Count Smaller Elements With Opposite Parity
Time O(nlogn) · Space O(n) · Official statement on LeetCode
Solutions
// Time: O(nlogn)
// Space: O(n)
// sort, coordinate compression, fenwick tree
class BIT {
public:
BIT(int n) : bit_(n + 1) { // 0-indexed
}
void add(int i, int val) {
++i;
for (; i < size(bit_); i += lower_bit(i)) {
bit_[i] += val;
}
}
int query(int i) const {
++i;
int total = 0;
for (; i > 0; i -= lower_bit(i)) {
total += bit_[i];
}
return total;
}
private:
inline int lower_bit(int i) const {
return i & -i;
}
vector<int> bit_;
};
class Solution {
public:
vector<int> countSmallerOppositeParity(vector<int>& nums) {
vector<int> sorted_nums(nums);
ranges::sort(sorted_nums);
sorted_nums.erase(unique(begin(sorted_nums), end(sorted_nums)), end(sorted_nums));
unordered_map<int, int> val_to_idx;
for (int i = 0; i < size(sorted_nums); ++i) {
val_to_idx[sorted_nums[i]] = i;
}
vector<BIT> bit(2, BIT(size(val_to_idx)));
vector<int> result(size(nums));
for (int i = size(nums) - 1; i >= 0; --i) {
const auto& idx = val_to_idx[nums[i]];
result[i] = bit[1 ^ (nums[i] % 2)].query(idx - 1);
bit[nums[i] % 2].add(idx, 1);
}
return result;
}
};
Beginner Explanation
What is Count Smaller Elements With Opposite Parity?
Count Smaller Elements With Opposite Parity (LeetCode #3907) is a Medium problem that primarily trains array.
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 sort and fenwick tree.
- 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: Sort, Coordinate Compression, BIT, Fenwick Tree.
AlgoForge explanations are original teaching notes. Always open the official problem statement on LeetCode for constraints and examples.
Interview Walkthrough
Interview approach for Count Smaller Elements With Opposite Parity
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 sort and fenwick tree.
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: sort and fenwick tree
Use the pattern as a checklist:
- sort — confirm the invariant holds after each step
- fenwick tree — 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 Count Smaller Elements With Opposite Parity
- Skipping edge cases — empty collections, single-element inputs, max constraints.
- Wrong invariant for sort and fenwick tree — 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 sort and fenwick tree:
- 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: array.
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 Count Smaller Elements With Opposite Parity in a second language (cpp, python).
- Drill 3–5 more problems tagged array.
- 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 sort and fenwick tree 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
Count Smaller Elements With Opposite Parity (#3907) — Medium. Pattern: sort and fenwick tree. Complexity: O(nlogn) time / O(n) space. Re-derive the invariant before coding.
FAQs
What is the time complexity of Count Smaller Elements With Opposite Parity?+
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 Count Smaller Elements With Opposite Parity use?+
It primarily maps to sort and fenwick tree, within the broader topic of array.
Is Count Smaller Elements With Opposite Parity 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/count-smaller-elements-with-opposite-parity/