Tree basics
- 1. Computer Science 2 Data Structures and Algorithms V22.0102 section 2 Introduction to Trees Professor: Evan Korth New York University
- 2. Road Map • Introduction to trees – Terminology • Binary trees • Tree traversal • Reading: 4.1 – 4.2
- 3. Tree • Tree defined recursively • A tree is a collection of nodes. The collection can be empty; otherwise, a tree consists of a distinguished node r, called the root, and zero or more non-empty (sub) trees T1, T2, …, Tk each of whose roots are connected by a directed edge from r. • A tree is a collection of N nodes, one of which is the root and N-1 edges. Source:Mark Allen Weiss
- 4. Tree terminology • The root of each subtree is said to be a child of r and r is said to be the parent of each subtree root. • Leaves: nodes with no children (also known as external nodes) • Internal Nodes: nodes with children • Siblings: nodes with the same parent Source:Mark Allen Weiss - edited by Evan Korth
- 5. Tree terminology (continued) • A path from node n1 to nk is defined as a sequence of nodes n1, n2, …, nksuch that ni is the parent of ni+1 for 1<= i <= k. • The length of this path is the number of edges on the path namely k-1. • The length of the path from a node to itself is 0. • There is exactly one path from from the root to each node. Source:Mark Allen Weiss
- 6. Tree terminology (continued) • Depth (of node): the length of the unique path from the root to a node. • Depth (of tree): The depth of a tree is equal to the depth of its deepest leaf. • Height (of node): the length of the longest path from a node to a leaf. – All leaves have a height of 0 – The height of the root is equal to the depth of the tree Source:Mark Allen Weiss
- 7. Tree terminology (continued) • Depth (of node): the length of the unique path from the root to a node. • Depth (of tree): The depth of a tree is equal to the depth of its deepest leaf. • Height (of node): the length of the longest path from a node to a leaf. – All leaves have a height of 0 – The height of the root is equal to the depth of the tree Source:Mark Allen Weiss