Question

find longest subarray whose sum divisible by K.
It is possible in O(n)?
If not can it be done in better then n^2 ?

Answer 1

Let s[i] = sum of first i elements modulo K.

We have:

s[i] = (s[i - 1] + a[i]) % K

We have to find, for each i, the smallest j such that s[i] == s[j]. You can find this by hashing the s[i] values. If K is small, you can just keep an array p[i] = first position for which s[k] == i.

The complexity is O(n).