Questions and Answers
What is an algorithm?
A finite set of precise instructions for solving a problem
Which of the following is NOT true about algorithms?
Algorithms are language-dependent
What is the role of pseudocode in algorithms?
Pseudocode is a way to represent algorithms using a mix of natural language and programming language constructs
Which of the following best describes an algorithm?
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Why are algorithms considered unambiguous specifications?
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What is the purpose of pseudocode in programming?
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In programming, what is the role of a flowchart?
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What does the term 'final grade' represent in the context of the provided algorithm?
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How does pseudocode differ from a specific programming language?
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What is the first step in problem-solving according to James Tam's approach?
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Why is it essential to refine an algorithm successively according to James Tam?
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What is the origin of the word 'algorithm'?
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Which algorithm did Greek mathematicians use for finding prime numbers?
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What was one of the problems addressed by the algorithms mentioned in the text?
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What was David Hilbert's contribution to the modern concept of algorithm?
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Which approach is described as 'Top-Down' in developing an algorithm?
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What is Euclid's algorithm used for?
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Study Notes
History of Algorithms
- Ancient Babylonian mathematicians used arithmetic algorithms around 2500 BC
- Egyptian mathematicians used algorithms around 1550 BC
- Greek mathematicians used algorithms in the sieve of Eratosthenes for finding prime numbers
- The word "algorithm" is derived from the 9th-century Persian mathematician Muḥammad ibn Mūsā al-Khwārizmī
Characteristics of Algorithms
- An algorithm is a finite set of precise instructions for performing a computation or solving a problem
- Algorithms are specific, unambiguous, and language-independent
- A program is a type of algorithm, but not all algorithms are programs
- Examples of algorithms include directions to somebody's house, a recipe for cooking a cake, and the steps to compute the cosine of 90°
Types of Algorithms
- Easy algorithms: finding the largest or smallest value in a list, finding a specific value in a list
- Medium-difficulty algorithms: sorting a list
- Hard algorithms: finding the shortest path between two locations
- Essentially impossible algorithms: factoring large composite numbers
Developing an Algorithm
- Top-down approach: abstract general approach, specific steps, and particular bottom
- Steps in problem solving: produce a general algorithm, refine the algorithm successively, implement the program in a programming language
Pseudocode and Algorithm
- Pseudocode is an artificial and informal language that helps programmers develop algorithms
- Pseudocode is similar to everyday English
- Example: write an algorithm to determine a student's final grade and indicate whether it's passing or failing
Flowcharts
- A schematic representation of a sequence of operations
- A graphical representation of the sequence of operations in an information system or program
- Flowcharts show how data flows from source documents through the computer to final distribution to users
Computer Software
- A model for creating computer software: specify the problem, implement the design, maintain the design
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