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CS 104 Introduction to Computer Science and Graphics Problems Data Structure & Algorithms (4) Data Structures 11/18/2008 Yang Song

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Data Structure In computer science, a data structure is a way of storing and organizing data in the computer, so that the data can be used efficiently. Some data structures we often use Linked List Queue Stack Tree Graph

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Linked List One of the fundamental data structures and can be used to implement other data structures. It consists of a sequence of nodes, each node has two kinds of fields: Data, to store the date Link, to point to the next node (may have One or Two links) Basic Operations: Search O(n) Insertion O(1) Deletion O(1)

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Linked List (Cont.) For a linked list, if each node has only one link, which points to its next node, we call it singly-linked list: For a linked list, if each node has two links, which point to its next and previous nodes, we call it doubly-linked list:

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Queue Queue is a common and important data structure in computer science. It can be described with the analogy of waiting in a line. There is no cutting allowed in the line, so the first element stored in the line is the fist item to picked out of the line, we call it First In First Out (FIFO). Recall the memory in Operating Systems, we have FCFS, they are same. Basic Operations: Enqueue: Add new items to the queue, it will add the new items only to the back of the queue. Dequeue: Remove items from the queue, it will remove the items only from the front of the queue. Example: From an empty Queue, we have following operations: Enqueue (3), Enqueue (5), Enqueue (7), Dequeue, Dequeue. Result is: (7)

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Stack Stack is an abstract data type and data structure based on the principle of Last In First Out (LIFO). Basic Operations: Push: Add the new item to the top Pop: Get the item from the top Example: From an empty Stack, we have the following operations: Push (3), Push (5), Push (7), Pop, Pop. Result is: (3) Different from Queue: FIFO v.s. LIFO

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Tree A data structure accessed beginning at the root node. Each node is either a leaf or an interior node. An interior node has one or more child nodes and is called the parent of its child nodes. Contrary to a physically real tree, the root is usually at the top of the structure and the leaves are at the bottom.

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Tree (Cont.) Level, Height Node: Root, Leaf, Child, Parent, Sibling Sub-Tree Basic Operations Traversal Insertion Deletion Binary Tree A tree in which each node has AT MOST two children, called Left Child and Right Child Traversal: In-Order, Pre-Order, Post-Order In-Order: Left Child->Root->Right Child Pre-Order: Root->Left Child->Right Child Post-Order: Left Child->Right Child->Root Application: Binary Search Tree, Heap

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Binary Search Tree (BST) A BST is a Binary Tree Data Structure with following properties: Each node has a value The Left sub-tree of a node contains only values less than the node’s value The Right sub-tree of a node contains only values greater than the node’s value A major advantage of BST over other data structures is that the related sorting algorithms and search algorithms can be very efficient. What kind of traversal do we need to make all the values in BST be sorted? Why? A good link to see the animation of insertion, deletion and search: http://www.cs.jhu.edu/~goodrich/dsa/trees/btree.html

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