To solve the Shortest Unsorted Continuous Subarray problem, focus on identifying the boundaries where the array stops being sorted. Use two-pointer scanning to track these boundaries. After determining the subarray, check its length and return it to get the result.
Problem Statement
Given an integer array nums, you need to find the shortest continuous subarray such that if you sort only that subarray in non-decreasing order, the entire array will become sorted in non-decreasing order.
Return the length of the shortest subarray that needs to be sorted. If the entire array is already sorted, return 0.
Examples
Example 1
Input: nums = [2,6,4,8,10,9,15]
Output: 5
You need to sort [6, 4, 8, 10, 9] in ascending order to make the whole array sorted in ascending order.
Example 2
Input: nums = [1,2,3,4]
Output: 0
Example details omitted.
Example 3
Input: nums = [1]
Output: 0
Example details omitted.
Constraints
- 1 <= nums.length <= 104
- -105 <= nums[i] <= 105
Solution Approach
Two-pointer Scanning
Start with two pointers, one from the left and one from the right, and scan the array to find where the unsorted portion starts and ends. This helps identify the boundaries of the subarray that requires sorting.
Invariant Tracking
As you scan the array, track the invariant that should hold for a sorted array. The subarray to be sorted can be found where this invariant breaks, and by adjusting the pointers accordingly, you can define the bounds of the required subarray.
Return Subarray Length
Once the boundaries of the subarray are identified, calculate the length of this subarray and return the result. This length represents the smallest subarray that needs to be sorted to achieve a fully sorted array.
Complexity Analysis
| Metric | Value |
|---|---|
| Time | Depends on the final approach |
| Space | Depends on the final approach |
The time complexity depends on the final implementation but is typically O(n) where n is the length of the array. Space complexity can vary, but an optimal solution uses O(1) space with two-pointer scanning.
What Interviewers Usually Probe
- The candidate should efficiently identify the boundaries of the unsorted subarray using a two-pointer technique.
- The interviewee should demonstrate how they maintain the invariant during the scanning process.
- Look for a clear and optimal solution where the candidate explains the reasoning behind their approach.
Common Pitfalls or Variants
Common pitfalls
- Not updating the pointers correctly when scanning for the unsorted boundaries.
- Overlooking edge cases, like an already sorted array or a very short array.
- Confusing the invariant, leading to unnecessary subarray checks or inefficiencies.
Follow-up variants
- Modify the problem to handle arrays that may contain duplicate elements.
- Extend the problem by asking to sort the identified subarray and return the fully sorted array.
- Introduce constraints on time complexity, such as requiring a solution that operates in O(n log n) or better.
How GhostInterview Helps
- GhostInterview offers clear guidance on the two-pointer approach and invariant tracking, helping the candidate efficiently find the unsorted subarray boundaries.
- By reviewing example solutions and problem-specific patterns, GhostInterview helps candidates understand common pitfalls and how to avoid them.
- The solver also assists in explaining edge cases and testing strategies, ensuring interview-ready solutions.
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
How do I approach the Shortest Unsorted Continuous Subarray problem?
You can solve it efficiently using two-pointer scanning and invariant tracking to identify the smallest subarray that needs sorting.
What is the time complexity of the optimal solution?
The optimal solution typically has a time complexity of O(n), where n is the length of the array.
What if the array is already sorted?
In that case, the length of the subarray to be sorted is 0, as no sorting is needed.
How do I handle edge cases in this problem?
Edge cases, like arrays with one element or already sorted arrays, should be handled by checking for the absence of unsorted segments.
What is invariant tracking, and how does it help solve the problem?
Invariant tracking involves ensuring that the array maintains a sorted order. By tracking where this invariant breaks, you can pinpoint the boundaries of the subarray to sort.
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