Virtu Financial·Software Engineer·Technical Phone Screen·Intermediate

Intermediate

May 2026

Summary

Virtu Financial coding round with a string manipulation problem that sounds deceptively clean but has some tricky edge cases once you start thinking about it carefully.

Questions Asked (1)

Given a binary string, an integer m, and an integer k, where the string cannot contain m consecutive 0s, find the minimum number of operations to satisfy this constraint. Each operation lets you flip k consecutive positions to 1.

Algorithms & Data Structures

Author's notes

Took me a minute to even parse what was being asked.

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AI HintsAI Generated

Suggested Approach

Model the problem as covering all runs of m consecutive 0s with minimum flips of length k, using a greedy left-to-right scan. When a violation is found, flip the window starting at the current position (or as far right as possible to cover the violation) and continue. If a violation cannot be covered by any valid flip, return -1.

Pro tip: Clarify with the interviewer whether flips can overlap and whether flipping already-1 positions is allowed; these details often change the greedy choice and edge cases.

1. Clarify constraints and edge cases

Confirm the meaning of 'flip k consecutive positions to 1' (does it set them to 1 regardless of current value?), whether operations can overlap, and what to return if impossible.

2. Identify violations

Scan the string to find any run of m consecutive 0s. Each such run must be broken by at least one flip that covers at least one position in the run.

3. Greedy covering strategy

Process left to right. When a violation is detected (e.g., m consecutive 0s ending at index i), place a flip window as far right as possible while still covering the violation, to maximize future coverage.

4. Simulate flips and count

Apply each flip (set k positions to 1), increment the operation count, and continue scanning from the affected region. Use a data structure to efficiently track 0-runs if needed.

5. Handle impossibility and complexity

If a violation cannot be covered by any valid flip (e.g., near the end of the string), return -1. Analyze time complexity (O(n) with careful implementation) and space complexity.

Key Points to Mention

Greedy choice: always flip as far right as possible to cover the current leftmost violation, maximizing future benefit.
Sliding window or two-pointer technique to efficiently detect runs of m consecutive 0s.
Edge cases: m > n, k > n, k = 0, string already valid, impossible cases.
Time and space complexity analysis: aim for O(n) time and O(1) extra space if possible.
Proof of optimality: exchange argument showing greedy is optimal.
Handling overlapping flips and ensuring no double-counting of operations.

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