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CS 310 Unit 11 Binary Search Trees

# CS 310 Unit 11 Binary Search Trees - CS 310 Unit 11 Binary...

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Unformatted text preview: CS 310 Unit 11 Binary Search Trees Furman Haddix Ph.D. Assistant Professor Minnesota State University, Mankato Spring 2008 Binary Search Tree Objectives • Binary Search Tree Definitions • Binary Search Tree Algorithms – Insert() – Traversal() – Search() – Minimum() – Maximum() – Successor() – Predecessor() – Delete() • Text, Chapter 12 Binary Search Tree Definitions • Important Methodology for Dynamic Sets • Many Dynamic Set Operations are O(h) where h is the height of the tree • Can be constructed as a linked data structure where each node is an object • root is a pointer to the root of the tree • Each node minimally contains: – key data, key – pointer to left child, left – pointer to right child, right – pointer to parent, p • Properties – If y is in left subtree of x then key[y] ≤ key[x] – If y is in right subtree of x then key[y] ≥ key[x] Binary Search Tree F D B A K H J L C K E F • Build in order binary search tree with keys, F, D, B, A, K, H, J, L, C, K, E, F: Insert() • Insert new node as leaf in “in order position” • Example insert(G); F D B A K H J L C K E F ≥ < < ≥ G Binary Search Tree insert() void insert(Node *x) { Node *y = root, *z = null; while (y != null) z = y; if (x->key() < y->key()) y = y->left(); else y = y->right(); } x->setP(z); if(z == null) root = x; else if (x->key() < z->key()) z->setLeft(x); else z->setRight(x); return; } Node *p; Node *left; Node *right;...
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CS 310 Unit 11 Binary Search Trees - CS 310 Unit 11 Binary...

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