Minimum Total Space Wasted With K Resizing Operations
Time O(k * n^2) · Space O(k * n) · Official statement on LeetCode
Solutions
// Time: O(k * n^2)
// Space: O(k * n)
class Solution {
public:
int minSpaceWastedKResizing(vector<int>& nums, int k) {
static const int INF = numeric_limits<int>::max();
++k;
vector<vector<int>> dp(size(nums) + 1, vector<int>(k + 1, INF));
dp[0][0] = 0;
for (int i = 1; i <= size(nums); ++i) {
int total = 0, max_num = 0;
for (int j = i; j >= 1; --j) {
total += nums[j - 1];
max_num = max(max_num, nums[j - 1]);
for (int m = 1; m <= k; ++m) {
if (dp[j - 1][m - 1] != INF) {
dp[i][m] = min(dp[i][m], dp[j - 1][m - 1] + (max_num * (i - j + 1) - total));
}
}
}
}
return dp.back().back();
}
};
Beginner Explanation
What is Minimum Total Space Wasted With K Resizing Operations?
Minimum Total Space Wasted With K Resizing Operations (LeetCode #1959) 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.
AlgoForge explanations are original teaching notes. Always open the official problem statement on LeetCode for constraints and examples.
Interview Walkthrough
Interview approach for Minimum Total Space Wasted With K Resizing Operations
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(k * n^2)) and space (O(k * 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(k * n^2) time and O(k * n) 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(k * n^2) |
| Space | O(k * 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 Minimum Total Space Wasted With K Resizing Operations
- 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 minimum-total-space-wasted-with-k-resizing-operations.
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 Minimum Total Space Wasted With K Resizing Operations 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
Minimum Total Space Wasted With K Resizing Operations (#1959) — Medium. Pattern: dynamic programming. Complexity: O(k * n^2) time / O(k * n) space. Re-derive the invariant before coding.
FAQs
What is the time complexity of Minimum Total Space Wasted With K Resizing Operations?+
The reference solutions aim for O(k * n^2) time and O(k * n) space. Always re-derive complexity from the code you write in the interview.
What pattern does Minimum Total Space Wasted With K Resizing Operations use?+
It primarily maps to dynamic programming, within the broader topic of dynamic programming.
Is Minimum Total Space Wasted With K Resizing Operations 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/minimum-total-space-wasted-with-k-resizing-operations/