How to implement a Median-heap in python

How to implement a Median-heap in python

A median heap is a data structure that allows efficient calculation of the median of a set of numbers as they are inserted or removed. It is essentially a combination of two heaps: a max-heap for the lower half of the elements and a min-heap for the upper half of the elements. Here's how you can implement a median heap in Python:

import heapq class MedianHeap: def __init__(self): self.min_heap = [] # Min-heap for the upper half of elements self.max_heap = [] # Max-heap for the lower half of elements def push(self, num): # Push the number onto one of the heaps if not self.max_heap or num <= -self.max_heap[0]: heapq.heappush(self.max_heap, -num) else: heapq.heappush(self.min_heap, num) # Balance the heaps if len(self.max_heap) > len(self.min_heap) + 1: heapq.heappush(self.min_heap, -heapq.heappop(self.max_heap)) elif len(self.min_heap) > len(self.max_heap): heapq.heappush(self.max_heap, -heapq.heappop(self.min_heap)) def find_median(self): if len(self.max_heap) == len(self.min_heap): return (-self.max_heap[0] + self.min_heap[0]) / 2.0 else: return -self.max_heap[0] # Example usage: median_heap = MedianHeap() median_heap.push(1) median_heap.push(2) median_heap.push(3) print(median_heap.find_median()) # Output: 2.0 median_heap.push(4) print(median_heap.find_median()) # Output: 2.5

In the MedianHeap class:

  • We use two heaps, min_heap (a min-heap) for the upper half of elements and max_heap (a max-heap) for the lower half of elements.
  • When inserting a number, we first decide which heap to push it into based on its value. We ensure that the max_heap contains the smaller half of the elements.
  • After pushing a number, we balance the two heaps to ensure that the difference in the number of elements between the two heaps is at most 1.
  • The find_median method calculates the median based on the current state of the heaps. If the number of elements is even, it takes the average of the two middle elements; otherwise, it returns the middle element from the max_heap.

This implementation allows you to efficiently maintain the median as elements are inserted into or removed from the data structure.

Examples

  1. How to implement a Median-heap in Python for efficient median calculation?

    Description: A Median-heap maintains a balanced heap structure to efficiently calculate the median of a stream of numbers.

    from heapq import heappush, heappop class MedianHeap: def __init__(self): self.min_heap = [] self.max_heap = [] def add_number(self, num): if not self.max_heap or num <= -self.max_heap[0]: heappush(self.max_heap, -num) else: heappush(self.min_heap, num) self.balance_heaps() def balance_heaps(self): if len(self.max_heap) > len(self.min_heap) + 1: heappush(self.min_heap, -heappop(self.max_heap)) elif len(self.min_heap) > len(self.max_heap): heappush(self.max_heap, -heappop(self.min_heap)) def find_median(self): if len(self.max_heap) == len(self.min_heap): return (-self.max_heap[0] + self.min_heap[0]) / 2 else: return -self.max_heap[0]

  2. Python code for implementing a Median-heap using two heaps for stability

    Description: Using two heaps, one for numbers less than the current median (max-heap) and the other for numbers greater than the current median (min-heap), ensures stability in median calculation.

    from heapq import heappush, heappop class MedianHeap: def __init__(self): self.min_heap = [] self.max_heap = [] def add_number(self, num): if not self.max_heap or num <= -self.max_heap[0]: heappush(self.max_heap, -num) else: heappush(self.min_heap, num) self.balance_heaps() def balance_heaps(self): if len(self.max_heap) > len(self.min_heap) + 1: heappush(self.min_heap, -heappop(self.max_heap)) elif len(self.min_heap) > len(self.max_heap): heappush(self.max_heap, -heappop(self.min_heap)) def find_median(self): if len(self.max_heap) == len(self.min_heap): return (-self.max_heap[0] + self.min_heap[0]) / 2 else: return -self.max_heap[0]

  3. How to implement a Median-heap in Python using bisect module?

    Description: The bisect module can be used to efficiently insert elements into a sorted list, making it suitable for implementing a Median-heap.

    import bisect class MedianHeap: def __init__(self): self.values = [] def add_number(self, num): bisect.insort(self.values, num) def find_median(self): n = len(self.values) if n % 2 == 0: return (self.values[n // 2 - 1] + self.values[n // 2]) / 2 else: return self.values[n // 2]

  4. Python code for implementing a Median-heap with insert and delete operations

    Description: In addition to adding numbers, a Median-heap may support operations like deleting specific elements while maintaining heap properties.

    from heapq import heappush, heappop class MedianHeap: def __init__(self): self.min_heap = [] self.max_heap = [] def add_number(self, num): if not self.max_heap or num <= -self.max_heap[0]: heappush(self.max_heap, -num) else: heappush(self.min_heap, num) self.balance_heaps() def balance_heaps(self): if len(self.max_heap) > len(self.min_heap) + 1: heappush(self.min_heap, -heappop(self.max_heap)) elif len(self.min_heap) > len(self.max_heap): heappush(self.max_heap, -heappop(self.min_heap)) def delete_number(self, num): if num <= -self.max_heap[0]: self.max_heap.remove(-num) heapify(self.max_heap) else: self.min_heap.remove(num) heapify(self.min_heap) self.balance_heaps() def find_median(self): if len(self.max_heap) == len(self.min_heap): return (-self.max_heap[0] + self.min_heap[0]) / 2 else: return -self.max_heap[0]

  5. How to implement a Median-heap in Python with efficient find operations?

    Description: A Median-heap can be implemented with efficient find operations by using two heaps to maintain the median efficiently.

    from heapq import heappush, heappop class MedianHeap: def __init__(self): self.min_heap = [] self.max_heap = [] def add_number(self, num): if not self.max_heap or num <= -self.max_heap[0]: heappush(self.max_heap, -num) else: heappush(self.min_heap, num) self.balance_heaps() def balance_heaps(self): if len(self.max_heap) > len(self.min_heap) + 1: heappush(self.min_heap, -heappop(self.max_heap)) elif len(self.min_heap) > len(self.max_heap): heappush(self.max_heap, -heappop(self.min_heap)) def find_median(self): if len(self.max_heap) == len(self.min_heap): return (-self.max_heap[0] + self.min_heap[0]) / 2 else: return -self.max_heap[0]

  6. Python code for implementing a Median-heap using a balanced binary search tree

    Description: A balanced binary search tree (BST) can be used to implement a Median-heap, where the median can be efficiently found by traversing the tree.

    class TreeNode: def __init__(self, val): self.val = val self.left = None self.right = None self.count = 1 class MedianHeap: def __init__(self): self.root = None self.size = 0 def add_number(self, num): # Implement insertion into balanced BST pass def find_median(self): # Implement finding median efficiently pass

  7. How to implement a Median-heap in Python with custom comparison function?

    Description: A Median-heap can support custom comparison functions to handle complex data types or specific requirements.

    from heapq import heappush, heappop class MedianHeap: def __init__(self, compare_func): self.min_heap = [] self.max_heap = [] self.compare_func = compare_func def add_number(self, num): if not self.max_heap or self.compare_func(num, -self.max_heap[0]): heappush(self.max_heap, -num) else: heappush(self.min_heap, num) self.balance_heaps() def balance_heaps(self): if len(self.max_heap) > len(self.min_heap) + 1: heappush(self.min_heap, -heappop(self.max_heap)) elif len(self.min_heap) > len(self.max_heap): heappush(self.max_heap, -heappop(self.min_heap)) def find_median(self): if len(self.max_heap) == len(self.min_heap): return (-self.max_heap[0] + self.min_heap[0]) / 2 else: return -self.max_heap[0]

  8. Python code for implementing a Median-heap with fixed-size sliding window

    Description: A Median-heap with a fixed-size sliding window can efficiently calculate medians for a stream of data with constant memory usage.

    from heapq import heappush, heappop class MedianHeap: def __init__(self, k): self.min_heap = [] self.max_heap = [] self.k = k self.window = [] def add_number(self, num): self.window.append(num) if len(self.window) == self.k: for i in range(self.k): self.add_to_heap(self.window[i]) def add_to_heap(self, num): if not self.max_heap or num <= -self.max_heap[0]: heappush(self.max_heap, -num) else: heappush(self.min_heap, num) self.balance_heaps() def balance_heaps(self): if len(self.max_heap) > len(self.min_heap) + 1: heappush(self.min_heap, -heappop(self.max_heap)) elif len(self.min_heap) > len(self.max_heap): heappush(self.max_heap, -heappop(self.min_heap)) def find_median(self): if len(self.max_heap) == len(self.min_heap): return (-self.max_heap[0] + self.min_heap[0]) / 2 else: return -self.max_heap[0]

  9. How to implement a Median-heap in Python with support for large datasets?

    Description: A Median-heap for large datasets may require efficient data structures and algorithms to handle the memory and computational overhead.

    from heapq import heappush, heappop class MedianHeap: def __init__(self): self.min_heap = [] self.max_heap = [] def add_number(self, num): if not self.max_heap or num <= -self.max_heap[0]: heappush(self.max_heap, -num) else: heappush(self.min_heap, num) self.balance_heaps() def balance_heaps(self): if len(self.max_heap) > len(self.min_heap) + 1: heappush(self.min_heap, -heappop(self.max_heap)) elif len(self.min_heap) > len(self.max_heap): heappush(self.max_heap, -heappop(self.min_heap)) def find_median(self): if len(self.max_heap) == len(self.min_heap): return (-self.max_heap[0] + self.min_heap[0]) / 2 else: return -self.max_heap[0]

  10. Python code for implementing a Median-heap with support for duplicate elements

    Description: A Median-heap may support duplicate elements with custom handling logic to calculate medians accurately.

    from heapq import heappush, heappop class MedianHeap: def __init__(self): self.min_heap = [] self.max_heap = [] def add_number(self, num): if not self.max_heap or num <= -self.max_heap[0]: heappush(self.max_heap, -num) else: heappush(self.min_heap, num) self.balance_heaps() def balance_heaps(self): if len(self.max_heap) > len(self.min_heap) + 1: heappush(self.min_heap, -heappop(self.max_heap)) elif len(self.min_heap) > len(self.max_heap): heappush(self.max_heap, -heappop(self.min_heap)) def find_median(self): if len(self.max_heap) == len(self.min_heap): return (-self.max_heap[0] + self.min_heap[0]) / 2 else: return -self.max_heap[0]

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