#2149

Medium

auto_awesomeTwo-pointer scanning with invariant tracking

LeetCode Problem Workspace

Rearrange Array Elements by Sign

Rearrange an array by alternating positive and negative integers using a two-pointer approach with invariant tracking.

Problem Statement

Given a 0-indexed integer array nums of even length with an equal number of positive and negative integers, you need to rearrange the elements such that the array alternates between positive and negative values.

The output should be the modified array where positive and negative integers are alternately arranged. The solution should focus on rearranging the elements with minimal complexity, ensuring the correctness and efficiency of the approach.

Examples

Example 1

Input: nums = [3,1,-2,-5,2,-4]

Output: [3,-2,1,-5,2,-4]

The positive integers in nums are [3,1,2]. The negative integers are [-2,-5,-4]. The only possible way to rearrange them such that they satisfy all conditions is [3,-2,1,-5,2,-4]. Other ways such as [1,-2,2,-5,3,-4], [3,1,2,-2,-5,-4], [-2,3,-5,1,-4,2] are incorrect because they do not satisfy one or more conditions.

Example 2

Input: nums = [-1,1]

Output: [1,-1]

1 is the only positive integer and -1 the only negative integer in nums. So nums is rearranged to [1,-1].

Constraints

2 <= nums.length <= 2 * 105
nums.length is even
1 <= |nums[i]| <= 105
nums consists of equal number of positive and negative integers.

Solution Approach

Two-Pointer Scanning

Use two pointers to separately track the positive and negative integers in the array. One pointer should traverse the positive integers, while the other moves through the negative integers. This allows the array to be rearranged in an alternating positive-negative pattern efficiently.

Invariant Tracking

Ensure that the positive and negative integers are placed in the correct order by maintaining an invariant that the position of positive integers remains fixed as we traverse the array. Similarly, the negative integers should maintain their respective positions to achieve the alternating pattern.

Efficient Rearrangement

After identifying the positions of the positive and negative integers, swap them in place, ensuring the rearranged array follows the required alternating sign pattern. This step can be performed in linear time with minimal additional space usage.

Complexity Analysis

Metric	Value
Time	O(n)
Space	O(n)

The time complexity of this solution is O(n), as we only need to pass through the array once using two pointers. The space complexity is O(n) due to the use of additional space for tracking the positions of positive and negative integers, though in-place swaps are possible to minimize space usage in some implementations.

What Interviewers Usually Probe

Does the candidate demonstrate an understanding of two-pointer techniques for separating positive and negative integers?
Can the candidate describe how they would handle large input sizes efficiently?
Does the candidate focus on maintaining the alternating pattern while ensuring minimal computational overhead?

Common Pitfalls or Variants

Common pitfalls

Mixing up the order of positive and negative integers when swapping or rearranging them.
Failing to consider edge cases, such as arrays with only two elements.
Not maintaining the required alternating sign pattern after rearrangement.

Follow-up variants

Handling arrays with additional constraints, such as arrays of larger sizes.
Modifying the solution to handle other conditions, such as multiple positive-negative swaps.
Optimizing for space complexity, using in-place swapping or tracking positions more efficiently.

FAQ

What is the key approach for solving the 'Rearrange Array Elements by Sign' problem?

The problem can be efficiently solved using a two-pointer technique where one pointer tracks positive integers and the other tracks negative integers. These pointers can then be used to rearrange the elements in the correct alternating order.

How do I handle edge cases like arrays with only two elements?

For small arrays, such as those with just two elements, the solution should simply swap the elements if necessary, as they are already small enough to handle directly.

What is the time complexity of the solution?

The time complexity is O(n), where n is the length of the array, as the array is traversed once during the rearrangement process.

How does GhostInterview help with the 'Rearrange Array Elements by Sign' problem?

GhostInterview guides you through the solution by reinforcing two-pointer scanning techniques and helping you practice the logic necessary to maintain the alternating pattern efficiently.

Can I optimize the space complexity of this problem?

Yes, the space complexity can be optimized to O(1) by performing in-place swaps to rearrange the elements instead of using additional space for tracking the positions of positive and negative integers.

terminal

Solution

Solution 1: Two Pointers

First, we create an array $\textit{ans}$ of length $n$. Then, we use two pointers $i$ and $j$ to point to the even and odd indices of $\textit{ans}$, respectively, with initial values $i = 0$, $j = 1$.

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class Solution:
    def rearrangeArray(self, nums: List[int]) -> List[int]:
        ans = [0] * len(nums)
        i, j = 0, 1
        for x in nums:
            if x > 0:
                ans[i] = x
                i += 2
            else:
                ans[j] = x
                j += 2
        return ans

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