Squares Of a Sorted Array

Introduction

The "Squares of a Sorted Array" problem is a common question that helps us understand arrays and the two-pointer technique.

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Problem Statement

Given a sorted array of integers (which may include negative numbers), return a new array of the squares of each number, also sorted in non-decreasing order.

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Approach (Two-Pointer Technique)

Since negative numbers become positive after squaring, we use two pointers:

1. Initialize:

   • left = 0
   • right = n - 1

2. Compare squares of left and right elements

3. Place the larger square at the end of result array

4. Move the corresponding pointer

5. Repeat until all elements are processed

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Python Code

python
def sorted_squares(nums):
    n = len(nums)
    result = [0] * n

    left, right = 0, n - 1
    pos = n - 1

    while left <= right:
        if abs(nums[left]) > abs(nums[right]):
            result[pos] = nums[left] ** 2
            left += 1
        else:
            result[pos] = nums[right] ** 2
            right -= 1
        pos -= 1

    return result

# Example
nums = [-4, -1, 0, 3, 10]
print("Sorted Squares:", sorted_squares(nums))


## Input
  [-4, -1, 0, 3, 10]

## Output
   [0, 1, 9, 16, 100]