My hash has 3 fields
f1 = size of interval
f2 = sum of array elements over interval(a[i] +a[i+1]...a[j])
f2 = sum of squares of array elements over interval(a[i]^2 + a[i+1]^2 .. a[j]^2).
if all 3 matches, then elements are indeed same. Can this be broken?
P.S. While in attempt to solve D from previous contest(https://codeforces.me/contest/1284/problem/D). I was looking for this question.
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(5, 12, 10) and (6, 8, 13) have the same hash.
I think adding a cube power may make this hash a perfect hash.
Sorry to disappoint you, but probably not. It can be shown by a simple Dirichlet. There are a lot more arrays of size 1000 than there are possible outputs for your hash if you bound the numbers by let's say 1000.
On a contest, lets say we choose 3 random powers.
I guess that would be optimistically a good hash?
It will be perfect only if you consider at least $$$n$$$ distinct powers.
Adding powers up to k can easily be hacked with a test with n=2^(k+2).