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

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

Options:

Correct Answer: It flattens the trees to make future queries faster

Solution:

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

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

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

Correct Answer: Path compression flattens the trees in the Disjoint Set Union.

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.

Path Compression – A technique used in Disjoint Set Union to flatten the structure of trees, leading to more efficient future operations.
Disjoint Set Union (DSU) – A data structure that keeps track of a partition of a set into disjoint subsets, supporting union and find operations.
Tree Depth – The maximum distance from the root to any leaf in the tree structure of the Disjoint Set Union, which affects the efficiency of operations.