Introduction to Algorithms
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 6.5, Problem 5E
Program Plan Intro

To describe the correctness of HEAP-INCREASE-KEY for the loop invariants.

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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 destinationvertex of each of the removed vertex’s edges.
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.
30. In the implementation for a breadth-first search we studied, a queue was used. The code below replaces the queue with a stack. List the pre-order enumeration that the vertices in the graph below are visited using this modified method, starting from vertex 0. } 3 /** stack-based search */ static void modSearch (Graph G, int start) { Stack S new AStack (G.n()); S.push(start); } 6 G.setMark (start, VISITED); while (S.length) > 0) { } modSearch: intv S.pop(); PreVisit (G, v); for (int w = G.first (v); w < G.n(); w = G.next(v, w)) if (G.getMark (w) == UNVISITED) { G.setMark (w, VISITED); S.push(w);
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