Schaum's Outline of Discrete Mathematics, Third Edition (Schaum's Outlines)

CHAP. 9] DIRECTED GRAPHS 225 Fig. 9-24 LINKED REPRESENTATION OF GRAPHS 9.10. LetGbe the graph presented by the following table: ...

226 DIRECTED GRAPHS [CHAP. 9 (a) Since START=3, the list begins with the vertexB. Then NEXT-V tells us to go to 1(D), then 7(C), ...

CHAP. 9] DIRECTED GRAPHS 227 However, when there are many, many flights, such a representation does not easily answer the follow ...

228 DIRECTED GRAPHS [CHAP. 9 SupplementaryProblems GRAPH TERMINOLOGY 9.18. Consider the graphGin Fig. 9-28(a). (a) Find the inde ...

CHAP. 9] DIRECTED GRAPHS 229 Fig. 9-29 ROOTED TREES, ORDERED ROOTED TREES 9.24. LetTbe the rooted tree in Fig. 9-29(b). (a) Iden ...

230 DIRECTED GRAPHS [CHAP. 9 Fig. 9-31 LINKED REPRESENTATION OF GRAPHS 9.31.A weighted graphGwith six vertices,A, B, ..., F, is ...

CHAP. 9] DIRECTED GRAPHS 231 Fig. 9-33 9.36. Using the data in Fig. 9-33, write a procedure with input CITYXand CITYYwhich finds ...

232 DIRECTED GRAPHS [CHAP. 9 9.43. Suppose a graphGis input by means of an integerM, representing the vertices 1, 2 ,...,M, and ...

CHAP. 9] DIRECTED GRAPHS 233 Fig. 9-35 9.29. (a)A=[ 0 , 0 , 1 , 0 , 0 ; 1 , 0 , 0 , 0 , 0 ; 0 , 1 , 0 , 0 , 0 ; 1 , 0 , 0 , 0 , ...

234 DIRECTED GRAPHS [CHAP. 9 Fig. 9-38 9.43. (i)A=[ 0 , 0 , 0 , 0 , 0 ; 0 , 0 , 0 , 1 , 0 ; 1 , 1 , 0 , 1 , 0 ; 0 , 1 , 0 , 0 , ...

CHAPTER 10 Binary Trees 10.1Introduction The binary tree is a fundamental structure in mathematics and computer science. Some of ...

236 BINARY TREES [CHAP. 10 Accordingly, in Fig. 10-1(a): (a) Bis a left successor andCis a right successor of the rootA. (b) The ...

CHAP. 10] BINARY TREES 237 10.3Complete and Extended Binary Trees This section considers two special kinds of binary trees. Comp ...

238 BINARY TREES [CHAP. 10 Fig. 10-3 Converting a binary treeTinto a 2-tree Algebraic Expressions and Polish Notation LetEbe any ...

CHAP. 10] BINARY TREES 239 10.4Representing Binary Trees in Memory LetTbe a binary tree. This section discusses two ways of repr ...

240 BINARY TREES [CHAP. 10 Fig. 10-6 Furthermore, the nodeNat TREE[K] contains an empty left subtree or an empty right subtree a ...

CHAP. 10] BINARY TREES 241 EXAMPLE 10.3 Consider the binary treeTin Fig. 10-7(a). Observe thatAis the root ofT, that the left su ...

242 BINARY TREES [CHAP. 10 10.6Binary Search Trees This section discusses one of the most important data structures in computer ...

CHAP. 10] BINARY TREES 243 Searching and Inserting in a Binary Search Tree A search and insertion algorithm in a binary search t ...

244 BINARY TREES [CHAP. 10 Fig. 10-10 number of moves cannot exceed the depthdof the tree. Thus the running timef (n)of either a ...