Algorithms and Data Structures

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N.Wirth. Algorithms and Data Structures. Oberon version 196 found. Note that one side of the rectangle lies on the x-axis, i.e. the lower bound for y is 0. This guarantees that enumeration requires at most O(log(N) + s) operations, where N is the cardinality of the search space in x and s is the number of nodes enumerated. PROCEDURE enumerate (p: Ptr; x0, x1, y1, xL, xR: INTEGER); VAR xm: INTEGER; (* ADenS48_PrioritySearchTrees *) BEGIN IF p # NIL THEN IF (p.y
N.Wirth. Algorithms and Data Structures. Oberon version 197 Fig. 4.52. Circular list 4.6. A bidirectional list is a list of elements that are linked in both ways. (See Fig. 4.53) Both links are originating from a header. Analogous to the preceding exercise, construct a module with procedures for searching, inserting, and deleting elements. Fig. 4.53. Bidirectional list 4.7. Does the given program for topological sorting work correctly if a certain pair occurs more than once in the input? 4.8. The message "This set is not partially ordered" in the program for topological sorting is not very helpful in many cases. Extend the program so that it outputs a sequence of elements that form a loop, if there exists one. 4.9. Write a program that reads a program text, identifies all procedure definitions and calls, and tries to establish a topological ordering among the subroutines. Let P 〈 Q mean that P is called by Q. 4.10. Draw the tree constructed by the program shown for constructing the perfectly balanced tree, if the input consists of the natural numbers 1, 2, 3, ... , n. 4.11. Which are the sequences of nodes encountered when traversing the tree of Fig. 4.23 in preorder, inorder, and postorder? 4.12. Find a composition rule for the sequence of n numbers which, if applied to the program for straight search and insertion, yields a perfectly balanced tree. 4.13. Consider the following two orders for traversing binary trees: a1. Traverse the right subtree. a2. Visit the root. a3. Traverse the left subtree. b1. Visit the root. b2. Traverse the right subtree. b3. Traverse the left subtree. Are there any simple relationships between the sequences of nodes encountered following these orders and those generated by the three orders defined in the text? 4.14. Define a data structure to represent n-ary trees. Then write a procedure that traverses the n-ary tree and generates a binary tree containing the same elements. Assume that the key stored in an element
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Algorithms and Data Structures

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