LeetCode #2149 — MEDIUM

Rearrange Array Elements by Sign

Move from brute-force thinking to an efficient approach using array strategy.

Solve on LeetCode
The Problem

Problem Statement

You are given a 0-indexed integer array nums of even length consisting of an equal number of positive and negative integers.

You should return the array of nums such that the array follows the given conditions:

  1. Every consecutive pair of integers have opposite signs.
  2. For all integers with the same sign, the order in which they were present in nums is preserved.
  3. The rearranged array begins with a positive integer.

Return the modified array after rearranging the elements to satisfy the aforementioned conditions.

Example 1:

Input: nums = [3,1,-2,-5,2,-4]
Output: [3,-2,1,-5,2,-4]
Explanation:
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]
Explanation:
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.
It is not required to do the modifications in-place.
Patterns Used

Roadmap

  1. Brute Force Baseline
  2. Core Insight
  3. Algorithm Walkthrough
  4. Edge Cases
  5. Full Annotated Code
  6. Interactive Study Demo
  7. Complexity Analysis
Step 01

Brute Force Baseline

Problem summary: You are given a 0-indexed integer array nums of even length consisting of an equal number of positive and negative integers. You should return the array of nums such that the array follows the given conditions: Every consecutive pair of integers have opposite signs. For all integers with the same sign, the order in which they were present in nums is preserved. The rearranged array begins with a positive integer. Return the modified array after rearranging the elements to satisfy the aforementioned conditions.

Baseline thinking

Start with the most direct exhaustive search. That gives a correctness anchor before optimizing.

Pattern signal: Array · Two Pointers

Example 1

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

Example 2

[-1,1]

Related Problems

  • Wiggle Subsequence (wiggle-subsequence)
  • Sort Array By Parity II (sort-array-by-parity-ii)
  • Partition Array According to Given Pivot (partition-array-according-to-given-pivot)
  • Largest Number After Digit Swaps by Parity (largest-number-after-digit-swaps-by-parity)
Step 02

Core Insight

What unlocks the optimal approach

  • Divide the array into two parts- one comprising of only positive integers and the other of negative integers.
  • Merge the two parts to get the resultant array.
Interview move: turn each hint into an invariant you can check after every iteration/recursion step.
Step 03

Algorithm Walkthrough

Iteration Checklist

  1. Define state (indices, window, stack, map, DP cell, or recursion frame).
  2. Apply one transition step and update the invariant.
  3. Record answer candidate when condition is met.
  4. Continue until all input is consumed.
Use the first example testcase as your mental trace to verify each transition.
Step 04

Edge Cases

Minimum Input
Single element / shortest valid input
Validate boundary behavior before entering the main loop or recursion.
Duplicates & Repeats
Repeated values / repeated states
Decide whether duplicates should be merged, skipped, or counted explicitly.
Extreme Constraints
Upper-end input sizes
Re-check complexity target against constraints to avoid time-limit issues.
Invalid / Corner Shape
Empty collections, zeros, or disconnected structures
Handle special-case structure before the core algorithm path.
Step 05

Full Annotated Code

Source-backed implementations are provided below for direct study and interview prep.

// Accepted solution for LeetCode #2149: Rearrange Array Elements by Sign
class Solution {
    public int[] rearrangeArray(int[] nums) {
        int[] ans = new int[nums.length];
        int i = 0, j = 1;
        for (int x : nums) {
            if (x > 0) {
                ans[i] = x;
                i += 2;
            } else {
                ans[j] = x;
                j += 2;
            }
        }
        return ans;
    }
}
Step 06

Interactive Study Demo

Use this to step through a reusable interview workflow for this problem.

Press Step or Run All to begin.
Step 07

Complexity Analysis

Time
O(n)
Space
O(n)

Approach Breakdown

BRUTE FORCE
O(n²) time
O(1) space

Two nested loops check every pair of elements. The outer loop picks one element, the inner loop scans the rest. For n elements that is n × (n−1)/2 comparisons = O(n²). No extra memory — just two loop variables.

TWO POINTERS
O(n) time
O(1) space

Each pointer traverses the array at most once. With two pointers moving inward (or both moving right), the total number of steps is bounded by n. Each comparison is O(1), giving O(n) overall. No auxiliary data structures are needed — just two index variables.

Shortcut: Two converging pointers on sorted data → O(n) time, O(1) space.
Coach Notes

Common Mistakes

Review these before coding to avoid predictable interview regressions.

Off-by-one on range boundaries

Wrong move: Loop endpoints miss first/last candidate.

Usually fails on: Fails on minimal arrays and exact-boundary answers.

Fix: Re-derive loops from inclusive/exclusive ranges before coding.

Moving both pointers on every comparison

Wrong move: Advancing both pointers shrinks the search space too aggressively and skips candidates.

Usually fails on: A valid pair can be skipped when only one side should move.

Fix: Move exactly one pointer per decision branch based on invariant.