Minimum Flips to Make a OR b Equal to c
Time O(1) · Space O(1) · Official statement on LeetCode
Solutions
// Time: O(5)
// Space: O(1)
class Solution {
public:
int minFlips(int a, int b, int c) {
return number_of_1_bits((a | b) ^ c) + number_of_1_bits(a & b & ~c);
}
private:
int number_of_1_bits(int n) {
n = (n & 0x55555555) + ((n >> 1) & 0x55555555);
n = (n & 0x33333333) + ((n >> 2) & 0x33333333);
n = (n & 0x0F0F0F0F) + ((n >> 4) & 0x0F0F0F0F);
n = (n & 0x00FF00FF) + ((n >> 8) & 0x00FF00FF);
n = (n & 0x0000FFFF) + ((n >> 16) & 0x0000FFFF);
return n;
}
};
// Time: O(logn/4) = O(32/4) = O(8)
// Space: O(1)
class Solution2 {
public:
int minFlips(int a, int b, int c) {
// be care of evaluation order https://en.cppreference.com/w/cpp/language/eval_order
// return __builtin_popcount(c ^= (a | b)) + __builtin_popcount(c & (a & b)); // Sequenced-before rules (since c++11)
return (c ^= (a | b)) ? __builtin_popcount(c) + __builtin_popcount(c & (a & b)) : 0; // compatible before c++11
}
};
// Time: O(31)
// Space: O(1)
class Solution3 {
public:
int minFlips(int a, int b, int c) {
int diff = (a | b) ^ c;
return number_of_1_bits(diff) + number_of_1_bits(diff & (a & b));
}
private:
int number_of_1_bits(int n) {
int result = 0;
for (; n; n &= n - 1, ++result);
return result;
}
};
// Time: O(31)
// Space: O(1)
class Solution4 {
public:
int minFlips(int a, int b, int c) {
int result = 0;
for (int i = 0; i < 31; ++i) {
int a_i = a & 1, b_i = b & 1, c_i = c & 1;
if ((a_i | b_i) != c_i) {
result += (a_i == b_i && b_i == 1) ? 2 : 1;
}
a = a >> 1, b = b >> 1, c = c >> 1;
}
return result;
}
};
Beginner Explanation
What is Minimum Flips to Make a OR b Equal to c?
Minimum Flips to Make a OR b Equal to c (LeetCode #1318) is a Medium problem that primarily trains bit manipulation.
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 bit manipulation.
- 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 Flips to Make a OR b Equal to c
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 bit manipulation.
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(1)) and space (O(1)) 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(1) time and O(1) space.
Pattern focus: bit manipulation
Use the pattern as a checklist:
- bit manipulation — 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(1) |
| Space | O(1) |
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 Flips to Make a OR b Equal to c
- Skipping edge cases — empty collections, single-element inputs, max constraints.
- Wrong invariant for bit manipulation — 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 bit manipulation:
- 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: bit manipulation.
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 Flips to Make a OR b Equal to c in a second language (cpp, python).
- Drill 3–5 more problems tagged bit manipulation.
- 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 bit manipulation 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 Flips to Make a OR b Equal to c (#1318) — Medium. Pattern: bit manipulation. Complexity: O(1) time / O(1) space. Re-derive the invariant before coding.
FAQs
What is the time complexity of Minimum Flips to Make a OR b Equal to c?+
The reference solutions aim for O(1) time and O(1) space. Always re-derive complexity from the code you write in the interview.
What pattern does Minimum Flips to Make a OR b Equal to c use?+
It primarily maps to bit manipulation, within the broader topic of bit manipulation.
Is Minimum Flips to Make a OR b Equal to c 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-flips-to-make-a-or-b-equal-to-c/