1. Introduction:
Basic Concepts and Notations
Complexity analysis: time space tradeoff
Algorithmic notations, Big O notation
Introduction to omega, theta and little o
notation
2. Basic Concepts and Notations
Algorithm: Outline, the essence of a
computational procedure, step-by-step
instructions
Program: an implementation of an algorithm in
some programming language
Data Structure: Organization of data needed to
solve the problem
3. Classification of Data Structures
Data Structures
Primitive
Data Structures
Non-Primitive
Data Structures
Linear
Data Structures
Non-Linear
Data Structures
• Integer
• Real
• Character
• Boolean
• Array
• Stack
• Queue
• Linked List
• Tree
• Graph
4. Data Structure Operations
Data Structures are processed by using certain operations.
1.Traversing: Accessing each record exactly once so that certain
items in the record may be processed.
2.Searching: Finding the location of the record with a given key
value, or finding the location of all the records that satisfy one or
more conditions.
3.Inserting: Adding a new record to the structure.
4.Deleting: Removing a record from the structure.
5. Special Data Structure-
Operations
• Sorting: Arranging the records in some logical order
(Alphabetical or numerical order).
• Merging: Combining the records in two different sorted
files into a single sorted file.
6. Algorithmic Problem
Infinite number of input instances satisfying the
specification. For example: A sorted, non-
decreasing sequence of natural numbers of non-
zero, finite length:
1, 20, 908, 909, 100000, 1000000000.
3.
Specification
of input ?
Specification
of output as a
function of
input
7. Algorithmic Solution
Algorithm describes actions on the input
instance
Infinitely many correct algorithms for the same
algorithmic problem
Specification
of input
Algorithm
Specification
of output as a
function of
input
8. What is a Good Algorithm?
Efficient:
Running time
Space used
Efficiency as a function of input size:
The number of bits in an input number
Number of data elements(numbers, points)
9. Complexity analysis
Why we should analyze algorithms?
Predict the resources that the algorithm requires
Computational time (CPU consumption)
Memory space (RAM consumption)
Communication bandwidth consumption
The running time of an algorithm is:
The total number of primitive operations executed
(machine independent steps)
It is a determination of order of magnitude of statement.
Also known as algorithm complexity
10. Time Complexity
Worst-case
An upper bound on the running time for any input
of given size
Average-case
Assume all inputs of a given size are equally likely
Best-case
The lower bound on the running time
11. Time Complexity – Example
Sequential search in a list of size n
Worst-case:
n comparisons
Best-case:
1 comparison
Average-case:
n/2 comparisons
12. time space tradeoff
A time space tradeoff is a situation where the
memory use can be reduced at the cost of slower
program execution (and, conversely, the
computation time can be reduced at the cost of
increased memory use).
A space-time or time-memory tradeoff is a way of
solving a problem or calculation in less time by using
more storage space (or memory), or by solving a
problem in very little space by spending a long time.
13. time space tradeoff
As the relative costs of CPU cycles, RAM space, and
hard drive space change—hard drive space has for
some time been getting cheaper at a much faster rate
than other components of computers—the
appropriate choices for time space tradeoff have
changed radically.
Often, by exploiting a time space tradeoff, a program
can be made to run much faster.
14. Asymptotic notations
Algorithm complexity is rough estimation of
the number of steps performed by given
computation depending on the size of the
input data
Measured through asymptotic notation
O(g) where g is a function of the input data
size
Examples:
Linear complexity O(n) – all elements are processed once
(or constant number of times)
Quadratic complexity O(n2
) – each of the elements is
processed n times
25. Big O notation
f(n)=O(g(n)) iff there exist a positive constant c
and non-negative integer n0 such that
f(n) cg(n) for all nn0.
g(n) is said to be an upper bound of f(n).
26. Basic rules
1. Nested loops are multiplied together.
2. Sequential loops are added.
3. Only the largest term is kept, all others are
dropped.
4. Constants are dropped.
5. Conditional checks are constant (i.e. 1).
32. At first you might say that the upper bound is
O(2n); however, we drop constants so it becomes
O(n)
33. Example 4
//linear
for(int i = 0; i < n; i++) {
cout << i << endl;
}
//quadratic
for(int i = 0; i < n; i++) {
for(int j = 0; j < n; j++){
//do constant time stuff
}
}
34. Ans : In this case we add each loop's Big O, in this
case n+n^2. O(n^2+n) is not an acceptable
answer since we must drop the lowest term. The
upper bound is O(n^2). Why? Because it has the
largest growth rate
35. Example 5
for(int i = 0; i < n; i++) {
for(int j = 0; j < 2; j++){
//do stuff
}
}
36. Ans: Outer loop is 'n', inner loop is 2, this we
have 2n, dropped constant gives up O(n)
#3:PRIMITIVE DATATYPE
The primitive data types are the basic data types that are available in most of the programming languages. The primitive data types are used to represent single values.
NON PRIMITIVE DATATYPES
The data types that are derived from primary data types are known as non-Primitive data types. These datatypes are used to store group of values.
#4:목차
자바의 생성배경
자바를 사용하는 이유
과거, 현재, 미래의 자바
자바의 발전과정
버전별 JDK에 대한 설명
자바와 C++의 차이점
자바의 성능
자바 관련 산업(?)의 경향
#5:목차
자바의 생성배경
자바를 사용하는 이유
과거, 현재, 미래의 자바
자바의 발전과정
버전별 JDK에 대한 설명
자바와 C++의 차이점
자바의 성능
자바 관련 산업(?)의 경향
