找出列表中有多少组

Question

I have a list with each value in the interval 0..100.

Ex:

[0,1,2,20,21,29,30,31,31,32,89,90,91,92,92,92,92]

Is there an algorithm that will determine how many groups are in this list? For the above list it should say that there are 3 groups (0..2), (20..32), (89..92) .

As far as I know there is the k-means algorithm that will split the list in a certain number of groups, but in my case, I need to determine how many groups are in the first place, so k-means doesn;t really help for this.

I will need to do this in PHP if the language has any relevance.

Answer 1

If you know that your groups are separable by a certain minimum distance d , you can count the groups as by counting all consecutive elements that are not in the same group:

Input: A, d
Output: num_groups

sort(A)
for i = 0 ... size(A) - 2
    if A[i + 1] - A[i] >= d
        num_groups++

If you have yet to determine the optimal minimum distance such that there are at most k groups, you can determine this value by computing the adjacent differences and selecting the k th largest element:

Input: A of size n, k
Output: d

sort(A)
adj_diff = array of n - 1 elements
for i = 0 ... n - 2
    adj_diff[i] = A[i + 1] - A[i]
sort(adj_diff)
d = adj_diff[n - 1 - k]
if d == adj_diff[n - 2 - k] // to make sure there are at most k groups,
    d++                     // otherwise we might have multiple groups
                            // with the same distance to their neighbors