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Problem solution · Python

Absolute Difference Between Maximum and Minimum K Elements

Absolute Difference Between Maximum and Minimum K Elements: a Python solution using sliding window or two pointers. Learn the idea, check the complexity, and read the full code, with credit to Kamyu LeetCode Solutions.

Technique
Sliding window or two pointers
Source
Kamyu LeetCode Solutions
Length
60 lines
Start with the idea.

Try the problem first. If you get stuck, read the approach below, then write your own solution. The full code is at the bottom.

Approach

Sliding window or two pointers

For Absolute Difference Between Maximum and Minimum K Elements, the implementation maintains a moving interval and updates only the information that enters or leaves the window.

  1. Choose the invariant that makes a window valid or useful.
  2. Advance the right boundary and add the new element.
  3. Move the left boundary only as needed while maintaining the invariant and updating the answer.

Code notes

  • 60 lines of Python from the credited upstream file absolute-difference-between-maximum-and-minimum-k-elements.py.
  • The implementation visibly relies on sequence storage.
  • No explicit loop blocks detected.

Complexity

Confirm that neither pointer moves backwards; if so, the scan is usually linear apart from the window’s data-structure operations.

Check the problem constraints before deciding whether this complexity will pass.

Source

Code and credit

This code comes from Kamyu LeetCode Solutions by kamyu104 and is used under the MIT licence.

Open problem ↗Original source ↗
Full codeAbsolute Difference Between Maximum and Minimum K Elements · PythonPython
Use this to learn the idea, then write your own version.
# Time:  O(n)# Space: O(1) import random  # quick selectclass Solution(object):    def absDifference(self, nums, k):        """        :type nums: List[int]        :type k: int        :rtype: int        """        def nth_element(nums, n, left=0, compare=lambda a, b: a < b):            def tri_partition(nums, left, right, target, compare):                mid = left                while mid <= right:                    if nums[mid] == target:                        mid += 1                    elif compare(nums[mid], target):                        nums[left], nums[mid] = nums[mid], nums[left]                        left += 1                        mid += 1                    else:                        nums[mid], nums[right] = nums[right], nums[mid]                        right -= 1                return left, right                        right = len(nums)-1            while left <= right:                pivot_idx = random.randint(left, right)                pivot_left, pivot_right = tri_partition(nums, left, right, nums[pivot_idx], compare)                if pivot_left <= n <= pivot_right:                    return                elif pivot_left > n:                    right = pivot_left-1                else:  # pivot_right < n.                    left = pivot_right+1         nth_element(nums, k-1)        total1 = sum(nums[i] for i in xrange(k))        nth_element(nums, k-1, compare=lambda a, b: a > b)        total2 = sum(nums[i] for i in xrange(k))        return abs(total1-total2)  # Time:  O(nlogn)# Space: O(1)# sortclass Solution2(object):    def absDifference(self, nums, k):        """        :type nums: List[int]        :type k: int        :rtype: int        """        nums.sort()        return abs(sum(nums[i] for i in xrange(k))-sum(nums[~i] for i in xrange(k)))

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