Algorithm Design and Analysis

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Questions and Answers

What is the definition of an algorithm?

A step-by-step process that describes how to solve a problem in a way that always gives a correct answer.

What are the three fundamental building blocks of an algorithm?

Sequencing, selection, and iteration.

Define sequencing in the context of algorithms.

Putting commands in the correct order so computers can read and execute them sequentially.

What is selection in an algorithm?

<p>Determining different sets of steps to execute based on a Boolean expression (a condition).</p>
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What is iteration in an algorithm?

<p>Executing steps a certain number of times or until a specific condition is met.</p>
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Which of the following can be used to express an algorithm? (Select all that apply)

<p>Natural languages (A), Programming languages (B), Pseudocode (C), Flow charts (D)</p>
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What are the main goals when verifying an algorithm's correctness?

<p>It must always produce the expected output for the specified range of inputs and it must terminate eventually (not run forever).</p>
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What is empirical analysis of an algorithm?

<p>Analysis based on actual experimentation and observation of results, typically by running the algorithm as a program and measuring its performance (e.g., time taken).</p>
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What is formal reasoning in the context of algorithms?

<p>Using logic and mathematical proof techniques to demonstrate an algorithm's correctness and properties over all possible valid inputs.</p>
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What are the key characteristics of an efficient algorithm?

<p>An efficient algorithm takes the least amount of time (time complexity) and memory (space complexity) possible while consistently yielding the correct result.</p>
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Explain best-case, worst-case, and average-case scenarios in algorithm analysis.

<p>Best-case: The input requires the fewest operations. Worst-case: The input requires the most operations. Average-case: The typical number of operations over likely inputs.</p>
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What do empirical measurements like execution time reveal about an algorithm, and what are their limitations?

<p>Measuring execution time empirically gives practical performance data for specific inputs and systems. However, the raw number of operations doesn't directly equate to time, as hardware and other factors influence speed.</p>
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How is the run time of algorithms typically categorized?

<p>Run time is categorized according to how the number of steps (or execution time) grows as the input size increases.</p>
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What does 'constant time' complexity mean for an algorithm?

<p>The algorithm takes a fixed number of steps regardless of the input size.</p>
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Define logarithmic time complexity.

<p>The number of steps increases proportionally to the logarithm of the input size (log n).</p>
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What is linear time complexity?

<p>The number of steps increases in direct proportion to the input size (n).</p>
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Define quadratic time complexity.

<p>The number of steps increases in proportion to the square of the input size (n^2).</p>
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What characterises exponential time complexity?

<p>The number of steps increases exponentially as the input size grows (e.g., 2^n).</p>
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What constitutes polynomial time complexity?

<p>Any run time that does not increase faster than n^k for some constant k (includes constant, logarithmic, linear, quadratic, cubic, etc.).</p>
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What is superpolynomial time complexity?

<p>Any run time that increases faster than n^k for any constant k.</p>
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How are polynomial and superpolynomial run times generally categorized in terms of problem solvability?

<p>Polynomial time is generally considered 'reasonable' or 'tractable', while superpolynomial time is considered 'unreasonable' or 'intractable' for solving problems, especially with large inputs.</p>
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What is a heuristic in the context of algorithms?

<p>A technique or shortcut that guides an algorithm to find good, but not necessarily optimal, choices quickly, often used for finding approximate solutions to computationally hard problems.</p>
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What factors are considered when analyzing the effectiveness of a heuristic?

<p>Analysis typically looks at how close its approximate solution gets to the optimal solution, how much time it saves compared to an exact algorithm, and how often scenarios leading to poor performance (worst cases) occur.</p>
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What are undecidable problems in computer science?

<p>Problems that require a yes/no answer, but for which no algorithm exists that can correctly provide the answer for all possible inputs.</p>
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Define parallel computing.

<p>A computational model that breaks programs into smaller, independent sequential operations and performs those smaller operations concurrently (in parallel) using multiple processing units.</p>
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What is a key requirement for operations to be suitable for parallel computing?

<p>The operations intended to run in parallel must be independent of each other, meaning the outcome of one does not affect the inputs or execution of another running concurrently.</p>
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What is sequential computing?

<p>The traditional computational model where a computer executes each operation of a program in a strict order, one at a time.</p>
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What is 'speedup' in parallel computing?

<p>The ratio of the time taken to run a program sequentially (using one processor) to the time taken to run the same program using parallel or distributed computing (using multiple processors/devices).</p>
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In a parallel execution, how is the minimum time taken for a set of parallel operations determined?

<p>The total time is determined by the duration of the longest individual operation among those running in parallel. Efficient systems can assign ready tasks to available processors while waiting for longer tasks.</p>
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What is hyperthreading?

<p>A technology where a single CPU core can manage and execute instructions from two different threads concurrently, provided the threads use different functional units within the core.</p>
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Define distributed computing.

<p>A model where components of a software system or a computational problem are shared among multiple independent computing devices connected via a network.</p>
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Distributed computing and parallel computing can be used together.

<p>True (A)</p>
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What is a potential drawback of distributed computing regarding performance?

<p>Performance can suffer if the time required for communication (sending messages or data) between networked devices outweighs the time saved by distributing the workload.</p>
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What is cluster computing?

<p>A form of distributed computing where multiple computers (nodes) are co-located (often in the same room or data center) and connected by a high-speed local network to work collaboratively on tasks.</p>
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How can functionality be distributed in a distributed computing system?

<p>Different parts of an application's functionality can be assigned to various computing devices based on factors like the device capabilities (processing power, memory, storage) and the time sensitivity or specific requirements of each task.</p>
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The World Wide Web is an example of a distributed computing system.

<p>True (A)</p>
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What is the definition of an algorithm?

<p>A step by step process that describes how to solve a problem in a way that always gives a correct answer</p>
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What are the three fundamental building blocks (control structures) of an algorithm?

<p>Sequencing, selection, and iteration</p>
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What is sequencing in an algorithm?

<p>Putting commands in correct order so computers can read the commands.</p>
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What is selection in an algorithm?

<p>Determining different sets of steps to execute based on a Boolean expression</p>
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What is iteration in an algorithm?

<p>Executing steps a certain number of times or until a condition is met</p>
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What are different ways an algorithm can be expressed?

<p>Pseudocode, flow charts, programming languages, natural languages</p>
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What are the main goals when verifying an algorithm?

<p>It must always produce the expected output for the range of inputs and terminate eventually</p>
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What is empirical analysis in the context of algorithms?

<p>Analysis based on actual experimentation and observation of results (tested with program)</p>
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What is formal reasoning in the context of algorithms?

<p>Only way to prove correctness over all possible inputs, use logic etc to do so</p>
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What characteristics define an efficient algorithm?

<p>Takes the least amount of time and memory while yielding the right result</p>
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What do best-case, worst-case, and average-case refer to in algorithm analysis?

<p>The situation that requires the least/most/average operations</p>
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What are empirical measurements used for in algorithm analysis, and what is their limitation?

<p>Measuring with time, number of operations does not tell us amount of time</p>
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How is the run time of algorithms typically categorized?

<p>According to how the number of steps increase as the input size increases</p>
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What is constant time complexity?

<p>Fixed number of steps no matter input size</p>
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What is logarithmic time complexity?

<p>Number of steps increases proportionally to the logarithm of the input size</p>
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What is linear time complexity?

<p>Number of steps increases in direct proportion to the input size</p>
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What is quadratic time complexity?

<p>Number of steps increases in proportion to the input size squared</p>
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What is exponential time complexity?

<p>Number of steps increase exponentially</p>
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What constitutes polynomial time complexity?

<p>Any run time that does not increase faster than n^k (constant, logarithmic, linear, quadratic, n^3)</p>
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What constitutes superpolynomial time complexity?

<p>Any run time that increases faster than n^k (exponential, factorial)</p>
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How are polynomial and superpolynomial run times generally classified in terms of feasibility?

<p>Reasonable vs unreasonable</p>
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What is a heuristic?

<p>A technique that guides an algorithm to find good choices in order to come up with approximate solutions to hard problems</p>
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How is a heuristic typically analyzed?

<p>Look at how close it gets to the perfect solution, how much time it takes, and how often the worst case happens</p>
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What are undecidable problems?

<p>Problems that should give a yes or no answer but no algorithm exists that can answer correctly on all inputs</p>
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What is parallel computing?

<p>A computational model that breaks programs into smaller sequential operations and performs those smaller operations in parallel</p>
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What property must operations have for parallel computing to be effective?

<p>The operations must be independent of each other</p>
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What is sequential computing?

<p>The computer executes each operation of the program in order one at a time (standard)</p>
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What is speedup in the context of parallel/distributed computing?

<p>The ratio of the the time taken to run the program sequentially to the time taken to run it with parallel/distributed computing. Used to compare and measure benefits</p>
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How long will the parallel portion of a program take relative to the length of its operations?

<p>As long as the longest operation, but can send tasks to which process is ready to do multiple while waiting</p>
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What is hyperthreading?

<p>When a single CPU core can run two threads concurrently as long as the threads are doing different types of computations that utilize different parts of the CPU</p>
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What is distributed computing?

<p>Distributes a problem across multiple networked computing devices</p>
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Can distributed and parallel computing be used together?

<p>yes</p>
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What is a potential drawback of distributed computing?

<p>Performance can suffer if time to send messages is greater than time saved by distributing</p>
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What is cluster computing?

<p>Co-located computers on a local network that all work on similar tasks - reduces communication time, expensive, but can get through companies with cloud computing services now</p>
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How might functionality be distributed in a distributed computing system?

<p>Split different pieces of functionality across computing devices according to capability of devices and time sensitivity of task</p>
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Is the World Wide Web an example of distributed computing?

<p>Yes</p>
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What is the definition of an algorithm?

<p>A step by step process that describes how to solve a problem in a way that always gives a correct answer.</p>
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What are the three fundamental building blocks of an algorithm?

<p>Sequencing, selection, and iteration.</p>
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What is sequencing in the context of algorithms?

<p>Putting commands in correct order so computers can read the commands.</p>
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What is selection in the context of algorithms?

<p>Determining different sets of steps to execute based on a Boolean expression.</p>
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What is iteration in the context of algorithms?

<p>Executing steps a certain number of times or until a condition is met.</p>
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In what ways can an algorithm be expressed?

<p>Pseudocode, flow charts, programming languages, natural languages.</p>
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What are the main goals when verifying an algorithm?

<p>It must always produce the expected output for the range of inputs and terminate eventually.</p>
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What is empirical analysis of an algorithm?

<p>Analysis based on actual experimentation and observation of results (tested with program).</p>
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What is formal reasoning about an algorithm?

<p>Only way to prove correctness over all possible inputs, use logic etc to do so.</p>
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What characteristics define an efficient algorithm?

<p>Takes the least amount of time and memory while yielding the right result.</p>
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Define best case, worst case, and average case analysis for algorithms.

<p>The situation that requires the least/most/average operations respectively.</p>
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What are empirical measurements in the context of algorithm analysis?

<p>Measuring with time, number of operations does not tell us amount of time.</p>
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How is the run time of an algorithm typically categorized?

<p>According to how the number of steps increase as the input size increases.</p>
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What does constant time complexity mean?

<p>Fixed number of steps no matter input size.</p>
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What does logarithmic time complexity mean?

<p>Number of steps increases proportionally to the logarithm of the input size.</p>
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What does linear time complexity mean?

<p>Number of steps increases in direct proportion to the input size.</p>
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What does quadratic time complexity mean?

<p>Number of steps increases in proportion to the input size squared.</p>
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What does exponential time complexity mean?

<p>Number of steps increase exponentially.</p>
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What is polynomial time complexity?

<p>Any run time that does not increase faster than n^k (constant, logarithmic, linear, quadratic, n^3).</p>
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What is superpolynomial time complexity?

<p>Any run time that increases faster than n^k (exponential, factorial).</p>
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How are polynomial and superpolynomial run times generally characterized in terms of practicality?

<p>Reasonable vs unreasonable.</p>
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What is a heuristic?

<p>A technique that guides an algorithm to find good choices in order to come up with approximate solutions to hard problems.</p>
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How is a heuristic typically analyzed?

<p>Look at how close it gets to the perfect solution, how much time it takes, and how often the worst case happens.</p>
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What are undecidable problems?

<p>Problems that should give a yes or no answer but no algorithm exists that can answer correctly on all inputs.</p>
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What is parallel computing?

<p>A computational model that breaks programs into smaller sequential operations and performs those smaller operations in parallel.</p>
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What condition must be met for operations to be suitable for parallel computing?

<p>The operations must be independent of each other.</p>
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What is sequential computing?

<p>The computer executes each operation of the program in order one at a time (standard).</p>
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What is speedup in parallel computing?

<p>The ratio of the the time taken to run the program sequentially to the time taken to run it with parallel/distributed computing. Used to compare and measure benefits.</p>
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In parallel computing, how long does the parallel portion of a program take relative to the length of its operations?

<p>As long as the longest operation, but can send tasks to which process is ready to do multiple while waiting.</p>
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What is hyperthreading?

<p>When a single CPU core can run two threads concurrently as long as the threads are doing different types of computations that utilize different parts of the CPU.</p>
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What is distributed computing?

<p>Distributes a problem across multiple networked computing devices.</p>
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Can distributed and parallel computing be used together?

<p>True (A)</p>
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What is a potential drawback of distributed computing?

<p>Performance can suffer if time to send messages is greater than time saved by distributing.</p>
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What is cluster computing?

<p>Co-located computers on a local network that all work on similar tasks - reduces communication time, expensive, but can get through companies with cloud computing services now.</p>
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How is functionality distributed in distributed computing?

<p>Split different pieces of functionality across computing devices according to capability of devices and time sensitivity of task.</p>
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Is the World Wide Web an example of distributed computing?

<p>True (A)</p>
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Flashcards

Algorithm Definition

A step by step process to solve a problem with a correct answer.

Three Blocks of an Algorithm

Sequencing, selection, and iteration are the fundamental building blocks.

Sequencing

Arranging commands in the correct order for computer execution.

Selection

Choosing different sets of steps based on a Boolean condition.

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Iteration

Repeating steps a certain number of times or until a condition is met.

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Expressing an Algorithm

Pseudocode, flow charts, programming, and natural languages can all express algorithms.

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Verifying an Algorithm

Produce the expected output for all valid inputs and must eventually stop.

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Empirical Analysis

Analysis based on experimentation and observation of results.

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Formal Reasoning

Using logic to prove correctness over all possible inputs.

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Efficient Algorithm

The efficient algorithm takes the least time and memory while yielding the right result.

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Best/Worst/Average Case

The situation that requires the least/most/average number of operations.

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Empirical Measurements

Measuring time, as the number of operations does not tell the full story.

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Categorizing Run Time

Categorizing by how the number of steps increases as the input size increases.

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Constant Time

A fixed number of steps regardless of input size.

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Logarithmic Time

Steps increase proportionally to the logarithm of the input size.

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Linear Time

Steps increase in direct proportion to the input size.

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Quadratic Time

Steps increase in proportion to the square of the input size.

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Exponential Time

Steps increase exponentially with input size.

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Polynomial Time

Any run time that does not increase faster than n^k.

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Superpolynomial Time

Any run time that increases faster than n^k.

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Polynomial vs. Superpolynomial

Polynomial time is considered reasonable, superpolynomial is unreasonable.

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Heuristic

A technique that guides an algorithm to find good, approximate solutions to hard problems.

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Analyze a Heuristic

Assess closeness to the perfect solution, time taken, and frequency of worst-case scenarios.

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Undecidable Problems

Problems that should return yes/no but where no algorithm can answer correctly for all inputs.

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Parallel Computing

Breaking programs into smaller operations and performing them simultaneously.

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Parallel Computing Requirements

Operations must be independent of each other to enable parallel processing.

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Sequential Computing

Computer executes operations sequentially, one at a time (standard).

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Speedup

Ratio of sequential run time to parallel run time; measures benefits of parallelization.

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Parallel Program Time

Parallel portion of program will take as long as the longest operation.

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Hyperthreading

When a single CPU core can run two threads concurrently doing different computations.

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Distributed Computing

Distributing a problem across multiple networked computing devices.

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Distributed and Parallel

Yes, distributed and parallel computing can be combined.

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Drawback of Distributed Computing

Performance suffers if message sending time exceeds time saved by distributing.

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Cluster Computing

Co-located computers on a local network working on similar tasks.

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Distributed Functionality

Split different functionalities across computing devices based on capability and time sensitivity.

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Is the Web Distributed?

Yes, the web is an example of distributed computing.

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Study Notes

  • An algorithm is a step-by-step process for solving a problem that consistently provides the correct answer.

Algorithm Blocks

  • Algorithms are built upon sequencing, selection, and iteration.

Sequencing

  • Sequencing involves arranging commands in the correct order for computer execution.

Selection

  • Selection is choosing different sets of steps based on Boolean expressions.

Iteration

  • Iteration means repeating steps a specific number of times or until a condition is satisfied.

Algorithm Expression

  • Algorithms can be expressed through pseudocode, flow charts, programming languages, and natural languages.

Verifying Algorithm Goals

  • An algorithm must produce the expected output for all inputs and eventually stop.

Empirical Analysis

  • Empirical analysis relies on experimentation and observation of results, usually tested with a program.

Formal Reasoning

  • Formal reasoning uses logic to prove correctness across all possible inputs.

Efficient Algorithms

  • Efficient algorithms use the least time and memory while providing the correct result.

Algorithm Cases

  • Algorithms have best, worst, and average-case scenarios relating to operational requirements.

Empirical Measurements

  • Empirical measurements use time, as the number of operations doesn't always indicate time.

Run Time Categorization

  • Run time is categorized by how the number of steps increases with input size.

Constant Time

  • Constant time means a fixed number of steps, regardless of input size.

Logarithmic Time

  • Logarithmic time means the number of steps increases proportionally to the logarithm of the input size.

Linear Time

  • Linear time means the number of steps increases in direct proportion to the input size.

Quadratic Time

  • Quadratic time means the number of steps increases proportionally to the square of the input size.

Exponential Time

  • Exponential time means the number of steps increases exponentially.

Polynomial Time

  • Polynomial time includes run times that don't increase faster than n^k.
  • This includes: constant, logarithmic, linear, quadratic, and n^3.

Superpolynomial Time

  • Superpolynomial time includes run times that increase faster than n^k.
  • This includes: exponential and factorial.

Polynomial vs Superpolynomial

  • Polynomial run time is considered reasonable, while superpolynomial is unreasonable.

Heuristic

  • A heuristic is a technique that guides an algorithm to find good approximate solutions to difficult problems.

Heuristic Analysis

  • Heuristics are analyzed by proximity to the perfect solution, time taken, and frequency of worst-case scenarios.

Undecidable Problems

  • These problems require a yes or no answer, but no algorithm can answer correctly for all inputs.

Parallel Computing

  • This computational model divides programs into smaller operations and executes them in parallel.
  • This requires operations to be independent of each other.

Sequential Computing

  • Sequential computing means the computer executes each operation of a program in order.

Speedup Measurement

  • Speedup is the ratio of sequential to parallel execution time, measuring benefits.

Parallel Program Length

  • The duration of the parallel portion of a program equates to the longest operation.
  • Tasks can be assigned to whichever process is ready.

Hyperthreading

  • A single CPU core runs two threads if they use different parts of the CPU.

Distributed Computing

  • Distributed computing spreads a problem across multiple networked devices.
  • Distributed and parallel computing can be used together.

Distributed Computing Drawbacks

  • Performance suffers if message sending time exceeds time saved.

Cluster Computing

  • Co-located computers on a local network work on similar tasks, reducing communication time, but is expensive.
  • Cloud computing services mitigate expenses.

Distribution of Functionality

  • Functionality is split across computing devices by capability and time sensitivity.

Web as Distributed Computing

  • The web is an example of distributed computing.

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