Datos estructurados
Fall, 2007
Part I: Data Structures & Algorithm Analysis
CSCI 362: Data Structure (Fall, 2007 )
Dept. of Computer and Information Science, IUPUI
Chap. 1Introduction
1.1 Introduction – Data Structures: methods of organizing large amount of data (input data, output data, run-time data)
– Algorithm analysis: estimation of running time of algorithms – Goals• Various data structures, their properties, operations, implementations, & applications • Data structure design skills for problem solving • Algorithm design and analysis skill
CSCI 362: DataStructure (Fall, 2007 )
Dept. of Computer and Information Science, IUPUI
1
– Algorithm analysis examples
• Finding the kth largest number among a group of N numbers
Bubble sort vs. k elementspartition
N2 k
k2+(N-k)(i+k-i) < N2 i • Traveling salesman problem • Street scanning problem
CSCI 362: Data Structure (Fall, 2007 )
Dept. of Computer and Information Science, IUPUI
1.2Mathematics review – Exponents
X A X B X A B X A / X B X A B
( X A ) B X AB
– Logarithms
X A B log X B A log A B log C B / log C A log AB log A log B log l A/ B l Al B loglog
log( A B ) B log A log X X (for all X 0) log 1 0, log 2 1, log 1024 10,...
CSCI 362: Data Structure (Fall, 2007 )
Dept. of Computer and Information Science, IUPUI
( B, X 0, X 1)
log 2 A log A log10 A lg A log e A ln A
2
– Series
A
i 0
N
i
A N 1 1 , A 1
N 0
2
0
N
i
2 N 1 1 1 1 A
If 0 A 1
A
i
A
i 0 N 1
i
1 (0 A 1) : geometric series 1 A
i i
1 N 2
N ( N 1) N2 /2 2 N ( N 1)(2 N 1) N3 /3 6
ex. 2 5 8 ... (2k 1)
i
1
N
k
Nk 1 | k 1 | (k 1)
N 1 H N log e N ln N 1 i
Harmonic number Euler’s Constant:
f ( N ) Nf ( N )
i 1 N i n0
N
lim | H N ln N | 0.57721566
N
f ( N ) ...
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