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Problem solution · Python

Sliding Window Median

Sliding Window Median: 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
114 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 Sliding Window Median, 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

  • 114 lines of Python from the credited upstream file sliding-window-median.py.
  • The implementation visibly relies on sequence storage, hash lookup, work queue.
  • 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 codeSliding Window Median · PythonPython
Use this to learn the idea, then write your own version.
# Time:  O(nlogk)# Space: O(k) from sortedcontainers import SortedList  class Solution(object):    def medianSlidingWindow(self, nums, k):        """        :type nums: List[int]        :type k: int        :rtype: List[float]        """        sl = SortedList(float(nums[i])for i in xrange(k))        result = [(sl[k//2]+sl[k//2-(1-k%2)])/2]        for i in xrange(k, len(nums)):            sl.add(float(nums[i]))            sl.remove(nums[i-k])            result.append((sl[k//2]+sl[k//2-(1-k%2)])/2)        return result  # Time:  O(nlogk)# Space: O(k)import collectionsimport heapq  class Solution2(object):    def medianSlidingWindow(self, nums, k):        """        :type nums: List[int]        :type k: int        :rtype: List[float]        """        def lazy_delete(heap, to_remove, sign):            while heap and sign*heap[0] in to_remove:                to_remove[sign*heap[0]] -= 1                if not to_remove[sign*heap[0]]:                    del to_remove[sign*heap[0]]                heapq.heappop(heap)         def full_delete(heap, to_remove, sign):  # Time: O(k), Space: O(k)            result = []            for x in heap:                if sign*x not in to_remove:                    result.append(x)                    continue                to_remove[sign*x] -= 1                if not to_remove[sign*x]:                    del to_remove[sign*x]            heap[:] = result            heapq.heapify(heap)         min_heap, max_heap = [], []        for i in xrange(k):            if i%2 == 0:                heapq.heappush(min_heap, -heapq.heappushpop(max_heap, -nums[i]))            else:                heapq.heappush(max_heap, -heapq.heappushpop(min_heap, nums[i]))        result = [float(min_heap[0])] if k%2 else [(min_heap[0]-max_heap[0])/2.0]        to_remove = collections.defaultdict(int)        for i in xrange(k, len(nums)):            heapq.heappush(max_heap, -heapq.heappushpop(min_heap, nums[i]))            if nums[i-k] > -max_heap[0]:                heapq.heappush(min_heap, -heapq.heappop(max_heap))            to_remove[nums[i-k]] += 1            lazy_delete(max_heap, to_remove, -1)            lazy_delete(min_heap, to_remove, 1)            if len(min_heap)+len(max_heap) > 2*k:                full_delete(max_heap, to_remove, -1)                full_delete(min_heap, to_remove, 1)            result.append(float(min_heap[0]) if k%2 else (min_heap[0]-max_heap[0])/2.0)        return result  # Time:  O(nlogn) due to lazy delete# Space: O(n)import collectionsimport heapq  class Solution3(object):    def medianSlidingWindow(self, nums, k):        """        :type nums: List[int]        :type k: int        :rtype: List[float]        """        def lazy_delete(heap, to_remove, sign):            while heap and sign*heap[0] in to_remove:                to_remove[sign*heap[0]] -= 1                if not to_remove[sign*heap[0]]:                    del to_remove[sign*heap[0]]                heapq.heappop(heap)         min_heap, max_heap = [], []        for i in xrange(k):            if i%2 == 0:                heapq.heappush(min_heap, -heapq.heappushpop(max_heap, -nums[i]))            else:                heapq.heappush(max_heap, -heapq.heappushpop(min_heap, nums[i]))        result = [float(min_heap[0])] if k%2 else [(min_heap[0]-max_heap[0])/2.0]        to_remove = collections.defaultdict(int)        for i in xrange(k, len(nums)):            heapq.heappush(max_heap, -heapq.heappushpop(min_heap, nums[i]))            if nums[i-k] > -max_heap[0]:                heapq.heappush(min_heap, -heapq.heappop(max_heap))            to_remove[nums[i-k]] += 1            lazy_delete(max_heap, to_remove, -1)            lazy_delete(min_heap, to_remove, 1)            result.append(float(min_heap[0]) if k%2 else (min_heap[0]-max_heap[0])/2.0)        return result

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