By Gilles Brassard

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**Additional resources for Algorithmics: Theory and Practice**

**Example text**

2 Graphs Intuitively speaking, a graph is a set of nodes joined by a set of lines or arrows. 2 for instance. We distinguish directed and undirected graphs. In the case of a directed graph the nodes are joined by arrows called edges. 2 there exists an edge from alpha to gamma and another from gamma to alpha; beta and delta, however, are joined only in the direction indicated. In the case of an undirected graph, the nodes are joined by lines with no direction indicated, also called edges. In every case, the edges may form paths and cycles.

4 that this algorithm allows the creation of a heap in linear time. (a) The starting situation. Q Ta0 (b) The level I subtrees are made into heaps. (c) One level 2 subtree is made into a heap (the other already is a heap). 9. Making a heap. Preliminaries 30 Chap. 2. Let T[l .. 12] be an array such that T[i] =i for each i < 12. Exhibit the state of the array after each of the following procedure calls: make-heap (T) alter-heap(T, 12, 10) alter-heap (T. 1, 6) alter-heap(T, 5, 8) . 3. Exhibit a heap T [1 n] containing distinct values, such that the following sequence results in a different heap: m v- find-max (T) delete-max (T) insert-node(T[1 ..

This implementation is particularly efficient for the important structure known as the stack, which we obtain by restricting the permitted operations on a list: addition and deletion of elements are allowed only at one particular end of the list. However, it presents the major disadvantage of requiring that all the memory space potentially required be reserved from the outset of a program. On the other hand, if pointers are used to implement a list structure, the nodes are usually represented by some such structure as type node = record value: information next: node, where each node includes an explicit pointer to its successor.