To solve this problem, first sort the array and enforce that each element is at most one greater than the previous, applying a greedy choice. By iterating through the sorted array and adjusting values to maintain the invariant, we ensure the maximum element is minimized correctly. This guarantees the largest value after allowed operations is the smallest achievable.
Problem Statement
Given an array of positive integers, you may perform operations to decrease elements or rearrange them so that the array satisfies specific adjacency constraints. Each element can be reduced any number of times, and the goal is to adjust the array to meet the rules while keeping all values positive.
You must return the maximum element possible in the array after performing these operations optimally. The challenge is to determine how to rearrange and decrease values using a greedy approach to maintain the invariant that each element is at most one greater than its predecessor.
Examples
Example 1
Input: arr = [2,2,1,2,1]
Output: 2
We can satisfy the conditions by rearranging arr so it becomes [1,2,2,2,1]. The largest element in arr is 2.
Example 2
Input: arr = [100,1,1000]
Output: 3
One possible way to satisfy the conditions is by doing the following:
- Rearrange arr so it becomes [1,100,1000].
- Decrease the value of the second element to 2.
- Decrease the value of the third element to 3. Now arr = [1,2,3], which satisfies the conditions. The largest element in arr is 3.
Example 3
Input: arr = [1,2,3,4,5]
Output: 5
The array already satisfies the conditions, and the largest element is 5.
Constraints
- 1 <= arr.length <= 105
- 1 <= arr[i] <= 109
Solution Approach
Sort and Initialize
Start by sorting the array to simplify the greedy adjustments. Initialize the first element as 1 since the smallest value must remain positive.
Iterate with Greedy Adjustment
Traverse the sorted array, setting each element to the minimum of its current value or the previous element plus one. This preserves the invariant while minimizing the maximum element.
Return Maximum Value
After processing all elements, the last element in the adjusted array represents the largest possible value. Return this value as the result.
Complexity Analysis
| Metric | Value |
|---|---|
| Time | O(n) |
| Space | O(n) |
Sorting takes O(n log n) but can be simplified to O(n) with counting sort if values are bounded. Iterating and adjusting is O(n). The space complexity is O(n) if a separate array is used for adjustment, or O(1) in-place.
What Interviewers Usually Probe
- Look for sorting the array before applying operations.
- Check if each element can be at most one greater than its previous.
- Validate the maximum value after greedy adjustments.
Common Pitfalls or Variants
Common pitfalls
- Forgetting to sort before applying greedy decreases.
- Not enforcing the invariant that arr[i] <= arr[i-1] + 1.
- Returning the initial max instead of the adjusted maximum element.
Follow-up variants
- Find maximum after only decreasing elements without rearranging.
- Return the array configuration instead of just the maximum element.
- Apply the same approach for arrays with negative numbers allowed.
How GhostInterview Helps
- GhostInterview provides step-by-step reasoning to apply the greedy invariant pattern correctly.
- It simulates element adjustments to quickly find the maximum after rearrangements.
- The solver highlights failure modes if the invariant is violated and guides proper sorting.
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 pattern used in Maximum Element After Decreasing and Rearranging?
The key pattern is greedy choice plus invariant validation, ensuring each element is at most one greater than its predecessor after sorting.
Can we avoid sorting the array?
Sorting is necessary to enforce the greedy invariant efficiently; without sorting, determining the correct maximum becomes complex.
What is the time complexity of the optimal solution?
The solution runs in O(n) for the adjustment step and O(n log n) if standard sorting is used, with O(n) space for storing adjusted values.
Does rearranging affect the final maximum value?
Yes, rearranging allows the elements to be positioned optimally so that the invariant holds and the maximum element is minimized.
What are common mistakes in this problem?
Common mistakes include not sorting, failing to enforce the invariant, and returning the original maximum instead of the adjusted maximum value.
Need direct help with Maximum Element After Decreasing and Rearranging instead of spending more time grinding it?
Download GhostInterview when you want a LeetCode solver, not another long practice loop. Capture Maximum Element After Decreasing and Rearranging 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
Maximize the frequency of an element in an array by incrementing at most `k` elements. Use binary search and greedy techniques to find the solution.
Open problem page#1833 Maximum Ice Cream BarsMaximize the number of ice cream bars a boy can buy by applying a greedy choice strategy based on cost sorting.
Open problem page#1877 Minimize Maximum Pair Sum in ArrayMinimize the maximum pair sum in an array by optimally pairing its elements.
Open problem page