Introduction to Algorithms
3rd Edition
ISBN: 9780262033848
Author: Thomas H. Cormen, Ronald L. Rivest, Charles E. Leiserson, Clifford Stein
Publisher: MIT Press
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Chapter 21.3, Problem 1E
Program Plan Intro
To redo the exercise 21.2-2 with a disjoint-sets forest by using the rank and path compression method.
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Develop a topological sort implementation thatmaintains a vertex-indexed array that keeps track of the indegree of each vertex. Initialize the array and a queue of sources in a single pass through all the edges. Then, perform the following operations until the source queue is empty:■ Remove a source from the queue and label it.■ Decrement the entries in the indegree array corresponding to the destination vertex of each of the removed vertex’s edges
If decrementing any entry causes it to become 0, insert the corresponding vertex onto the source queue.
Consider the implementation of disjoint
sets using forests. Assume the union is
done by weight, i.e., the root of the tree
with lesser nodes points to the root of the
tree with more nodes: The following
operations are applied on an initial set of
elements {x, x2, X3, X4, X5} : union (x, x2);
union (x1, x3); union (x4, xg); union
(x4, x1). Show the forest after each
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Your second function is called “isTree". Its input is a graph G, which is a dictionary
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the given vertex. Its output is True if G is a tree and False if G is not a tree. Hint: You
may want to make use of your "connected" function from the last coding assignment.
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