lecture-13

# This will be helpful as we compute over trees cpsc

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Unformatted text preview: B B A F C E G subtree rooted at G CPSC 223  ­ ­ Fall 2010 15 Trees (Terminology) In a “binary” tree, every node has at most 2 children More formally, T is a binary tree if –  T has no nodes (is empty), or –  T has the form r TL TR –  where r is a node, and TL and TR are binary trees –  TL is the left subtree of r and TR is the right subtree of r … note that this deﬁnition employs recursion! (this will be helpful as we compute over trees) CPSC 223  ­ ­ Fall 2010 16 8 10/14/10 Trees (Terminology) The “height” of a tree is the length of the longest path –  The number of nodes that lie on the longest path from the root to a leaf D the height of this tree is 3 B A F C E G CPSC 223  ­ ­ Fall 2010 17 Trees (Terminology) An “empty” binary tree has no nodes D this is a not an empty binary tree B A CPSC 223  ­ ­ Fall 2010 F C E G 18 9 10/14/10 Trees (Terminology) A “full” binary tree has a height h with no missing nodes –  i.e., every internal node has exactly 2 children D this is a full binary tree B A F C E G CPSC 223  ­ ­ Fall 2010 19 Trees (Terminology) A “complete” binary tree of height h is –  a full binary tree at height h – 1, and –  the nodes at height h are ﬁlled in from left to right … sometimes we say “level” h to mean the nodes at height h D this is a complete binary tree B A CPSC 223  ­ ­ Fall 2010 F C E 20 10 10/14/10 Trees (Terminology) A “balanced” binary tree has for every node –  left and right subtrees that differ in height by at most 1 D B A this is not a balanced binary tree F D C E B this is a balanced binary tree A F C E E CPSC 223  ­ ­ Fall 2010 21 Binary Tree versus Binary Search Tree (BST) •  A Binary Search Tree stipulates where nodes are placed in a Binary Tree … •  In such a way as to maintain the items in sorted order (based on a sort key) CPSC 223  ­ ­ Fall...
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