The problem asks to generate the next lexicographically greater permutation of an array. By identifying the largest decreasing suffix, the next permutation is found by swapping an element with the smallest element larger than it. This process follows two-pointer scanning and invariant tracking principles, ensuring an optimal solution in linear time.
Problem Statement
Given an array of integers, find its next permutation in lexicographical order. If the current permutation is the largest possible, return the smallest permutation. A permutation is an arrangement of numbers in a sequence, and the next permutation is the one that comes after it in sorted order. If no larger permutation exists, return the array sorted in ascending order.
To solve this, we need to identify the largest suffix that is in decreasing order. Once identified, we swap the rightmost element of this suffix with the smallest element from the suffix that is larger than it, and then reverse the suffix. This approach guarantees that the next permutation is generated with minimal changes.
Examples
Example 1
Input: nums = [1,2,3]
Output: [1,3,2]
Example details omitted.
Example 2
Input: nums = [3,2,1]
Output: [1,2,3]
Example details omitted.
Example 3
Input: nums = [1,1,5]
Output: [1,5,1]
Example details omitted.
Constraints
- 1 <= nums.length <= 100
- 0 <= nums[i] <= 100
Solution Approach
Identifying the Decreasing Suffix
Scan the array from right to left to find the largest suffix that is in decreasing order. This identifies the point where the permutation stops being in increasing order.
Finding the Swap Candidate
Find the smallest number in the suffix that is greater than the element before the decreasing suffix. This will be the element to swap to get the next greater permutation.
Reversing the Suffix
Once the swap is done, reverse the suffix to ensure the next permutation is the smallest possible arrangement after the swap.
Complexity Analysis
| Metric | Value |
|---|---|
| Time | O(n) |
| Space | O(1) |
The solution runs in O(n) time because we scan the array once to identify the suffix, perform a swap, and reverse the suffix. The space complexity is O(1) as no additional space is required beyond the input array.
What Interviewers Usually Probe
- Checks for efficient in-place manipulation of the array.
- Assesses understanding of permutations and their properties.
- Tests ability to apply two-pointer techniques and invariant tracking in array problems.
Common Pitfalls or Variants
Common pitfalls
- Forgetting to reverse the suffix after swapping.
- Not correctly identifying the largest decreasing suffix.
- Misunderstanding the termination condition when no next permutation is possible.
Follow-up variants
- Generate the previous permutation instead of the next.
- Handle larger arrays with more elements.
- Optimize the solution for specific types of input arrays.
How GhostInterview Helps
- The GhostInterview solver guides you through the process of identifying the key operations in the next permutation algorithm.
- It provides detailed explanations of the two-pointer scanning technique and invariant tracking to ensure efficient execution.
- The solver's step-by-step guidance helps you avoid common mistakes and master the critical elements of this problem.
Topic Pages
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- LeetCode Interview Copilot - Use GhostInterview as a live solver when you want direct help with LeetCode-style coding questions.
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- 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 the Next Permutation problem?
The main pattern involves two-pointer scanning with invariant tracking to efficiently generate the next permutation.
How can I ensure that the next permutation is generated correctly?
You must identify the largest decreasing suffix, swap elements appropriately, and reverse the suffix to obtain the next permutation.
What is the time complexity of the Next Permutation algorithm?
The time complexity is O(n) because we scan the array and perform constant-time operations (swap and reverse).
Is the Next Permutation problem solvable in constant space?
Yes, the solution uses O(1) extra space, as the operations are done in-place on the input array.
What is the failure mode of the Next Permutation problem?
The failure mode occurs when the array is in descending order, and the next permutation is the smallest, requiring a complete rearrangement of the array.
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