CS/IT 341 Algorithms Lecture 1

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Questions and Answers

What must an algorithm do with respect to all instances of the problem it aims to solve?

Have a varying number of outputs

Work correctly on all instances of the problem (correct)

Provide correct outputs only for some instances

Only run efficiently for the average case

Which of the following describes a characteristic of a correctly functioning algorithm?

It must consist of an ordered sequence of precise steps (correct)

It should run indefinitely for an unspecified input

It may have an ambiguous sequence of instructions

It can have an infinite number of instructions

Which property of algorithms is crucial to ensure they will finish running?

Correctness

Termination (correct)

Efficiency

Completeness

What distinguishes the semantics of an algorithm from its syntax?

Semantics deal with the meaning of instructions Signup and view all the answers

What is a risk when an algorithm is syntactically correct but semantically incorrect?

It can lead to erroneous results without syntax errors Signup and view all the answers

What distinguishes an algorithm from a computer program?

An algorithm is a general set of instructions, while a program is a specific implementation in code. Signup and view all the answers

Which of the following is an example of a problem statement for an algorithm?

Given an array of numbers, sort them into non-decreasing order. Signup and view all the answers

What requirement must a correct algorithm fulfill?

It must return a correct output for every possible input. Signup and view all the answers

What does the term 'deterministic' imply in the context of an algorithm?

The algorithm provides a single and predictable output for any given input. Signup and view all the answers

Which of the following sorting algorithms is not mentioned as a solution algorithm?

Bubble Sort Signup and view all the answers

What is the first step in solving a problem according to the outlined process?

Clearly define the problem Signup and view all the answers

What do we call a general solution derived from observing patterns in specific cases?

Algorithm Signup and view all the answers

Which of the following best describes an algorithm?

A step-by-step procedure for solving problems Signup and view all the answers

Why is it important to study algorithms?

They help avoid unnecessary coding and testing Signup and view all the answers

What is a common use case for algorithms mentioned in the examples?

Cooking recipes Signup and view all the answers

What might the process of developing an algorithm help prevent?

Wasting time on impractical solutions Signup and view all the answers

Which statement correctly describes the relationship between inputs and outputs in an algorithm?

An algorithm processes an input collection to produce a correct output collection Signup and view all the answers

What is one characteristic of the problems that algorithms aim to address?

They can often be classified by complexity Signup and view all the answers

Study Notes

Course Information

Course: CS/IT 341
Course Title: Algorithms Analysis and Design
Lecture: 1

Solving Problems (1)

Problem Solving Steps:
- Clearly define the problem.
- Think of possible solutions.
- Select the best solution based on current circumstances.
- Apply the selected solution.
- If the solution works, proceed; otherwise, return to step 2.

Solving Problems (2)

Common approach: solve a problem for specific cases, analyze patterns and trends to develop a general solution (algorithm).

Algorithm Definition

Algorithm: a step-by-step procedure for solving a problem using finite resources (time, space, bandwidth).
Algorithm (more general): any well-defined computational procedure that takes input, processes it using defined resources, and produces output.

Algorithm Examples

Repairing a lamp
Cooking a recipe
Calling a friend
Playing a game
Driving directions
Car repair manual
Human Brain Project
Internet communication links (graph)
Matrix multiplication

Why Study Algorithms (1)

Real-time systems: Prove algorithm termination within a specified time.
Identify optimal solutions: Determine the best and fastest solution without extensive testing.
Complex problems: Some problems lack practical algorithms within complexity classes.

Why Study Algorithms (2)

Web search, packet routing, file sharing
Human genome project, protein folding
Circuit layouts, compilers
Video games, virtual reality
Cell phones, ecommerce, voting machines
Multimedia (MP3, JPG, HDTV)
Social networks (recommendations, newsfeeds)
Physics: N-body simulation, particle collisions

Why Study Algorithms (3)

Programmer: Develops a working solution
Client: Wants efficient problem solutions
Theorist: Wants to understand
Practical reason: Avoid performance bugs.

Why Study Algorithms (4)

Program practical input size.
Program running slow.
Program running out of memory

Algorithm vs. Program

Program: concrete representation of an algorithm in programming language.
Algorithm: A sequence of instructions describing how to do a task

One Problem, Many Algorithms (1)

Problem statement: Specifies desired input/output relationship.
Binary relationship: Input to output
Verifiable property: Describes correct outputs for inputs.
Specific instance: (e.g., pair of students with same birthday in a room)
General instance: (e.g. pair of students with same birthday in a large group)
Pigeonhole principle: When input size exceeds the number of outputs, a guaranteed pair exists.

One Problem, Many Algorithms (2)

Algorithm: Specific computational procedure for achieving input/output relationship.
Deterministic: Each input maps to a single output.
Problem example: Sorting a sequence of numbers into non-decreasing order.
Solution algorithms: Merge sort, quick sort, heap sort

Problem Instances

Input sequence = problem instance
Algorithms must correctly handle all instances of a problem.
Finite resources: limit instances to manageable numbers in practical situations.

Problem-Algorithm Example

Problem: Find two students with the same birthday, given student list.
Algorithm:
- Create empty record of names/birthdays.
- Interview each student and check for matching birthdays.
- If match found, return pair.
- Store interviewed student's data in the record.
- If no match occurs, return None (no such pair).

Properties of Algorithms

Ordered sequence of precise steps.
Finite number of well-defined instructions/steps.
Unambiguous instruction sequence
Correct results
Termination required

Syntax & Semantics

Algorithm is correct if semantics and syntax are correct.
Semantics: Embedded concept, the "soul"
Syntax: Representation of the algorithm, the "body"

Algorithm Summary

Problem Statement: Input/output relationship
Algorithm: Procedure to achieve the relationship
Definition: Sequence of steps to transform input to output
Instance: Input data used for problem computation
Correct Algorithm: Returns correct output for all inputs; halts.

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Description

This quiz covers the fundamental concepts introduced in Lecture 1 of the CS/IT 341 course on Algorithms Analysis and Design. It focuses on the problem-solving steps, algorithm definitions, and practical examples of algorithms in various contexts. Test your understanding of the crucial components of algorithm design and analysis.