平方有序数组：从线性顺序到平方世界

2023-12-08 20:35:46

在计算机科学中，算法是用于解决特定问题的步骤集合。算法的效率通常用时间复杂度和空间复杂度来衡量。时间复杂度是指算法执行所花费的时间，而空间复杂度是指算法执行所需要的内存空间。

在本篇文章中，我们将介绍两种算法来解决有序数组的平方问题：暴力法和双指针法。暴力法是一种简单而直接的算法，它通过遍历数组中的每个元素并计算其平方来生成新的数组。这种方法的时间复杂度是O(n^2)，其中n是数组的长度。双指针法是一种更有效率的算法，它通过使用两个指针来遍历数组，一个指针指向数组的开头，另一个指针指向数组的结尾。这两个指针同时向中间移动，并比较当前元素的平方。时间复杂度为O(n)。

暴力法

def square_array_brute_force(nums):
  """
  Squares the elements of a sorted array in ascending order.

  Args:
    nums: A list of integers sorted in ascending order.

  Returns:
    A list of integers containing the squares of the elements of nums,
    also sorted in ascending order.
  """

  # Initialize the result array.
  result = []

  # Iterate over the input array.
  for num in nums:
    # Square the current number.
    squared_num = num ** 2

    # Append the squared number to the result array.
    result.append(squared_num)

  # Sort the result array.
  result.sort()

  # Return the result array.
  return result

双指针法

def square_array_two_pointers(nums):
  """
  Squares the elements of a sorted array in ascending order.

  Args:
    nums: A list of integers sorted in ascending order.

  Returns:
    A list of integers containing the squares of the elements of nums,
    also sorted in ascending order.
  """

  # Initialize the result array.
  result = []

  # Initialize the two pointers.
  left = 0
  right = len(nums) - 1

  # While the left pointer is less than or equal to the right pointer.
  while left <= right:
    # Get the squared values of the current elements.
    left_squared = nums[left] ** 2
    right_squared = nums[right] ** 2

    # Compare the squared values.
    if left_squared < right_squared:
      # Append the squared value of the left element to the result array.
      result.append(left_squared)

      # Move the left pointer to the right.
      left += 1
    else:
      # Append the squared value of the right element to the result array.
      result.append(right_squared)

      # Move the right pointer to the left.
      right -= 1

  # Return the result array.
  return result