What is the worst-case time complexity of the union operation in a basic Disjoin

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Question: What is the worst-case time complexity of the union operation in a basic Disjoint Set Union without optimizations?

Options:

Correct Answer: O(n)

Solution:

The worst-case time complexity of the union operation in a basic Disjoint Set Union without optimizations is O(n).

What is the worst-case time complexity of the union operation in a basic Disjoint Set Union without optimizations?

What is the worst-case time complexity of the union operation in a basic Disjoint Set Union without optimizations?

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: Know that the union operation is used to combine two subsets into a single subset.
Step 3: In a basic DSU without optimizations, each element points to its parent. If we want to union two sets, we may need to traverse the entire set to find the root parent of each element.
Step 4: In the worst case, if we have n elements in a single set, we may need to check each of these n elements to find the root parent.
Step 5: Therefore, the time it takes to perform the union operation in this case can be as bad as checking all n elements, leading to a time complexity of O(n).

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