Find X Value of Array II
Time O(n * k + q * k * logn) · Space O(n * k) · Official statement on LeetCode
Solutions
// Time: O(n * k + q * k * logn)
// Space: O(n * k)
// segment tree
class Solution {
public:
vector<int> resultArray(vector<int>& nums, int k, vector<vector<int>>& queries) {
const auto& build = [&](int i) {
const int x = nums[i] % k;
vector<int> cnt(k + 1);
++cnt[x];
cnt.back() = x;
return cnt;
};
const auto& update = [&](const auto& c) {
const int x = c % k;
vector<int> cnt(k + 1);
++cnt[x];
cnt.back() = x;
return cnt;
};
const auto& query = [&](const auto& x, const auto& y) {
if (empty(x)) {
return y;
}
if (empty(y)) {
return x;
}
vector<int> cnt(x);
for (int i = 0; i < k; ++i) {
cnt[x.back() * i % k] += y[i];
}
cnt.back() = x.back() * y.back() % k;
return cnt;
};
SegmentTree<vector<int>> st(size(nums), build, update, query);
vector<int> result(size(queries));
for (int idx = 0; idx < size(queries); ++idx) {
const int i = queries[idx][0];
const int v = queries[idx][1];
const int s = queries[idx][2];
const int x = queries[idx][3];
st.update(i, v);
result[idx] = st.query(s, size(nums) - 1)[x];
}
return result;
}
private:
// Template:
// https://github.com/kamyu104/LeetCode-Solutions/blob/master/C++/booking-concert-tickets-in-groups.cpp
template <typename T>
class SegmentTree {
public:
explicit SegmentTree(
int N,
const function<T(const int&)>& build_fn,
const function<T(const int&)>& update_fn,
const function<T(const T&, const T&)>& query_fn)
: tree(N > 1 ? 1 << (__lg(N - 1) + 2) : 2),
base(N > 1 ? 1 << (__lg(N - 1) + 1) : 1),
build_fn_(build_fn),
query_fn_(query_fn),
update_fn_(update_fn) {
for (int i = base; i < base + N; ++i) {
tree[i] = build_fn_(i - base);
}
for (int i = base - 1; i >= 1; --i) {
tree[i] = query_fn_(tree[i << 1], tree[(i << 1) + 1]);
}
}
void update(int i, int h) {
int x = base + i;
tree[x] = update_fn_(h);
while (x > 1) {
x >>= 1;
tree[x] = query_fn_(tree[x << 1], tree[(x << 1) + 1]);
}
}
T query(int L, int R) {
L += base;
R += base;
T left, right;
for (; L <= R; L >>= 1, R >>= 1) {
if (L & 1) {
left = query_fn_(left, tree[L]);
++L;
}
if ((R & 1) == 0) {
right = query_fn_(tree[R], right);
--R;
}
}
return query_fn_(left, right);
}
vector<T> tree;
int base;
private:
const function<T(const int&)> build_fn_;
const function<T(const int&)> update_fn_;
const function<T(const T&, const T&)> query_fn_;
};
};
Beginner Explanation
What is Find X Value of Array II?
Find X Value of Array II (LeetCode #3525) is a Hard 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 and segment tree.
- 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, Segment Tree.
AlgoForge explanations are original teaching notes. Always open the official problem statement on LeetCode for constraints and examples.
Interview Walkthrough
Interview approach for Find X Value of Array II
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 and segment 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(n * k + q * k * logn)) and space (O(n * k)) 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 * k + q * k * logn) time and O(n * k) space.
Pattern focus: dynamic programming and segment tree
Use the pattern as a checklist:
- dynamic programming — confirm the invariant holds after each step
- segment 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(n * k + q * k * logn) |
| Space | O(n * k) |
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 Find X Value of Array II
- Skipping edge cases — empty collections, single-element inputs, max constraints.
- Wrong invariant for dynamic programming and segment 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 dynamic programming and segment 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: 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 Find X Value of Array II 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 and segment 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
Find X Value of Array II (#3525) — Hard. Pattern: dynamic programming and segment tree. Complexity: O(n * k + q * k * logn) time / O(n * k) space. Re-derive the invariant before coding.
FAQs
What is the time complexity of Find X Value of Array II?+
The reference solutions aim for O(n * k + q * k * logn) time and O(n * k) space. Always re-derive complexity from the code you write in the interview.
What pattern does Find X Value of Array II use?+
It primarily maps to dynamic programming and segment tree, within the broader topic of dynamic programming.
Is Find X Value of Array II 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/find-x-value-of-array-ii/