);
}
max_heap.emplace(*it);
}
return result;
};
return min(f(cbegin(nums), cend(nums)), f(crbegin(nums), crend(nums)));
}
};
// Time: O(n^2)
// Space: O(n)
// dp
class Solution2 {
public:
int convertArray(vector<int>& nums) {
unordered_set<int> nums_set(cbegin(nums), cend(nums));
vector<int> vals(cbegin(nums_set), cend(nums_set));
sort(begin(vals), end(vals));
const auto& f = [&](const auto& begin, const auto& end) {
int result = 0;
unordered_map<int, int> dp; // dp[i]: min(cnt(j) for j in vals if j <= i)
for (auto it = begin; it != end; ++it) {
int prev = -1;
for (const auto& i : vals) {
dp[i] = (prev != -1) ? min(dp[i] + abs(i - *it), dp[prev]) : dp[i] + abs(i - *it);
prev = i;
}
}
return dp[vals.back()];
};
return min(f(cbegin(nums), cend(nums)), f(crbegin(nums), crend(nums)));
}
};
Beginner Explanation
What is Make Array Non-decreasing or Non-increasing?
Make Array Non-decreasing or Non-increasing (LeetCode #2263) is a Hard problem that primarily trains greedy.
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, greedy, and heap.
- 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, Greedy, Heap.
AlgoForge explanations are original teaching notes. Always open the official problem statement on LeetCode for constraints and examples.
Interview Walkthrough
Interview approach for Make Array Non-decreasing or Non-increasing
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, greedy, and heap.
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(nlogn)) 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(nlogn) time and O(n) space.
Pattern focus: dynamic programming, greedy, and heap
Use the pattern as a checklist:
- dynamic programming — confirm the invariant holds after each step
- greedy — confirm the invariant holds after each step
- heap — 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(nlogn) |
| 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 Make Array Non-decreasing or Non-increasing
- Skipping edge cases — empty collections, single-element inputs, max constraints.
- Wrong invariant for dynamic programming, greedy, and heap — 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, greedy, and heap:
- 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: greedy.
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 Make Array Non-decreasing or Non-increasing in a second language (cpp, python).
- Drill 3–5 more problems tagged greedy.
- 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, greedy, and heap 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
Make Array Non-decreasing or Non-increasing (#2263) — Hard. Pattern: dynamic programming, greedy, and heap. Complexity: O(nlogn) time / O(n) space. Re-derive the invariant before coding.
FAQs
What is the time complexity of Make Array Non-decreasing or Non-increasing?+
The reference solutions aim for O(nlogn) time and O(n) space. Always re-derive complexity from the code you write in the interview.
What pattern does Make Array Non-decreasing or Non-increasing use?+
It primarily maps to dynamic programming, greedy, and heap, within the broader topic of greedy.
Is Make Array Non-decreasing or Non-increasing 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/make-array-non-decreasing-or-non-increasing/