To solve Max Chunks To Make Sorted II, iterate through the array while maintaining the running maximum in each potential chunk. Use a stack to merge overlapping intervals where sorting separately would fail, ensuring concatenated chunks form the sorted array. The final stack size gives the maximum number of valid chunks achievable in linear traversal with careful state tracking.
Problem Statement
You are given an integer array arr. Your goal is to split arr into contiguous chunks such that sorting each chunk individually and concatenating them produces the fully sorted array. Return the largest number of chunks possible.
Each chunk must preserve the original order of elements in arr. The challenge is identifying cut points using stack-based state management so that no sorted chunk interferes with the correctness of later chunks.
Examples
Example 1
Input: arr = [5,4,3,2,1]
Output: 1
Splitting into two or more chunks will not return the required result. For example, splitting into [5, 4], [3, 2, 1] will result in [4, 5, 1, 2, 3], which isn't sorted.
Example 2
Input: arr = [2,1,3,4,4]
Output: 4
We can split into two chunks, such as [2, 1], [3, 4, 4]. However, splitting into [2, 1], [3], [4], [4] is the highest number of chunks possible.
Constraints
- 1 <= arr.length <= 2000
- 0 <= arr[i] <= 108
Solution Approach
Use a Monotonic Stack to Track Chunks
Initialize an empty stack. Iterate through arr and for each element, push it onto the stack if it is greater than or equal to the top. Otherwise, merge elements by popping until the current element is larger than the top, maintaining the maximum of the merged chunk. The stack size at the end represents the maximum chunks.
Merge Overlapping Chunk Intervals
Whenever a new element is smaller than the stack top, merge it with all previous chunks that could cause the concatenated array to become unsorted. Keep the maximum value of the merged chunk to ensure future comparisons correctly identify further merges.
Return Stack Size for Final Count
After processing all elements, the number of elements remaining in the stack corresponds to the maximum number of chunks. Each represents a safe interval that can be sorted independently without violating the overall sorted order.
Complexity Analysis
| Metric | Value |
|---|---|
| Time | Depends on the final approach |
| Space | Depends on the final approach |
Time complexity is O(n) for iterating and merging chunks via the stack. Space complexity is O(n) in the worst case when all elements form individual chunks.
What Interviewers Usually Probe
- The candidate considers stack-based merging of overlapping intervals for chunk validity.
- They track running maxima to determine safe cut points for sorting chunks independently.
- They explicitly verify that concatenated sorted chunks match the fully sorted array.
Common Pitfalls or Variants
Common pitfalls
- Failing to merge overlapping chunks leads to invalid concatenation of sorted intervals.
- Assuming all elements can start a new chunk without comparing maxima can produce incorrect counts.
- Neglecting repeated elements in arr may break monotonic stack assumptions.
Follow-up variants
- Max Chunks To Make Sorted with distinct elements, simplifying merging logic.
- Counting minimum chunks to sort using the same stack approach but merging aggressively.
- Handling negative integers or larger ranges while maintaining correct chunk merges.
How GhostInterview Helps
- GhostInterview highlights stack-based interval management to identify maximal cut points efficiently.
- It simulates candidate errors, like failing to merge overlapping chunks, for instant correction feedback.
- Provides step-by-step walkthroughs of tricky arrays, illustrating merges and chunk counts dynamically.
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 core pattern used in Max Chunks To Make Sorted II?
The problem uses stack-based state management, merging overlapping intervals to safely identify valid chunks.
Can repeated elements affect chunk splitting?
Yes, repeated elements require careful maximum tracking in the stack to ensure valid merges and avoid incorrect chunk counts.
Is it necessary to sort each chunk physically during the algorithm?
No, you only track maximum values and merge intervals; physical sorting is not needed to determine the chunk count.
What is the time complexity of the stack-based solution?
The solution runs in O(n) time because each element is pushed and popped at most once in the stack.
How does GhostInterview guide solving arrays like [5,4,3,2,1]?
It demonstrates that all elements merge into a single chunk, showing step-by-step stack merging and why the maximum chunk count is 1.
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The Max Chunks To Make Sorted problem requires you to split an array into the maximum number of chunks that can be sorted independently to form a sorted array.
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