# Given a list of arrays, find all pairs of arrays that share a single element [on hold]

I need to find a fast algorithm to perform this task. Possible O(n log n) or even O(n).

For example, giving following 5 arrays:
$$\begin{bmatrix}10,7,5,5,7\end{bmatrix}$$
$$\begin{bmatrix}1,7,5,2,2\end{bmatrix}$$
$$\begin{bmatrix}1, 2,3,4,5\end{bmatrix}$$
$$\begin{bmatrix}1,10,2,9,9\end{bmatrix}$$
$$\begin{bmatrix}6,6,6,6,6\end{bmatrix}$$
Result should be 6.

I think of an idea using inclusion-exclusion but I am not sure.

EDIT: array can will be small enough to negligible

## put on hold as unclear what you're asking by Evil, Hendrik Jan, David Richerby, Discrete lizard, Juho2 days ago

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• What have you tried? Whede did you get stuck? Could pairs be reused? – Evil Jan 5 at 2:59
• Only thing I have thought is brute force which too slow. I had idea of graph theory algorithm but still does not go fast enough. I tried using graph theory but still not fast. I do not know what you mean by reused but (0, 1)is same as(1, 0). @Evil Thank you for your help – user98580 Jan 5 at 3:04
• What if you sort them, does it get easier? In your case n = 25? Are arrays equal in length? Integers only? Bounded? Could you share more details? Where did you find this problem? Could you attribute source? – Evil Jan 5 at 3:17
• Please credit the original source of the problem. Please relieve our concern that this might be a problem of an ongoing programming contest. – Apass.Jack Jan 5 at 7:37