通过删除“中间”项从数组中删除条目的算法？

Question

Given a list of items of length n , where a maximum number of wanted items is m , and m < n , and in which the items in the list which are most valuable / useful are those that are furthest from any other item. How can I remove items from the list to reduce the size of the list to m .

• eg, for [ a, b, c, d, e ] with an m == 2 , we would get [ a, e]

• eg, for [ a, b, c, d, e ] with an m == 3 , we would get [ a, c, e ]

• eg, for [ a, b, c, d, e ] with an m == 4 , we would get [ a, b, c, e ] or [ a, c, d, e ] . (Either answer would be valid; but only one should be returned, and preferably it would be deterministically returned.)

Note: I am generalizing a real problem, which is selecting representative frames from a video. The code will be written in python.

Answer 1

Step through the list with steps of about size (n-1)/(m-1) , where "about" is there because we can't land on a non-integer.

def representatives(l, m):
    num, den = len(l)-1, m-1
    return [l[i * num // den] for i in range(m)]

Here, element i of the result is taken from element i*(n-1)//(m-1) of the input, where // is floor division.

Answer 2

For a collection c :

sparse_list = c[::len(c)//(m-1)]

This returns a list with a step size of len(c)//(m-1) (note integer division).

eg:

c = list(range(50))
m = 5
c[::len(c)//(m-1)] # [0, 12, 24, 36, 48]

It's not quite perfect because it goes for exact spacing, but it's quick and easy (and performant).