In the Vowels Game in a String, analyze the string to count vowels and apply optimal turn-based logic. Alice starts first, and the first player unable to make a move loses. Use a combination of string traversal and simple math to quickly decide whether Alice can force a win or if Bob will inevitably win.
Problem Statement
Alice and Bob play a game on a given lowercase string s. They take turns removing vowels, and the first player unable to move loses. Both players play optimally.
You must determine whether Alice can guarantee a win given the starting string. Consider the positions of vowels, potential moves, and the total length of s to decide the winner efficiently.
Examples
Example 1
Input: s = "leetcoder"
Output: true
Alice can win the game as follows:
Example 2
Input: s = "bbcd"
Output: false
There is no valid play for Alice in her first turn, so Alice loses the game.
Constraints
- 1 <= s.length <= 105
- s consists only of lowercase English letters.
Solution Approach
Count Vowels Efficiently
Iterate through the string s and count all vowels. This helps determine the number of potential moves and establishes if Alice has any first-move options.
Apply Turn-Based Logic
Use the total vowel count to simulate optimal moves: if the count is zero at Alice's first turn, Bob wins. Otherwise, alternate turns until one player cannot move, applying math to skip unnecessary simulations.
Return Winner
Based on the analysis, return true if Alice can force a win and false if Bob will win. This ensures a direct, efficient solution without iterating through all game states.
Complexity Analysis
| Metric | Value |
|---|---|
| Time | Depends on the final approach |
| Space | Depends on the final approach |
Time complexity depends on traversing the string once to count vowels, giving O(n). Space complexity is O(1) since only counters are needed.
What Interviewers Usually Probe
- Check if the candidate identifies counting vowels as the key first step.
- Observe if the candidate considers the failure mode when the string has no vowels.
- Look for recognition that optimal play can be predicted using simple math rather than full simulation.
Common Pitfalls or Variants
Common pitfalls
- Failing to check if the initial string has zero vowels, leading to incorrect winner prediction.
- Overcomplicating the game simulation instead of using vowel count and turn logic.
- Ignoring edge cases with single-character strings or strings with all consonants.
Follow-up variants
- Change the winning condition to removing consonants instead of vowels and analyze the impact on optimal strategy.
- Use a string with alternating vowels and consonants to see how move sequences affect the winner.
- Introduce a rule limiting moves per turn to 2 vowels, requiring adjusted math for optimal play.
How GhostInterview Helps
- GhostInterview highlights vowel positions and counts to instantly determine feasible moves for Alice.
- It identifies optimal play paths without simulating every game state, saving time during interviews.
- The tool explains the exact pattern of math plus string needed to predict the winner reliably.
Topic Pages
Related GhostInterview Pages
- LeetCode Interview Copilot - Use GhostInterview as a live solver when you want direct help with LeetCode-style coding questions.
- Coding Interview Assistant - See how GhostInterview supports array, string, linked list, graph, and tree interview workflows.
- How GhostInterview Works - Review the screenshot, reasoning, and answer flow before using the solver in a live interview.
FAQ
What is the main strategy to win the Vowels Game in a String?
Count vowels and apply turn-based logic; Alice wins if she has a first-move advantage and Bob wins otherwise.
How does the math plus string pattern apply here?
Vowel counting is the math part, string traversal is the string part, and combining them predicts the winner efficiently.
What should I do if the string has no vowels?
Alice cannot move, so Bob wins immediately. This edge case is critical for correct results.
Can this approach handle very long strings?
Yes, because counting vowels requires a single pass with O(n) time and O(1) space.
Are there variations of this game that change the optimal strategy?
Yes, altering the type of removable characters or limiting moves per turn changes the math calculation for winning.
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