Understanding the Problem
We are given an array of integers containing both positive and negative numbers. Our task is to rearrange this array so that the signs alternate: starting with a positive number, then a negative number, then a positive again, and so on.
There are a few key constraints to keep in mind:
- The rearrangement must happen in-place (without using extra arrays).
- The relative order of elements is not important.
- If one type (positive or negative) runs out before the other, the rest can remain at the end.
Approach: Step-by-Step Strategy
Step 1: Think in Terms of Index Positions
We’ll solve this using a two-pointer technique:
posIndex
will point to even indices (0, 2, 4, ...) where positive numbers should go.
negIndex
will point to odd indices (1, 3, 5, ...) where negative numbers should go.
We iterate through the array, and whenever we find a number at the wrong position based on its sign, we swap it with the correct index. After placing a number, we move the respective index forward by 2.
Step 2: Use an Example to Understand
Let’s take an example array:
[3, -2, 1, -7, -5, 6]
We want to rearrange this to something like:
[3, -2, 1, -7, 6, -5]
Notice how the signs alternate: positive, negative, positive, negative...
Step 3: Rearranging the Array
We go through the array, check each number’s sign, and place it at the correct posIndex
or negIndex
if needed. Swapping is allowed and we keep moving the pointers forward by 2.
Edge Cases and How We Handle Them
Case 1: Normal Case (Balanced Positives and Negatives)
This is the ideal case where we have an almost equal number of positive and negative numbers. Our strategy will produce a clean alternation of signs.
Case 2: Unequal Count
If we have more positives than negatives (or vice versa), then once we run out of the smaller group, the extra elements from the larger group are left at the end. This is acceptable based on the problem statement.
Case 3: All Positive or All Negative
There’s no way to alternate if we have all numbers of the same sign. So, we simply return the array as-is without making any changes.
Case 4: Empty Array
No elements to rearrange. We return an empty array.
Case 5: Single Element
With only one number (positive or negative), there’s nothing to alternate with. So, we return the array unchanged.
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