SlideServe
Télécharger Obtenir Pro
Menu
Accueil Pro
Préférences
ApparenceLight Aide et commentaires
© SlideServe · v2026

Contents of Chapter 6

zeroun avatar
zeroun
13 diapositives · 562 Views · Aug 07, 2014

Contents of Chapter 6. Chapter 6 Basic Traversal and Search Techniques 6.1 Techniques for binary trees 6.2 Techniques for graphs 6.3 Connected components and spanning trees 6.4 Biconnected components and DFS 6.5 References and readings. Chap. 6 Basic Traversal and Search Techniques.

Contents of Chapter 6 - slide 1
01 / 13Contents of Chapter 6
1 / 17

Télécharger la présentation

Contents of Chapter 6
Une image / un lien ci-dessous est fourni (tel quel) pour télécharger la présentation

Politique de téléchargement : le contenu du site vous est fourni TEL QUEL pour votre information et votre usage personnel ; il ne peut être vendu, concédé sous licence ni partagé sur d’autres sites sans l’accord de son auteur.Le contenu vous est fourni TEL QUEL, pour votre information et votre usage personnel uniquement. Téléchargez la présentation en cliquant sur ce lien. Lors du téléchargement, si vous ne parvenez pas à télécharger une présentation, l’éditeur a peut-être supprimé le fichier de son serveur.Pendant le téléchargement, si vous ne parvenez pas à obtenir une présentation, le fichier a peut-être été supprimé par l’éditeur.

F I N

Plus de contenu associé

Transcription de la présentation

  1. Contents of Chapter 6 • Chapter 6 Basic Traversal and Search Techniques • 6.1 Techniques for binary trees • 6.2 Techniques for graphs • 6.3 Connected components and spanning trees • 6.4 Biconnected components and DFS • 6.5 References and readings

  2. Chap. 6 Basic Traversal and Search Techniques • Traversal vs. search • Traversal • It examines every node in the given data object instance. • Search • It may not examine all vertices.

  3. struct treenode { Type data; struct treenode *lchild, *rchild; }; void InOrder(struct treenode *t) // t is a binary tree. Each node of t has // three fields lchild, data, and rchild. { if (t) { InOrder(t->lchild); Visit(t); InOrder(t->rchild); } } 6.1 Techniques for Binary Trees • Traversal • L (moving left), R (moving right), and D (printing the data) • Six possibilities: LDR, LRD, DLR, DRL, RDL, RLD • If left before right, three possibilities • LDR (inorder traversal) • LRD (postorder traversal) • DLR (preorder traversal) • Algorithms (Programs 6.1)

  4. void PreOrder(struct treenode *t) // t is a binary tree. Each node of t has // three fields lchild, data, and rchild. { if (t) { Visit(t); PreOrder(t->lchild); PreOrder(t->rchild); } } void PostOrder(struct treenode *t) // t is a binary tree. Each node of t has // three fields lchild, data, and rchild. { if (t) { PostOrder(t->lchild); PostOrder(t->rchild); Visit(t); } } 6.1 Techniques for Binary Trees • Algorithms (Programs 6.2)

  5. 6.1 Techniques for Binary Trees • Example (Figures 6.1 and 6.2)

  6. 6.2 Techniques for Graphs • Breath first search (BFS) and traversal (BFT) • BFS Algorithm (Program 6.5) void BFS( int v ) // A breadth first search of G is carried out beginning at vertex v. // For any node i, visited[i]==1 if i has at vertex v. The graph G and // array visited[] are global; visited[] is initialized to zero. { int u = v; Queue q(SIZE); // q is a queue of unexplored vertices. visited[v] = 1; do { for all vertices w adjacent from u { if (visited[w] == 0) { q.AddQ(w); // w is unexplored. visited[w]=1; } } if (q.Qempty()) return; // No unexplored vertex q.DeleteQ(u); // Get first unexplored vertex. } while(1); }

  7. 6.2 Techniques for Graphs • Breath first search (BFS) and traversal (BFT) (Continued) • Example 6.1 (Figure 6.4) • Visiting order: 1,2,3,4,5,6,7,8

  8. void BFT(struct treenode G[], int n) // Breadth first traversal of G { int i; boolean visited[SIZE]; for ( i = 1; i <= n; i ++ ) // Mark all vertices unvisited. visited[i] = 0; for ( i = 1; i <= n; i++ ) if ( !visited[i] ) BFS(i); } 6.2 Techniques for Graphs • Breath first search (BFS) and traversal (BFT) (Continued) • Breath first traversal (BFT) (Program 6.6)

  9. void DFS(int v) // Given an undirected (directed) graph G=(V,E) with // n vertices and an array visited[] initially set // to zero, this algorithm visits all vertices // reachable from v. G and visited[] are global. { visited[v] = 1; for each vertex w adjacent from v { if ( !visited[w] ) DFS(w); } 6.2 Techniques for Graphs • Depth first search (DFS) and traversal (DFT) • DFS Algorithm (Program 6.7) • Example 6.2 • Visiting order: 1,2,4,8,5,6,3,7

  10. 6.3 Connected Components and Spanning Trees • Connected component • Maximal connected subgraph (p.116 in Section 2.6.2) • E.g., Figure 2.28 (p.116) • Spanning trees (Figure 6.5) • We can easily obtain spanning trees using BFS (or DFS)

  11. 6.4 Biconnected Components and DFS • Terms • A vertex v in a connected graph G is an articulation point iff the deletion of vertex v together with all edges incident to v disconnects the graph into two or more nonempty components. • Example 6.3 (Figure 6.6) • A graph G is biconnected iff it contains no articulation point. • E.g.) • The graph of Figure 6.6(a) is not biconnected. • The graph of Figure 6.7 is biconnected.

  12. 6.4 Biconnected Components and DFS • Biconnected components • Maximal biconnected subgraph • Figure 6.8

  13. 1 for each articulation point a { • let B1, B2, …., Bk be the biconnected • components containing vertex a; • let vi, vi a, be a vertex in Bi, 1  i  k; • add to G the edges (vi, vi+1), 1  i  k; • 6 } 6.4 Biconnected Components and DFS • Lemma 6.1 Two biconnected components can have at most one vertex in common and this vertex is an articulation point. • Transforming a graph G into a biconnected graph (Program 6.8) • Example 6.4 • For articulation point 3, add edges (4,10) and (10,9) • For articulation point 2, add edge (1,5) • For articulation point 5, add edge (6,7)