Question

Use the following definition of the union operation, assuming the sentinel of x is not the same as the sentinel of y: union(x,y) = Make the sentinel of x point to the sentinel of y Imagine we start with an unconnected forest of nodes labeled 0 through 7. Then, we perform the following operations: union (0,1) union(2,3) union(0,2) union(4,0) union(5,6) union (7,5) union (5,4) find (5) Assuming we are not performing any weighting optimizations (i.e., don't use union-by-size or union- by-height) and assuming find does perform path compression, what is the array representation of our disjoint set?

Answer 1

As a result, the "Union-Find" data type is another name for the disjoint set.

An abstract data type called the disjoint set has been optimized to accommodate the following two operations:

Union: Combine the sets to which two elements, u and v, belong.

Find: Give me the set that element e belongs to.

As a result, the "Union-Find" data type is another name for the disjoint set.

If two sets don't share any elements, they are said to be disjoint sets. Two disjoint sets are equivalently two sets whose intersection is the empty set. As an illustration, 1, 2, 3, and 4, 5, 6 are disjoint sets, whereas 1, 2, 3, and 3, 4, 5 are not. If any two separate sets in a collection of two or more sets are not connected, the collection is said to be discontinuous.

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