1. Introduction to The Design & Analysis of Algorithms
Lecture:Hao Wu
Mobil:

2. Contents Introduction
Fundamentals of the Analysis of Algorithm Efficiency
Brute Force
Divide-and-Conquer
Decrease-and-conquer
Transform-and-conquer

3. Contents(continuous)
Space and Time Tradeoffs
Dynamic Programming
Greedy Technique
Limitations of Algorithm Power
Coping with Limitations of Algorithm Power

4. Introduction Notion of Algorithm
Fundamentals of Algorithmic Problem Solving
Important Problem Types
Fundamental Data Structures

5. Notion of Algorithm
An algorithm is a sequence unambiguous instructions for solving problem,i.e.,for obtaining a required output for any legitimate input in a finite amount of time.

6. Euclid algorithm
Step 1: If n=0,return the value of m. otherwise proceed to Step 2.
Step 2: r=m%n
Step 3:m← n,n← r. Go to step 1;
m,n,r1,r2,……rk,0
m,n>r1 >r2,……>rk>0
rk = GCD(m,n)=GCD(n,r1)=….

7. Consecutive integer checking algorithm(pseudocode)
t ←min(m,n)
While(m%t||n%t)
--t;
Return t;

8. Middle school procedure for computing gcd(m,n)
Step 1:Find the prime factors of m;
Step 2:Find the prime factors of n;
Step 3:Find the common factor(s).
p1≤p2≤p3≤p4…
Gcd(m,n)= p1*p2*p3*p4…

9. Algorithm for finding the list of primes not exceeding n
p is a prime,2p,3p,…,kp are not primes. …
…(p=2)
…(p=3)
If n<p2,and is not a prime,not remain on the list on the earlier passes.

10. Algorithm Sieve(n) //Implements the sieve of Eratosthenes
//Input :A positive integer
//Output:Array L of all prime numbers ≤n
For p=2 to n do a[p]=p
For p=2 to sqrt(n) do
if a[p] is a prime
j=p*p
while j ≤n do a[j]=0
j=j+p
for p=2 to n do
l[i]=p
i=i+1
Return L

11. Fundamentals of Algorithmic Problem Solving
Choosing between exact and approximate problem solving
Deciding on appropriate data structure
Algorithm design techniques
Method of specifying an algorithm
Proving an algorithm’s correctness
Analyzing an algorithm
Coding an algorithm

12. Important Problem Types
Sorting
Searching
String processing
Graph problems
Combinatorial problem
Geometric problems
Numerical problems

13. Fundamental Data Structures
Linear Data Structures
Graphs
Trees
Sets and Dictionaries