1. Basics Prof. Hsin-Mu (Michael) Tsai (蔡欣穆)
Department of Computer Science and Information Engineering
National Taiwan University

2. What is an algorithm?
A computable set of steps to achieve a desired result.
All algorithm must satisfy the following criteria:
Input
Output
Definiteness
Finiteness
Effectiveness
Input: there are zero or more quantities that are externally supplied. Output: At least one quantity is produced.
Definiteness: each instruction is clear and unambiguous. Finiteness: if we trace out instructions of an algorithm, then for all cases, the algorithm terminates after a finite number of steps.
Effectiveness: every instruction must be basic enough to be carried out, in principle, by a person using only pencil and paper. (must be feasible)
data structure and algorithm I
hsin-mu tsai, fall 2010

3. example
Statement 1: “Is n=2 the largest value of n for which there exist positive integers x, y, and z such that 𝑥 𝑛 + 𝑦 𝑛 = 𝑧 𝑛 has a solution?”
Statement 2: “Store 5 divided by zero into x and go to statement ㄆ.”
Which criterion do they violate?
Input
Output
Definiteness
Finiteness
Effectiveness
data structure and algorithm I
hsin-mu tsai, fall 2010