To solve Find Peak Element, apply binary search over the array to identify a peak element. The approach takes advantage of the array's structure, ensuring that the solution is both efficient and scalable. Multiple peak positions may exist, and any one can be returned as a valid answer.
Problem Statement
You are given a 0-indexed integer array nums. A peak element is an element that is strictly greater than its neighbors. If nums[-1] and nums[n] are imagined to be -∞, then an element at the edge is also considered a peak if it is larger than its one neighbor. Your task is to find any peak element and return its index.
The array can have multiple peaks. In that case, returning the index of any peak is considered correct. The input guarantees that nums[i] != nums[i + 1] for all valid i, which ensures there is at least one peak. Your solution must run efficiently with binary search over the valid answer space.
Examples
Example 1
Input: nums = [1,2,3,1]
Output: 2
3 is a peak element and your function should return the index number 2.
Example 2
Input: nums = [1,2,1,3,5,6,4]
Output: 5
Your function can return either index number 1 where the peak element is 2, or index number 5 where the peak element is 6.
Constraints
- 1 <= nums.length <= 1000
- -231 <= nums[i] <= 231 - 1
- nums[i] != nums[i + 1] for all valid i.
Solution Approach
Binary Search over the Array
Apply binary search to the array, where the mid element is compared with its neighbors. Depending on whether the element at mid is larger or smaller than its neighbors, adjust the search space to find the peak.
Edge Case Handling
Consider edge cases, especially with peak elements at the start or end of the array. These cases are handled naturally by the binary search approach as the array's virtual boundaries are treated as -∞.
Time and Space Complexity Optimization
The binary search approach ensures that the solution runs in O(log n) time, and with O(1) space complexity. This is a significant optimization compared to a brute-force approach, which would require O(n) time.
Complexity Analysis
| Metric | Value |
|---|---|
| Time | Depends on the final approach |
| Space | Depends on the final approach |
The binary search approach reduces the time complexity to O(log n) by halving the search space with each iteration. The space complexity is O(1) since the solution only requires a few variables for tracking indices.
What Interviewers Usually Probe
- Assessing the candidate's understanding of binary search and its application to specific problems.
- Looking for clarity in explaining why binary search works for this problem, especially with edge cases.
- Evaluating the candidate's ability to write efficient, optimal code without unnecessary operations.
Common Pitfalls or Variants
Common pitfalls
- Misunderstanding the concept of a peak at the edges of the array, especially when dealing with virtual boundaries (-∞).
- Forgetting to check both neighbors during the binary search, potentially missing the peak element.
- Using a brute-force approach that results in higher time complexity instead of utilizing binary search.
Follow-up variants
- Modify the problem to return all peak elements instead of just one.
- Extend the problem to find the global peak that is strictly larger than all elements in the array.
- Test variations on arrays with repeated elements and adapt the peak definition accordingly.
How GhostInterview Helps
- GhostInterview provides a systematic walkthrough for solving problems like Find Peak Element, enhancing your ability to perform under pressure.
- The platform helps you practice binary search efficiently, making you more confident when tackling similar problems during interviews.
- By analyzing multiple solution patterns, GhostInterview helps you refine your problem-solving approach and prepare for a variety of technical challenges.
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 approach for solving Find Peak Element?
The best approach is using binary search over the valid answer space, which ensures that the solution is both time-efficient and space-efficient.
How does binary search help in the Find Peak Element problem?
Binary search helps by narrowing down the search space to find a peak element in O(log n) time, compared to a brute force approach that would take O(n) time.
Can Find Peak Element have multiple correct answers?
Yes, there can be multiple peaks in the array, and the solution can return any index corresponding to a peak element.
What is the time complexity of the optimal solution for Find Peak Element?
The time complexity of the optimal binary search solution is O(log n), which is much faster than a linear scan of the array.
How does GhostInterview assist with the Find Peak Element problem?
GhostInterview helps by providing practice problems, feedback on binary search techniques, and tips on optimizing solutions for problems like Find Peak Element.
Need direct help with Find Peak Element instead of spending more time grinding it?
Download GhostInterview when you want a LeetCode solver, not another long practice loop. Capture Find Peak Element from a screenshot, get the answer path and complexity, and use supported stealth workflows that stay outside captured layers.
Capture the prompt fast instead of rewriting the problem by hand.
Get the solution path, trade-offs, and complexity summary in one pass.
Stay outside captured layers on supported screen-share workflows.
Stay in the same pattern family
Solve the Two Sum II problem efficiently using binary search over a valid answer space in a sorted array.
Open problem page#154 Find Minimum in Rotated Sorted Array IIFind the minimum in a rotated sorted array with possible duplicates using binary search.
Open problem page#153 Find Minimum in Rotated Sorted ArrayFind the minimum element in a rotated sorted array using binary search to efficiently identify the point of rotation.
Open problem page