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Oregon State University School of Electrical Engineering and Computer Science CS 261 – Recitation 9 & 10 Graphs & Final review Fall 2013 Graph: Reachability Problem • Given a single starting vertex, produce the set of vertices that can be reached starting from the initial location. • A depth-first search follows each path as far (deep) as possible before backtracking. • A breadth-first search looks at all possible paths at the same time. Order in which nodes are reached: (left) DFS; and (right) BFS. Source: Wikipedia Graph: Reachability Problem findReachable (graph g, vertex start) { create a set of reachable vertices, initially empty. call this r. create a container for vertices known to be reachable. call this c add start vertex to container c while the container c is not empty { remove first entry from the container c, assign to v if v is not already in the set of reachable vertices r { add v to the reachable set r add the neighbors of v to the container c } } return r } DFS: Container is a Stack BFS: Container is a Queue Exercise Simulate the DFS and BFS on the following graph starting at node A. Notes: (1) Nodes must be added to the container (Stack or Queue) in COUNTER-CLOCKWISE order; (2) We do not add neighbors to the container if they have already been visited. Outline – Final exam review • BST/AVL/Tree sort/Tree traversal/Tree iterator • Heaps/heap sort • Hash tables Materials in these slides were collected from different Internet sources. CS 261 – Data Structures 5 Question H J D F B A C E I K G CS 261 – Data Structures 6 Pre, In, Post-order traversal Pre-order: 10 – 5 – 1 – 8 – 7 – 6 – 34 – 56 – 40 - 60 In-order: 1 – 5 – 6 – 7 – 8 – 10 – 34 – 40 – 56 - 60 Post–order: 1 – 6 – 7 – 8 – 5 – 40 – 60 – 56 – 34 – 10 CS 261 – Data Structures 7 Adding 13??? 13 CS 261 – Data Structures 8 Removing 10??? CS 261 – Data Structures 9 TreeSort struct AVLTree* newAVLTree(); void addAVLTree(struct AVLTree *tree, TYPE val); void treeSort (TYPE data[], int n) {…} void _treeSortHelper(AVLNode *cur, TYPE *data, int *count) {…} CS 261 – Data Structures 10 treeSort void treeSort(TYPE data[], int n){ int i; int count = 0; /* declare an AVL tree */ struct AVLTree *tree = newAVLtree(); assert(data != NULL && n > 0); /* add elements to the tree */ for (i = 0; i < n; i++) addAVLTree(tree, data[i]); /* call the helper function */ _treeSortHelper(tree->root, data, &count); } CS 261 – Data Structures 11 _treeSortHelper /* *count goes from 0 to n-1 */ void _treeSortHelper(AVLNode *cur, TYPE *data, int *count){ if (cur != NULL) { _treeSortHelper(cur->left, data, count); data[*count] = cur->val; (*count)++; _treeSortHelper(cur->right, data, count); } } CS 261 – Data Structures 12 True or False CS 261 – Data Structures 13 Question • Add 12, remove 3, remove 5 CS 261 – Data Structures 14 When to do a double rotation? Balance Factor = height(right subtree) - height(left subtree) • At an unbalanced node N, a double rotation is needed when: – N’s BF is positive and N’s right subtree’s BF is negative – N’s BF is negative and N’s left subtree’s BF is positive. CS 261 – Data Structures 15 Heaps and priority queues • How to represent a binary heap? – Using an array (dyArray) • Suppose the root has index 0, what are the indices of the 2 children of a node at index i? 2 * i + 1, 2 * i + 2 • What is the index of the parent of a node at index i? (i-1)/2 2 3 5 9 14 10 12 11 7 16 8 0 1 2 3 4 5 6 2 3 5 9 10 7 8 14 12 11 16 CS 261 – Data Structures 7 8 9 10 17 Simulate heap sort for the following heap 3 10 9 14 12 11 CS 261 – Data Structures 16 18