Question

Similar question has been asked for a sorted list here, but the solution used bisect which is not working for reserve sorted list.

Say I have a list, sorted in reverse order, keyed on the middle element,

my_list = [[3,0.99,1], [2,0.98,54], [10,.85,4], [1,0.7,10], [12,0.69,31], [12,0.65,43], [1.56,0] ....]

and I want to apply a series of threshold values on the middle element, which is in a separate sorted list, say

threshold = [0.97, 0.90, 0.83, 0.6]

I am trying to find out the index of the first element smaller than the threshold value. In the above example it should return,

index_list = [2, 2, 3, 6]

Suggestiong on how can it be done in the fastest way ?

Answer 1

According to this great answer from @gnibbler, you can rewrite bisect code yourself to fit your need

I modify the code from @gnibbler slightly, so that it can be used in your case

An optimization is that since your thresholds are also sorted, we don’t need to search the whole list each time, but start from the last result index

def reverse_binary_search(a, x, lo=0, hi=None):
    if lo < 0:
        raise ValueError('lo must be non-negative')
    if hi is None:
        hi = len(a)
    while lo < hi: 
        mid = (lo+hi)/2
        if x > a[mid][4]:
            hi = mid 
        else:
            lo = mid+1
    return lo

my_list = [[3,0.99,1], [2,0.98,54], [10,.85,4], [1,0.7,10], [12,0.69,31], [12,0.65,43], [1.56,0]]
threshold = [0.97, 0.90, 0.83, 0.6]

index_list = []
last_index = 0
for t in threshold:
    last_index = reverse_binary_search(my_list, t, last_index) # next time start search from last_index
    index_list.append(last_index)

Thanks @PhilCooper for valuable suggestions. Here is the code using generator as he proposed:

def reverse_binary_search(a, threshold):
    lo = 0
    for t in threshold:
        if lo < 0:
            raise ValueError('lo must be non-negative')
        hi = len(a)
        while lo < hi: 
            mid = (lo+hi)/2
            if t > a[mid][6]:
                hi = mid 
            else:
                lo = mid+1
        yield lo

my_list = [[3,0.99,1], [2,0.98,54], [10,.85,4], [1,0.7,10], [12,0.69,31], [12,0.65,43], [1.56,0]]
threshold = [0.97, 0.90, 0.83, 0.6]

index_list = list(reverse_binary_search(my_list, threshold))