This problem requires identifying a secret number using the least number of guesses by applying a binary search over the valid range. Each guess receives immediate higher or lower feedback, allowing you to narrow down the search space efficiently. The key is maintaining low and high bounds and adjusting them correctly until the target number is found, ensuring O(log n) steps in the worst case.
Problem Statement
You are playing a guessing game where a number between 1 and n is selected, and your task is to identify it with minimal guesses. Each time you make a guess, you receive feedback indicating whether the secret number is higher, lower, or equal to your guess.
Implement a function that interacts with the guess API to determine the picked number. Your solution must efficiently reduce the search space using the feedback, leveraging the binary search pattern to achieve optimal guesses for any valid n.
Examples
Example 1
Input: n = 10, pick = 6
Output: 6
Example details omitted.
Example 2
Input: n = 1, pick = 1
Output: 1
Example details omitted.
Example 3
Input: n = 2, pick = 1
Output: 1
Example details omitted.
Constraints
- 1 <= n <= 231 - 1
- 1 <= pick <= n
Solution Approach
Initialize Search Bounds
Start with low = 1 and high = n. These bounds define the current search space, ensuring each guess halves the remaining possibilities.
Binary Search Iteration
While low is less than or equal to high, guess the midpoint. Use the feedback from the guess API to update low or high, shrinking the search space toward the picked number.
Return the Picked Number
Once the feedback indicates a correct guess, return that number. This guarantees you find the target efficiently, avoiding unnecessary guesses and leveraging the logarithmic nature of binary search.
Complexity Analysis
| Metric | Value |
|---|---|
| Time | Depends on the final approach |
| Space | Depends on the final approach |
Time complexity is O(log n) since each guess reduces the search space by half. Space complexity is O(1) because only the low, high, and mid variables are stored.
What Interviewers Usually Probe
- Expect you to explain why binary search fits this interactive guessing scenario.
- They may ask about edge cases like n = 1 or pick at the boundaries.
- Interviewers often check whether you handle integer overflow when computing mid = low + (high - low)/2.
Common Pitfalls or Variants
Common pitfalls
- Using (low + high)/2 directly can cause integer overflow for large n.
- Not updating low or high correctly based on the guess feedback leads to infinite loops.
- Failing to consider that pick could be at the initial bounds causes off-by-one errors.
Follow-up variants
- Modify the game to allow a range of valid picks and find any number in that range.
- Implement a version where guesses have a cost, requiring minimal total guess cost.
- Adapt the binary search approach to a descending ordered pick range instead of ascending.
How GhostInterview Helps
- Provides step-by-step binary search guidance tailored to interactive guess problems.
- Highlights potential pitfalls like integer overflow and off-by-one errors before they occur.
- Offers practice scenarios matching the exact feedback-driven narrowing pattern in this problem.
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 best strategy to solve Guess Number Higher or Lower?
Applying a binary search over the valid range ensures the minimal number of guesses and efficiently narrows the search space.
Can the picked number be at the bounds?
Yes, pick can be 1 or n, so your binary search must handle edge cases correctly without skipping bounds.
Why is using (low + high)/2 potentially dangerous?
It may overflow for large n values; instead, compute mid as low + (high - low)/2 to stay safe.
Does the algorithm require extra memory?
No, the search maintains only low, high, and mid variables, giving O(1) space complexity.
How does GhostInterview assist with this binary search pattern?
It guides you through adjusting search bounds interactively, ensuring correct application of the binary search pattern and avoiding common off-by-one errors.
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