K Highest Ranked Items Within a Price Range
Time O(m * n + klogk) · Space O(m * n) · Official statement on LeetCode
Solutions
// Time: O(m * n + klogk)
// Space: O(m * n)
// bfs, quick select
class Solution {
public:
vector<vector<int>> highestRankedKItems(vector<vector<int>>& grid, vector<int>& pricing, vector<int>& start, int k) {
static const vector<pair<int, int>> directions{{0, 1}, {1, 0}, {0, -1}, {-1, 0}};
vector<pair<int, int>> q = {{start[0], start[1]}};
vector<vector<int>> lookup(size(grid), vector<int>(size(grid[0]), -1));
int d = lookup[start[0]][start[1]] = 0;
auto compare = [&](const auto& x, const auto& y) {
return make_tuple(lookup[x[0]][x[1]], grid[x[0]][x[1]], x[0], x[1]) <
make_tuple(lookup[y[0]][y[1]], grid[y[0]][y[1]], y[0], y[1]);
};
vector<vector<int>> result;
while (!empty(q)) {
if (size(result) >= k) {
if (size(result) > k) {
nth_element(begin(result), begin(result) + k, end(result), compare);
result.resize(k);
}
break;
}
vector<pair<int, int>> new_q;
for (const auto& [r, c] : q) {
if (pricing[0] <= grid[r][c] && grid[r][c] <= pricing[1]) {
result.push_back({r, c});
}
for (const auto& [dr, dc] : directions) {
const int nr = r + dr, nc = c + dc;
if (!((0 <= nr && nr < size(grid)) && (0 <= nc && nc < size(grid[0])) &&
grid[nr][nc] && lookup[nr][nc] == -1)) {
continue;
}
lookup[nr][nc] = d + 1;
new_q.emplace_back(nr, nc);
}
}
q = move(new_q);
++d;
}
sort(begin(result), end(result), compare);
return result;
}
};
Beginner Explanation
What is K Highest Ranked Items Within a Price Range?
K Highest Ranked Items Within a Price Range (LeetCode #2146) is a Medium problem that primarily trains breadth first search.
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 queue bfs and sort.
- 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: BFS, Quick Select, Sort.
AlgoForge explanations are original teaching notes. Always open the official problem statement on LeetCode for constraints and examples.
Interview Walkthrough
Interview approach for K Highest Ranked Items Within a Price Range
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 queue bfs and sort.
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(m * n + klogk)) and space (O(m * 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(m * n + klogk) time and O(m * n) space.
Pattern focus: queue bfs and sort
Use the pattern as a checklist:
- queue bfs — confirm the invariant holds after each step
- sort — 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(m * n + klogk) |
| Space | O(m * 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 K Highest Ranked Items Within a Price Range
- Skipping edge cases — empty collections, single-element inputs, max constraints.
- Wrong invariant for queue bfs and sort — 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 queue bfs and sort:
- 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: breadth first search.
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 K Highest Ranked Items Within a Price Range in a second language (cpp, python).
- Drill 3–5 more problems tagged breadth first search.
- 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 queue bfs and sort 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
K Highest Ranked Items Within a Price Range (#2146) — Medium. Pattern: queue bfs and sort. Complexity: O(m * n + klogk) time / O(m * n) space. Re-derive the invariant before coding.
FAQs
What is the time complexity of K Highest Ranked Items Within a Price Range?+
The reference solutions aim for O(m * n + klogk) time and O(m * n) space. Always re-derive complexity from the code you write in the interview.
What pattern does K Highest Ranked Items Within a Price Range use?+
It primarily maps to queue bfs and sort, within the broader topic of breadth first search.
Is K Highest Ranked Items Within a Price Range 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/k-highest-ranked-items-within-a-price-range/