Longest equally-spaced subsequence

Question

I have a million integers in sorted order and I would like to find the longest subsequence where the difference between consecutive pairs is equal. For example

Answer 1

UPDATE: I've found a paper on this problem, you can download it here.

Here is a solution based on dynamic programming. It requires O(n^2) time complexity and O(n^2) space complexity, and does not use hashing.

We assume all numbers are saved in array a in ascending order, and n saves its length. 2D array l[i][j] defines length of longest equally-spaced subsequence ending with a[i] and a[j], and l[j][k] = l[i][j] + 1 if a[j] - a[i] = a[k] - a[j] (i < j < k).

lmax = 2
l = [[2 for i in xrange(n)] for j in xrange(n)]
for mid in xrange(n - 1):
    prev = mid - 1
    succ = mid + 1
    while (prev >= 0 and succ < n):
        if a[prev] + a[succ] < a[mid] * 2:
            succ += 1
        elif a[prev] + a[succ] > a[mid] * 2:
            prev -= 1
        else:
            l[mid][succ] = l[prev][mid] + 1
            lmax = max(lmax, l[mid][succ])
            prev -= 1
            succ += 1

print lmax