What is the time complexity of the 'find' operation in a Disjoint Set Union with
Practice Questions
Q1
What is the time complexity of the 'find' operation in a Disjoint Set Union with path compression?
O(1)
O(log n)
O(n)
O(α(n))
Questions & Step-by-Step Solutions
What is the time complexity of the 'find' operation in a Disjoint Set Union with path compression?
Step 1: Understand what a Disjoint Set Union (DSU) is. It is a data structure that keeps track of a partition of a set into disjoint (non-overlapping) subsets.
Step 2: Learn about the 'find' operation. This operation determines which subset a particular element belongs to.
Step 3: Recognize that path compression is an optimization technique used in the 'find' operation. It flattens the structure of the tree whenever 'find' is called, making future queries faster.
Step 4: Know that the time complexity of the 'find' operation without path compression is O(n) in the worst case, where n is the number of elements.
Step 5: With path compression, the time complexity improves significantly. It becomes O(α(n)), where α is the inverse Ackermann function, which grows very slowly.
Step 6: Understand that O(α(n)) means that for all practical purposes, the 'find' operation is nearly constant time for all reasonable sizes of n.
