1. Revision of C++

2. // function returning the max between two numbers
int max(int num1, int num2)
{ // local variable declaration int result;
if (num1 > num2) result = num1;
else result = num2; return result; }

3. Primitive operations Assigning a value to a variable
Calling a function
Performing an arithmetic operation
Comparing two values
Indexing to an array
Returning from a function

4. Describe: in natural language / pseudo- code / diagrams / etc.
Algorithm: Finite set of instructions that, if followed, accomplishes a particular task.
Describe: in natural language / pseudo- code / diagrams / etc.
Often more important than space complexity
space available (for computer programs!) tends to be larger and larger
time is still a problem for all of us
Algorithm Analysis I Weiss, chap.2

5. Algorithm Analysis Space complexity Time complexity
How much space is required
Time complexity
How much time does it take to run the algorithm
Often, we deal with estimates!

6. Pseudocode High-level description of an algorithm.
Algorithm arrayMax(A, n)
Input array A of n integers
Output maximum element of A
currentMax  A[0]
for i  1 to n  1 do
if A[i]  currentMax then
currentMax  A[i]
return currentMax
Example: find the max element of an array
High-level description of an algorithm.
More structured than plain English.
Less detailed than a program.
Preferred notation for describing algorithms.
Hides program design issues.
Algorithm Analysis I Weiss, chap.2

7. Best, worst, average-case time
We usually consider the worst-case while analyzing an algorithm
See pages in Malik
See examples with false condition loop

8. Running time
Suppose the program includes an if-then statement that may execute or not:  variable running time
Typically algorithms are measured by their worst case

9. Big-O notation f(n) = O(n) Reads: f(n) is Big-Oh of n Why?
It is becoming increasingly exact as a variable approaches a limit, usually infinity.
See Malik page 14

10. Algorithm Analysis (Time complexity)
The driver examples first 2N
N*N
2n and n*n, with real values of n … (Malik page 10)
By analyzing a particular algorithm, we usually count the number of Primitive Operations

11. Equation for running time = c1. n + d1 Time complexity is O(n)
What is the time complexity of search?
Binary Search algorithm at work
O(log n)
Sequential search?
O(n)
Equation for running time = c1. n + d1
Time complexity is O(n)

12. Examples
O(1)
  1. Accessing Array Index (int a = ARR[5];) Inserting a node in Linked List Pushing and Poping on Stack
O(n) time 1. Traversing an array 2. Traversing a linked list 3. Linear Search

13. O(log n) time Binary Search Finding largest/smallest number in a binary search tree
O(nlogn) time Merge Sort

14. Classes and Constructors

15. The end