Python:使用 Max-Heap 和 Min-Heap 查找运行中位数

Question

我正在尝试返回一系列流媒体数字的运行中位数。为此，我使用最大堆(将值存储在序列的下半部分)和最小堆(将值存储在序列的上半部分)。

特别是我使用 heapq 模块 ( https://docs.python.org/2/library/heapq.html ) 中的 Python (2.0) 内置最小堆数据结构。为了构建最大堆，我只需使用我需要插入堆中的数字的负数。

我的 Python 代码如下:

import heapq

maxh = []
minh = []
vals=[1,2,3,4,5,6,7,8,9,10]
for val in vals:

    # Initialize the data-structure and insert/push the 1st streaming value
    if not maxh and not minh:
        heapq.heappush(maxh,-val)
        print float(val)
    elif maxh:

        # Insert/push the other streaming values
        if val>-maxh[0]:
            heapq.heappush(minh,val)
        elif val<-maxh[0]:
            heapq.heappush(maxh,-val)

        # Calculate the median
        if len(maxh)==len(minh):
            print float(-maxh[0]+minh[0])/2
        elif len(maxh)==len(minh)+1:
            print float(-maxh[0])
        elif len(minh)==len(maxh)+1:
            print float(minh[0])

        # If min-heap and max-heap grow unbalanced we rebalance them by
        # removing/popping one element from a heap and inserting/pushing
        # it into the other heap, then we calculate the median
        elif len(minh)==len(maxh)+2:
            heapq.heappush(maxh,-heapq.heappop(minh))
            print float(-maxh[0]+minh[0])/2
        elif len(maxh)==len(minh)+2:
            heapq.heappush(minh,-heapq.heappop(maxh))
            print float(-maxh[0]+minh[0])/2

下面是我为检查我的代码而构建的测试用例的完整列表:

vals=[1,2,3,4,5,6,7,8,9,10] # positive numbers, increasing series
vals=[10,9,8,7,6,5,4,3,2,1] # positive numbers, decreasing series
vals=[10,9,11,8,12,7,13,6,14,5] # positive numbers, jumping series (keeping
                                # heaps balanced)

vals=[-10,-9,-8,-7,-6,-5,-4,-3,-2,-1] # negative numbers, increasing series
vals=[-1,-2,-3,-4,-5,-6,-7,-8,-9,-10] # negative numbers, decreasing series
vals=[-10,-9,-11,-8,-12,-7,-13,-6,-14,-5] # negative numbers
                                          # jumping series (keeping heaps
                                          # balanced)

vals=[-5,-4,-3,-2,-1,0,1,2,3,4,5] # mixed positive-negative numbers,
                                  # increasing series
vals=[5,4,3,2,1,0,-1,-2,-3,-4,-5] # mixed positive-negative numbers,
                                  # decreasing series
vals=[0,-1,1,-2,2,-3,3,-4,4,-5,5] # mixed positive-negative numbers,
                                  # jumping series (keeping heaps balanced)

我的代码对我来说似乎没问题，但我无法通过在线评判 (https://www.hackerrank.com/challenges/ctci-find-the-running-median/problem) 的 10 个测试用例中的 4 个。

你有什么提示吗？

Answer 1

问题出在这里:

    # Insert/push the other streaming values
    if val>-maxh[0]:
        heapq.heappush(minh,val)
    elif val<-maxh[0]:
        heapq.heappush(maxh,-val)

如果 val == maxh[0]，则该项目永远不会被插入任一堆。您应该能够通过测试用例 [1,1,2] 揭示错误。

一个简单的修复方法是:

    # Insert/push the other streaming values
    if val >= -maxh[0]:
        heapq.heappush(minh,val)
    else
        heapq.heappush(maxh,-val)