1. Data Structures and Algorithms (AT70. 02) Comp. Sc. and Inf. Mgmt
Data Structures and Algorithms (AT70.02) Comp. Sc. and Inf. Mgmt. Asian Institute of Technology
Instructor: Prof. Sumanta Guha
Slide Sources: CLRS “Intro. To Algorithms” book website
(copyright McGraw Hill)
adapted and supplemented

2. CLRS “Intro. To Algorithms” Ch. 3: Growth of Functions

4. More to Discuss o-notation
Monotonically/strictly increasing/decreasing
Floors and ceilings
Modular arithmetic
Fibonacci numbers:
0, i = 0
Fi = 1, i = 1
Fi-1 + Fi-2, i  2
How to write code to compute Fibonacci numbers (recursively or iteratively)?
lg* n = min{i: lg(i) n ≤ 1}

5. Problems Ex
Is 2n+1 = O(2n)? Is 22n = O(2n)? Ex
Prove Theorem 3.1.
Theorem 3.1
For any two functions f (n) and g(n), we have f (n) = θ(g(n)) if and only if f (n) = O(g(n)) and f (n) = Ω(g(n)). Ex
Prove equation (3.15).
a logb c = c logb a (3.15)