How to Solve Wiggle Sort II

Wiggle Sort II requires rearranging an array such that each element at an odd index is greater than its neighbors. The problem involves greedy choices along with invariant validation to efficiently ensure the correct order. The solution focuses on manipulating elements in a way that satisfies the 'wiggle' condition without unnecessary operations.

Problem Statement

Given an integer array nums, reorder it in such a way that nums[0] <= nums[1] >= nums[2] <= nums[3]... For example, if the input is [1,5,1,1,6,4], the reordered array should be [1,6,1,5,1,4] (although [1,4,1,5,1,6] is also acceptable).

You are guaranteed that a valid answer exists for the given input. The task emphasizes finding an efficient solution where each element's position respects the 'wiggle' condition. Make sure to consider a greedy approach and invariant validation for the solution to be optimal.

Examples

Example 1

Input: nums = [1,5,1,1,6,4]

Output: [1,6,1,5,1,4]

[1,4,1,5,1,6] is also accepted.

Example 2

Input: nums = [1,3,2,2,3,1]

Output: [2,3,1,3,1,2]

Example details omitted.

Constraints

• 1 <= nums.length <= 5 * 104
• 0 <= nums[i] <= 5000
• It is guaranteed that there will be an answer for the given input nums.

Solution Approach

Greedy Choice and Invariant Validation

The solution starts by focusing on the greedy choice to place the largest elements in odd indices, ensuring that every odd-indexed element is greater than its adjacent even-indexed elements. Then, after sorting the array, the elements are placed carefully to satisfy the 'wiggle' condition.

Array Sorting and Element Placement

By first sorting the array, we can easily select elements to position correctly at odd and even indices. Sorting helps simplify the arrangement process by ensuring that the largest elements are placed at the odd indices first, fulfilling the 'wiggle' condition with minimal swaps.

Efficient Invariant Check

After the array is rearranged, an invariant check is performed to ensure that each element at an odd index is greater than its neighbors. This check validates whether the 'wiggle' condition holds true across the entire array.

Complexity Analysis

The time complexity of this solution depends on the approach used to sort the array. If using Quickselect or a similar sorting technique, the time complexity is O(n log n), while the space complexity varies based on the specific approach but generally remains O(n) for storing temporary results or auxiliary data.

What Interviewers Usually Probe

• Assess how the candidate applies the greedy approach to solve the problem efficiently.
• Evaluate the candidate's ability to manage array manipulations and element positioning for this pattern.
• Check for understanding of the 'wiggle' condition and whether the candidate can optimize the process using sorting or selective placement.

Common Pitfalls or Variants

Common pitfalls

• Overcomplicating the solution by trying to compare every adjacent pair rather than focusing on the greedy choice and invariant validation.
• Failing to correctly handle the array sorting step, which is essential for ensuring the correct wiggle order.
• Not performing a final check after rearranging the array to ensure that the wiggle condition holds for all elements.

Follow-up variants

• Apply the same approach to larger datasets or arrays with different constraints for performance evaluation.
• Implement a solution with an alternative sorting method or use partition-based techniques like Quickselect.
• Test the approach by adding additional constraints, such as ensuring specific values in the array are placed at certain indices.

How GhostInterview Helps

• GhostInterview provides step-by-step guidance on understanding the greedy approach and how to validate the wiggle condition effectively.
• The solver will help visualize the placement of elements in the array and ensure that the candidate applies the correct sorting strategy.
• GhostInterview highlights common mistakes like improper element placement and missing validation checks, ensuring that your solution is both efficient and correct.

Topic Pages

• Array
• Divide and Conquer
• Greedy
• Sorting
• Quickselect

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FAQ

What is the key pattern in the Wiggle Sort II problem?

The key pattern is greedy choice plus invariant validation, where you place the largest elements in odd indices and validate the arrangement.

How does sorting help in solving this problem?

Sorting the array first ensures that the largest elements can be placed in odd indices, helping to satisfy the wiggle condition with minimal manipulation.

Is the wiggle condition required for all elements in the array?

Yes, the wiggle condition must hold true for every adjacent pair of elements, meaning each odd-indexed element must be greater than its neighbors.

How do I avoid common mistakes in this problem?

Ensure that the array is sorted correctly and that you check the final arrangement to verify that the wiggle condition is satisfied for every element.

What are some variations of the Wiggle Sort II problem?

Variations include applying the approach to arrays with additional constraints or exploring performance with larger datasets using alternative sorting methods.