Podcast
Questions and Answers
What must an algorithm do with respect to all instances of the problem it aims to solve?
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?
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?
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?
What distinguishes the semantics of an algorithm from its syntax?
What is a risk when an algorithm is syntactically correct but semantically incorrect?
What is a risk when an algorithm is syntactically correct but semantically incorrect?
What distinguishes an algorithm from a computer program?
What distinguishes an algorithm from a computer program?
Which of the following is an example of a problem statement for an algorithm?
Which of the following is an example of a problem statement for an algorithm?
What requirement must a correct algorithm fulfill?
What requirement must a correct algorithm fulfill?
What does the term 'deterministic' imply in the context of an algorithm?
What does the term 'deterministic' imply in the context of an algorithm?
Which of the following sorting algorithms is not mentioned as a solution algorithm?
Which of the following sorting algorithms is not mentioned as a solution algorithm?
What is the first step in solving a problem according to the outlined process?
What is the first step in solving a problem according to the outlined process?
What do we call a general solution derived from observing patterns in specific cases?
What do we call a general solution derived from observing patterns in specific cases?
Which of the following best describes an algorithm?
Which of the following best describes an algorithm?
Why is it important to study algorithms?
Why is it important to study algorithms?
What is a common use case for algorithms mentioned in the examples?
What is a common use case for algorithms mentioned in the examples?
What might the process of developing an algorithm help prevent?
What might the process of developing an algorithm help prevent?
Which statement correctly describes the relationship between inputs and outputs in an algorithm?
Which statement correctly describes the relationship between inputs and outputs in an algorithm?
What is one characteristic of the problems that algorithms aim to address?
What is one characteristic of the problems that algorithms aim to address?
Flashcards
Algorithm
Algorithm
A step-by-step procedure for solving a problem efficiently using limited resources (time, space, bandwidth).
Problem Solving
Problem Solving
A process that starts with defining a problem, considers possible solutions, and selects the optimal one before applying it. If it doesn't work, you start over.
Algorithm Input
Algorithm Input
The data or starting point provided to an algorithm.
Algorithm Output
Algorithm Output
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Algorithm Analysis
Algorithm Analysis
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Algorithm Complexity
Algorithm Complexity
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Algorithm Verification
Algorithm Verification
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Problem Definition
Problem Definition
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Algorithm vs. Program
Algorithm vs. Program
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Problem statement
Problem statement
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Problem Example
Problem Example
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Solution Algorithms
Solution Algorithms
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Algorithm Problem Instance
Algorithm Problem Instance
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Problem with Infinite Instances
Problem with Infinite Instances
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Algorithm: Correct & Efficient
Algorithm: Correct & Efficient
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Algorithm: Correct Syntax?
Algorithm: Correct Syntax?
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Algorithm: Correct Semantics?
Algorithm: Correct Semantics?
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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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