Virtu Financial·Software Engineer·Technical Phone Screen·Intermediate

Intermediate

May 2026

Summary

Virtu Financial coding round, one algorithmic problem about bit manipulation. Pretty niche problem space, felt like it was testing whether you'd seen this type of thing before rather than raw problem-solving.

Questions Asked (1)

You're given an array of integers. You can flip any single bit of any number in one operation. What's the minimum number of operations needed to make all elements in the array equal?

Algorithms & Data Structures

Author's notes

My first instinct was to think about XOR between pairs, which got me partway there.

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AI HintsAI Generated

Suggested Approach

Recognize that flipping a bit changes a number, so to make all elements equal, we need to choose a target value and compute the total number of bit flips required to transform each element into that target. The minimum operations is the minimum over all possible target values of the sum of Hamming distances between each element and the target. Since the target can be any integer, we can consider each bit position independently: for each bit, the optimal target bit is the majority bit among all elements, and the cost is the number of elements that differ from that majority.

Pro tip: Clarify that the target value is not restricted to the existing array elements; it can be any integer, and the optimal target is determined bit-by-bit by majority vote. This shows you understand the problem deeply and can avoid unnecessary constraints.

1. Understand the operation

Clarify that flipping a bit changes a 0 to 1 or 1 to 0 in the binary representation of a number, and each flip counts as one operation.

2. Define the goal

We need to make all elements equal to some target integer T, minimizing the total number of bit flips across all elements.

3. Decompose by bits

Since bits are independent, for each bit position, choose the target bit (0 or 1) that minimizes the number of flips. This is equivalent to taking the majority bit among all elements at that position.

4. Compute total operations

Sum the minimum flips for each bit position. The result is the minimum number of operations needed.

5. Consider constraints and edge cases

Discuss handling negative numbers (if allowed), large integers, and the time complexity (O(n * number of bits)).

Key Points to Mention

Bitwise independence: each bit can be optimized separately.
Majority vote per bit position to determine the optimal target bit.
Total operations = sum over bits of min(count of 0s, count of 1s).
The target value is not necessarily one of the array elements.
Time complexity: O(n * B) where B is the number of bits (e.g., 32 or 64).
Handling negative numbers: consider two's complement representation if needed.

AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.