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why can path compression help improve the speed of cycle detection (use a concrete example where...

why can path compression help improve the speed of cycle detection (use a concrete example where the disjoint set is represented as an array and show how path compression can speed things up to show this)

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Path compression

Path compression flattens the structure of the tree by making every node point to the root whenever Find is used on it. This is valid since each element visited on the way to root is part of the same set. The resulting flatter tree speeds up future operations not only on these elements but also on those referencing them.

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