Check if 2 arrays are similar without hashing or sorting

Question

We need to check if 2 arrays are similar or not. The elements can be duplicate as well. For example A = {2,3,4,5,6,6} and B = {3,6,2,4,6,5} are similar.

I have a nai

Answer 1

You can do it in O(max(L_A, L_B)) time, where L_A and L_B are lengths of A and B, respectively, but at the price of using O(M) space, where M is an allowed range of values in the arrays (i.e. there are such constants min and max, so that min <= a, b <= max holds true for every a in A and b in B).

seen = array[min..max]
foreach a in A
    seen[a] = 'a'

foreach b in B
    if seen[b] != 'a'
        // A didn't contain b
        return "A and B are not equivalent"
    else
       seen[b] = 'a,b'

foreach s in seen
    if s == 'a'
        // A did contain a which was not in B
        return "A and B are not equivalent"

return "A and B are equivalent"

This approach is practical if the arrays are very large, but all their values fit in a small range.