Find a Value of a Mysterious Function Closest to Target
Time O(nlogm) · Space O(logm) · Official statement on LeetCode
Solutions
// Time: O(nlogm), m is the max value of arr
// Space: O(logm)
class Solution {
public:
int closestToTarget(std::vector<int>& arr, int target) {
static const int LOGM = 20;
BitCount count(LOGM);
int result = numeric_limits<int>::max();
for (int left = 0, right = 0; right < arr.size(); ++right) {
count += arr[right];
while (left <= right) {
const auto& f = count.bitAnd();
result = min(result, abs(f - target));
if (f >= target) {
break;
}
count -= arr[left++];
}
}
return result;
}
private:
class BitCount {
public:
BitCount(int n)
: l_(0)
, n_(n)
, count_(n) {
}
int bitAnd() const {
int num = 0;
for (int i = 0; i < n_; ++i) {
if (count_[i] == l_) {
num |= 1 << i;
}
}
return num;
}
void operator+=(int num) {
++l_;
for (int i = 0; i < n_; ++i) {
if (num & (1 << i)) {
++count_[i];
}
}
}
void operator-=(int num) {
--l_;
for (int i = 0; i < n_; ++i) {
if (num & (1 << i)) {
--count_[i];
}
}
}
private:
int l_;
int n_;
vector<int> count_;
};
};
// Time: O(nlogm), m is the max value of arr
// Space: O(logm)
class Solution2 {
public:
int closestToTarget(vector<int>& arr, int target) {
int result = numeric_limits<int>::max();
unordered_set<int> dp; // at most O(logm) dp states
for (const auto& x : arr) {
unordered_set<int> new_dp = {x};
for (const auto& f: dp) {
new_dp.emplace(f & x);
}
for (const auto& f : new_dp) {
result = min(result, abs(f - target));
}
dp = move(new_dp);
}
return result;
}
};
Beginner Explanation
What is Find a Value of a Mysterious Function Closest to Target?
Find a Value of a Mysterious Function Closest to Target (LeetCode #1521) is a Hard problem that primarily trains two pointers.
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, two pointers, and sliding window.
- 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, Two Pointers, Sliding Window.
AlgoForge explanations are original teaching notes. Always open the official problem statement on LeetCode for constraints and examples.
Interview Walkthrough
Interview approach for Find a Value of a Mysterious Function Closest to Target
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, two pointers, and sliding window.
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(nlogm)) and space (O(logm)) 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(nlogm) time and O(logm) space.
Pattern focus: dynamic programming, two pointers, and sliding window
Use the pattern as a checklist:
- dynamic programming — confirm the invariant holds after each step
- two pointers — confirm the invariant holds after each step
- sliding window — 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(nlogm) |
| Space | O(logm) |
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 a Value of a Mysterious Function Closest to Target
- Skipping edge cases — empty collections, single-element inputs, max constraints.
- Wrong invariant for dynamic programming, two pointers, and sliding window — 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, two pointers, and sliding window:
- 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: two pointers.
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 a Value of a Mysterious Function Closest to Target in a second language (cpp, python).
- Drill 3–5 more problems tagged two pointers.
- 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, two pointers, and sliding window 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 a Value of a Mysterious Function Closest to Target (#1521) — Hard. Pattern: dynamic programming, two pointers, and sliding window. Complexity: O(nlogm) time / O(logm) space. Re-derive the invariant before coding.
FAQs
What is the time complexity of Find a Value of a Mysterious Function Closest to Target?+
The reference solutions aim for O(nlogm) time and O(logm) space. Always re-derive complexity from the code you write in the interview.
What pattern does Find a Value of a Mysterious Function Closest to Target use?+
It primarily maps to dynamic programming, two pointers, and sliding window, within the broader topic of two pointers.
Is Find a Value of a Mysterious Function Closest to Target 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-a-value-of-a-mysterious-function-closest-to-target/