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Overview of the course
Course homepage and discussion board
• sign up at
• It is recommended to ask questions on the Board instead of directly
Emailing the teaching staffs.
Grading will be done as follows:
• biweekly homework: 20%
• midterm: 40%
• final: 40%
• class and piazza participation & bonus problem: adjust borderline
Homework Policy
• Written homeworks are due at the start of class on their due date.
• If you do not know the answer of question, you will receive 15% of
the grade for the problem if you admit it up-front by writing “I don’t
know how to solve this problem” and nothing else. If your solution is
wrong, you get a score of 0 for that problem.
• You are encouraged to work in groups of 2 or 3. On all assignments
each person should hand-in their own writeup. That is, collaboration
should be limited to talking about the problems, so that your writeup
is written entirely by you alone, in your own words.
Homework Policy
• We will not accept late submission. To offset this strict policy,
• we will drop the lowest homework grade in the end so that the occasional absence
won’t hurt you.
• each individual student has a single 48 hours pass. This pass can be used to extend
the deadline for one homework by 48 hours.
• We prefer that you type up your solutions (preferably using LaTeX). You
may neatly hand-write your solutions, but if we have trouble reading them
you will be required to type up future solutions.
• If you find a solution from any other source, you must rewrite entirely
using your own words and cite properly.
• The TA rules when it comes to grading homework; their decisions are final.
However, they will be available to listen to your explanations.
Recommend Textbook for reading
• Introduction to Algorithms, by Cormen, Leiserson, Rivest, and Stein
(hereafter referred to as "CLRS").
• Algorithm Design by J. Kleinberg and E. Tardos (hereafter refererred
as "KT").
What is an algorithm?
• Any well defined computational procedure that takes some value, of
set of values, as input and produces some value, or set of values, as
output for a well defined computation problem.
Input:integer 𝑛
Output: then 𝑛-th Fibonacci number
What is the 𝑛-th Fibonacci number?
Definition of Fibonacci number. 𝐹0 = 0, 𝐹1 = 1, 𝐹𝑛 = 𝐹𝑛−1 + 𝐹𝑛
Alg 1.
Function f(n)
If n=0: return 1
If n =1: return 1
Return f(n-1)+f(n-2)
Things we care about an algorithm
• Performance
• Running time
• Space
• Correctness
Running time of the algorithm
Function f(n)
If n=0: return 1
If n =1: return 1
Return f(n-1)+f(n-2)
Why is this a bad running time?
Current State of Arts
Moore’s law
• Moore's law: the computing power doubles approximately every two
Algorithm 2.
Function f(n)
Create an array 𝐴 0 … 𝑛
A[0] =1, A[1] =1
For (i= 2..n)
A[i] = A[i-1]+A[i-2]
Return A[n]
Running time?
What will be covered in this course?
• Data Structure
• Algorithm Design Techniques
• Algorithm Analysis Techniques
Data structures:
We assume you already know what is a binary tree, head, and linked
• Treap
• Binomial heap
• Union find
• hasing
Design Techniques
• Greedy algorithm
• Dynamic programming
• Divide and Conquer
• Network Flow
• Linear Programming
• Randomized Algorithms
• DFS and BFSReduction
Tools for analyzing algorithms
• Asymptotic Analysis
• Amortized Analysis
• Probabilistic Analysis
Intractability and Complexity Theory
• Complexity class such as NP, coNP, RP,
• Reduction