How does path compression affect the structure of the Disjoint Set Union?

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Q: How does path compression affect the structure of the Disjoint Set Union?

Solution: Path compression flattens the trees in the Disjoint Set Union, making future queries faster by reducing the depth of the trees.

Steps: 6

Step 1: Understand that a Disjoint Set Union (DSU) is a data structure that keeps track of a collection of disjoint (non-overlapping) sets.
Step 2: Each set is represented as a tree, where each node points to its parent node, and the root node represents the set.
Step 3: When we perform a union operation to combine two sets, we connect the root of one tree to the root of another, which can make the trees taller.
Step 4: Path compression is a technique used during the find operation to make the trees shorter.
Step 5: When we find the root of a set, we make all nodes along the path point directly to the root, effectively flattening the tree.
Step 6: This flattening reduces the depth of the trees, which means that future find operations will be faster because there are fewer nodes to traverse.