如何对相同值的范围进行二分查找？

Question

我有一个排序的数字列表，我需要得到它 return 数字出现的索引范围。我的名单是：

daysSick = [0, 0, 0, 0, 1, 2, 3, 3, 3, 4, 5, 5, 5, 6, 6, 11, 15, 24]

如果我搜索了0，我需要return (0, 3)。现在我只能得到它来找到一个号码的位置！我知道如何进行二进制搜索，但我不知道如何让它从该位置上下移动以找到其他相同的值！

low = 0
high = len(daysSick) - 1
while low <= high :
    mid = (low + high) // 2
    if value < daysSick[mid]:
        high = mid - 1
    elif value > list[mid]:
        low = mid + 1
    else:
        return mid

Answer 1

你为什么不用python's bisection routines:

>>> daysSick = [0, 0, 0, 0, 1, 2, 3, 3, 3, 4, 5, 5, 5, 6, 6, 11, 15, 24]
>>> from bisect import bisect_left, bisect_right
>>> bisect_left(daysSick, 3)
6
>>> bisect_right(daysSick, 3)
9
>>> daysSick[6:9]
[3, 3, 3]

Answer 2

我提出的解决方案比 bisect 库

中的 raw functions taken 更快

解决方案

使用优化二进制搜索

def search(a, x):
    right = 0
    h = len(a)
    while right < h:
        m = (right+h)//2
        if x < a[m]: h = m
        else: 
            right = m+1
    # start binary search for left element only 
    # including elements from 0 to right-1 - much faster!
    left = 0
    h = right - 1
    while left < h:
        m = (left+h)//2
        if x > a[m]: left = m+1
        else: 
            h = m
    return left, right-1

search(daysSick, 5)
(10, 12)

search(daysSick, 2)
(5, 5)

对比 `Bisect`

使用自定义二分搜索...

%timeit search(daysSick, 3)
1000000 loops, best of 3: 1.23 µs per loop

正在将源代码从 bisect 复制到 python...

%timeit bisect_left(daysSick, 1), bisect_right(daysSick, 1)
1000000 loops, best of 3: 1.77 µs per loop

使用默认导入是迄今为止最快的，因为我认为它可能在幕后进行了优化...

from bisect import bisect_left, bisect_right
%timeit bisect_left(daysSick, 1), bisect_right(daysSick, 1)
1000000 loops, best of 3: 504 ns per loop

额外

没有分机。图书馆但不是二进制搜索

daysSick = [0, 0, 0, 0, 1, 2, 3, 3, 3, 4, 5, 5, 5, 6, 6, 11, 15, 24]

# using a function
idxL = lambda val, lst:  [i for i,d in enumerate(lst) if d==val]

allVals = idxL(0,daysSick)
(0, 3)

Answer 3

好的，这是另一种工作方式，它先尝试缩小范围，然后再对已缩小范围的一半执行 bisect_left 和 bisect_right。我写这段代码是因为我认为它 比调用 bisect_left 和 bisect_right 稍微 更有效，即使它具有相同的时间复杂度。

def binary_range_search(s, x):
    # First we will reduce the low..high range if possible
    # by using symmetric binary search to find an index pointing to x
    low, high = 0, len(s)
    while True:
        if low >= high:
            return None
        mid = (low + high) // 2
        mid_element = s[mid]
        if x == mid_element:
            break
        elif x < mid_element:
            high = mid
        else:
            low = mid + 1
    xindex = mid

    # Now we have found an index pointing to x called xindex
    # and potentially reduced the low..high range
    # now we can run bisect_left on low..xindex + 1

    lo, hi = low, xindex + 1
    while lo < hi:
        mid = (lo+hi)//2
        if x > s[mid]: lo = mid+1
        else: hi = mid
    first = lo

    # and also bisect_right on xindex..high

    lo, hi = xindex, high
    while lo < hi:
        mid = (lo+hi)//2
        if x < s[mid]: hi = mid
        else: lo = mid+1
    last = lo - 1

    return first, last

我认为时间复杂度是 O(log n) 就像简单的解决方案一样，但我相信无论如何这会更有效一些。我认为值得注意的是，您执行 bisect_left 和 bisect_right 的第二部分可以针对大型数据集并行化，因为它们是不交互的独立操作。

Answer 4

查找楼层：编号 < 键的索引
查找上限：数字索引 > 键
[floor + 1 , ceiling - 1] 给你范围。

# yields next highest or lowest number to the key
# isLessThan determines which way the pointer moves

def nextNumber(arr, key, isLessThan):
  lo, hi = 0, len(arr)-1
  
  while lo <= hi:
    mid = lo + (hi - lo) // 2

    if isLessThan(key, arr[mid]):
      hi = mid - 1
    else:
      lo = mid + 1
  
  return (lo, hi)

def ceiling(arr, key):
  lo,_ = nextNumber(arr, key, lambda x,y : x < y)
  return lo

def floor(arr, key):
  _,hi = nextNumber(arr, key, lambda x,y : x <= y)
  return hi


def find_range(arr, key):
  fl = floor(arr,key)

  # key not in array
  if fl+1 >= len(arr) or arr[fl+1] != key:
    return [-1,-1]
  
  cl = ceiling(arr,key)
  return [fl+1 , cl-1]

如何对相同值的范围进行二分查找？

How to do a binary search for a range of the same value?

python

binary-search

解决方案

对比 `Bisect`

额外

如何对相同值的范围进行二分查找？

How to do a binary search for a range of the same value?

python

binary-search

解决方案

对比 Bisect

额外

对比 `Bisect`