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02 Review Struktur Data

Kuliah PAAL 2012

Kelas C dan F

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Fundamental Data Structures

Linear data structures

Stacks, queues, and heaps

Graphs Trees

Sets

Dictionaries

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Linear Data Structures

Arrays A sequence ofn items of the same

data type that are stored contiguouslyin computer memory and madeaccessible by specifying a value of thearrays index.

Linked List A sequence of zero or more nodes

each containing two kinds ofinformation: some data and one ormore links called pointers to othernodes of the linked list.

Singly linked list (next pointer)

Doubly linked list (next + previouspointers)

Arrays

fixed length (need preliminary

reservation of memory)

contiguous memory locations

direct access

Insert/delete

Linked Lists

dynamic length

arbitrary memory locations

access by following links

Insert/delete

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Stacks, Queues, and Heaps (1)

Stacks A stack of plates

insertion/deletion can be done only at the top.

LIFO

Two operations (push and pop)

Queues

A queue of customers waiting for services

Insertion/enqueue from the rear and deletion/dequeue from the

front.

FIFO

Two operations (enqueue and dequeue)

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Stacks, Queues, and Heaps (2)

Priority queues (implemented using heaps)

A data structure for maintaining a set of elements, each associated with akey/priority, with the following operations

Finding the element with the highest priority

Deleting the element with the highest priority

Inserting a new element

Scheduling jobs on a shared computer.

Which of the following tree is a heap?

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Graphs

Formal definition A graph G = is defined by a pair of two sets: a finite

set V of items called vertices and a set E of vertex pairscalled edges.

Undirected and directed graphs (digraph).

Complete, dense, and sparse graph A graph with every pair of its vertices connected by an

edge is called complete. K|V|

A graph with relatively few possible edges missing is calleddense.

A graph with few edges relative to the number of itsvertices is called sparse.

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Graph Representation

Adjacency matrix

n x n boolean matrix if |V| is n.

The element on the ith row and jth column is 1 if theres an edge

from ith vertex to the jth vertex; otherwise 0. The adjacency matrix of an undirected graph is symmetric.

Adjacency linked lists

A collection of linked lists, one for each vertex, that contain all the

vertices adjacent to the lists vertex.

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Weighted Graphs

Weighted graphs

Graphs or digraphs with numbers assigned to the

edges.

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Graph Properties -- Paths and Connectivity

Paths

A path from vertex u to v of a graph G is defined as a sequence ofadjacent (connected by an edge) vertices that starts with u andends with v.

Simple paths: All edges of a path are distinct.

Path lengths: the number of edges, or the number of vertices 1.

Connected graphs

A graph is said to be connected if for every pair of its vertices u

and v there is a path from u to v.

Connected component

The maximum connected subgraph of a given graph.

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Graph Properties -- Acyclicity

Cycle

A simple path of a positive length that starts

and ends a the same vertex. Acyclic graph

A graph without cycles

DAG (Directed Acyclic Graph)

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Trees (I)

Trees A tree (or free tree) is a connected acyclic graph.

Forests: a graph that has no cycles but is not necessarilyconnected.

Properties of trees

For every two vertices in a tree there always exists exactlyone simple path from one of these vertices to the other.Why?

Rooted trees:The above property makes it possible to select anarbitrary vertex in a free tree and consider it as the root of the so-called rooted tree.

Levels of rooted tree.

|E| = |V| - 1

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Trees (II)

ancestors For any vertex vin a tree T, all the vertices on the simple path from the root to

that vertex are called ancestors.

descendants

All the vertices for which a vertex vis an ancestor are said to be descendants of

v.

parent, child and siblings

If(u, v) is the last edge of the simple path from the root to vertex v(and u v),u is said to be the parent ofvand vis called a child ofu.

Vertices that have the same parent are called siblings.

Leaves

A vertex without children is called a leaf.

Subtree

A vertex vwith all its descendants is called the subtree ofTrooted at v.

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Trees (III)

Depth of a vertex

The length of the simple path from the root to the

vertex.

Height of a tree

The length of the longest simple path from the root to

a leaf.

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Ordered Trees

Ordered trees An ordered tree is a rooted tree in which all the children of each vertex

are ordered.

Binary trees A binary tree is an ordered tree in which every vertex has no more than

two children and each children is designated s either a left child or aright child of its parent.

Binary search trees Each vertex is assigned a number.

A number assigned to each parental vertex is larger than all thenumbers in its left subtree and smaller than all the numbers in its rightsubtree.

log2n h n 1, where h is the height of a binary tree.

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Conclusion

Data structures are just another set of tools that should be in the kitof a seasoned programmer.

Comprehensive libraries and frameworks available with mostlanguages nowadays preempt the need for a full understanding of howto implement each of these tools.

The result is that developers are able to quickly produce qualitysolutions that take advantage of powerful ideas.

The challenge lies in knowing which one to select.

Nonetheless, knowing a little about how these tools work should helpto make the choices easier.

And, when the need arises, perhaps leave the programmer better

equipped to think up a new solution to a new problem; if not while onthe job doing work for a client, then perhaps while contemplating the1000 point problem 45 minutes into the coding phase of the next SRM(single round matches, used in TopCoder competition).