A Practical Introduction to Data Structures and Algorithm Analysis

398 Chap. 11 Graphspublic int weight(int i, int j) { // Return edge weightreturn matrix[i][j];}// Get and set markspublic void setMark(int v, int val) { Mark[v] = val; }public int getMark(int v) { return Mark[v]; }}Figure 11.6 (continued)// Edge class for Adjacency List graph representationclass Edge {private int vert, wt;}public Edge(int v, int w) // Constructor{ vert = v; wt = w; }public int vertex() { return vert; }public int weight() { return wt; }Implementation for Graphl member functions is straightforward in principle,with the key functions being setEdge, delEdge, and weight. The simplestimplementation would start at the beginning of the adjacency list and move along ituntil the desired vertex has been found. However, many graph algorithms work bytaking advantage of the first and next functions to process all edges extendingfrom a given vertex in turn. Thus, there is a significant time savings if setEdge,delEdge, and weight first check to see if the desired edge is the current one onthe relevant linked list. The implementation of Figure 11.7 does exactly this.11.3 Graph TraversalsOften it is useful to visit the vertices of a graph in some specific order based on thegraph’s topology. This is known as a graph traversal and is similar in concept toa tree traversal. Recall that tree traversals visit every node exactly once, in somespecified order such as preorder, inorder, or postorder. Multiple tree traversals existbecause various applications require the nodes to be visited in a particular order.For example, to print a BST’s nodes in ascending order requires an inorder traversalas opposed to some other traversal. Standard graph traversal orders also exist.Each is appropriate for solving certain problems. For example, many problems inartificial intelligence programming are modeled using graphs. The problem domainmay consist of a large collection of states, with connections between various pairsof states. Solving the problem may require getting from a specified start state to a