trees 10 - Trees Why Trees We need a representation for...

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Trees
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Trees 2 Why Trees? We need a representation for hierarchical data. Like what? ancestor – descendent superior – subordinate whole – part modular organization Definition: A tree t is a finite nonempty set of elements. One element is called the root , and all the remaining elements are partitioned into trees called subtrees.
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Trees 3 Tree Terms Elements are represented as nodes …usually drawn as a circle. Edges , lines, are drawn connecting a node to its subtree. This edge implies a relationship between nodes. A node can be a parent node or a child node. Other terms used to describe the relationship between nodes are: sibling, ancestor/descendent, grandchild/grandparent A leaf is an element with no children The term level is used to denote the tier of an element within a tree. The root is at level 1; its children are at level 2…and so on. The degree of an element is the number of kids it has. The degree of a tree is the max of its elements’ degrees.
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Trees 4 There are many types of trees: Binary Trees Binary Search Trees AVL Trees Red-Black Trees B-Trees
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Trees 5 Binary Trees A binary tree t is a finite, but possibly empty, collection of elements. When the tree is not empty, it contains a root , and all the remaining elements are partitioned into sub binary trees , which are called the left and right subtrees of t. How does a binary tree differ from a tree? We can use a binary tree to represent arithmetic expressions.
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Trees 6 A full binary tree is a binary tree in which all the leaves are on the same level and every nonleaf node has 2 children. It has height h and contains exactly 2 h - 1 elements. A complete binary tree is either full or full through the next-to-last level, with the leaves on the last level as far to the left as possible. A full binary tree is a special case of a complete
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trees 10 - Trees Why Trees We need a representation for...

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