Algorithms, flowcharts and pseudocode

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课程笔记

What is an Algorithm?

An algorithm is a precise sequence of instructions that solves a problem or performs a computation.
It must be finite – it stops eventually after a finite number of steps.
Algorithms are used as specifications for calculations and data processing.
They can be expressed in flowcharts, pseudocode, or a programming language.
A heuristic is a problem-solving approach without a well-defined correct result (e.g., social media recommendations).

An algorithm is a finite, unambiguous sequence of steps that turns an input into an output.

Expressing Algorithms: Flowcharts

A flowchart uses standard symbols to show the steps of an algorithm visually.
Oval (terminator) – start and end of the algorithm.
Rectangle (process) – a calculation or action (e.g., 'Add 1 to count').
Diamond (decision) – a yes/no question that branches the flow.
Parallelogram (input/output) – reading data or displaying results.
Arrows show the flow of control between steps.

The standard flowchart symbols - terminal, process, input/output and decision - and the same logic written as pseudocode.

Expressing Algorithms: Pseudocode

Pseudocode is a plain-language description of an algorithm, not tied to a specific programming language.
It uses keywords like IF, THEN, ELSE, WHILE, FOR, INPUT, OUTPUT.
It is more precise than natural language but easier to read than code.
Example: `IF score ≥ 50 THEN OUTPUT "Pass" ELSE OUTPUT "Fail"`.
Pseudocode helps plan and communicate algorithms before coding.

Pseudocode keywords for input, output, assignment and selection, with the same logic drawn as a flowchart.

Tracing an Algorithm

Tracing means manually following the steps of an algorithm with sample inputs to check it works.
Use a trace table with columns for variables, conditions, and output.
Record the value of each variable after every step.
Tracing helps find logic errors and verify correctness.
Example: trace a loop that sums numbers from 1 to 5 – track `sum` and `i`.

A trace table records one row per step: the input taken, the variable values, the decision made and any output.

Precision and Avoiding Ambiguity

Algorithms must be unambiguous – each step has exactly one meaning.
Vague instructions like 'add a few' are not algorithmic.
Use clear, specific language: 'Add 1 to count' not 'increase count'.
Flowcharts and pseudocode reduce ambiguity by using structured symbols and keywords.
A well-defined algorithm has a clear start, finite steps, and defined output.

Steps in the wrong order give the wrong result even when every step is correct.

History of Algorithms

Algorithms date back to ancient civilizations: Babylonian (c. 2500 BC), Egyptian (c. 1550 BC), Indian, Greek, Chinese, and Arabic.
The Euclidean algorithm (c. 300 BC) finds the greatest common divisor.
The Sieve of Eratosthenes (c. 240 BC) finds prime numbers.
Al-Khwarizmi (9th century) formalized algorithms as systematic, finite steps; the word 'algorithm' comes from his name.
Al-Kindi developed the first cryptographic algorithm using frequency analysis.

Key Takeaways

An algorithm is a step-by-step recipe for a computer or human to follow.
Flowcharts and pseudocode are two ways to represent algorithms.
Always trace your algorithm to ensure it works for all inputs.
Precision is key – avoid ambiguity.
Algorithms are fundamental to computer science and problem-solving.

One algorithm written three ways: structured English, pseudocode and a flowchart.

幻灯片

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练习题

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1.What is an algorithm?
Easy
- AA precise sequence of instructions to solve a problem
- BA random set of steps that may or may not work
- CA type of computer hardware
- DA programming language
2.An algorithm must always terminate (stop eventually).
Easy
True or false?
3.Which of the following is NOT a standard flowchart symbol?
Easy
- AOval
- BRectangle
- CDiamond
- DTriangle
4.In a flowchart, what does a diamond shape represent?
Easy
- AA process
- BA decision
- CInput/output
- DStart or end
5.Match each flowchart symbol to its meaning.
Easy
- Oval
- Rectangle
- Diamond
- Parallelogram
- Start/End
- Process
- Decision
- Input/Output
6.Pseudocode is written in a specific programming language such as Python.
Easy
True or false?
7.Which of the following is an example of an algorithm?
Medium
- AA recipe for baking a cake
- BA random guess at a number
- CA list of your favourite songs
- DA painting of a landscape
8.Arrange the following steps to make a simple algorithm for making a cup of tea:
Medium
- Boil water
- Add tea bag to cup
- Pour water into cup
- Remove tea bag

复习笔记

## Algorithms, Flowcharts and Pseudocode ### What is an Algorithm? An **algorithm** is a finite sequence of mathematically rigorous instructions, typically used to solve a class of specific problems or to perform a computation. It is a precise sequence of instructions that produces an output and stops eventually. Algorithms can use **conditionals** to divert execution through various routes (automated decision-making) and deduce valid inferences (automated reasoning). - **Heuristic** vs Algorithm: A heuristic is an approach to solving problems without well-defined correct or optimal results. For example, social media recommender systems are often called algorithms but actually rely on heuristics. - **Key properties**: An algorithm must be expressed within a finite amount of space and time, in a well-defined formal language. It starts from an initial state and input, performs computations at each step, and eventually produces output and terminates. ### Expressing Algorithms Algorithms can be expressed in several ways: - **Flowcharts**: Use standard symbols to represent steps, decisions, and flow of control. - **Pseudocode**: A plain-language description of the steps, not tied to any programming language. ### Tracing an Algorithm Tracing means following the algorithm step by step with a specific input, recording the values of variables and the output at each step. This helps verify correctness and understand behavior. ### Precision and Ambiguity Algorithms must be **precise** and **unambiguous**. Ambiguous instructions can lead to different interpretations, so each step must be clearly defined. ### History (Brief) - Ancient algorithms: Babylonian division (c. 2500 BC), Egyptian arithmetic (Rhind Papyrus c. 1550 BC), Euclidean algorithm (c. 300 BC). - Al-Khwarizmi (9th century) established algorithms as systematic, finite sequences; the term 'algorithm' derives from his name. - Al-Kindi developed the first cryptographic algorithm (frequency analysis). ### Key Points to Remember - An algorithm must always terminate. - Flowcharts use standard symbols: start/end (oval), process (rectangle), decision (diamond), input/output (parallelogram). - Pseudocode is readable and language-independent. ### Example Pseudocode ``` START INPUT a, b SET sum = a + b OUTPUT sum STOP ```

Algorithm: A finite sequence of mathematically rigorous instructions, typically used to solve a class of specific problems or to perform a computation.
Heuristic: An approach to solving problems without well-defined correct or optimal results.
Flowchart: A diagram that uses standard symbols to represent the steps, decisions, and flow of an algorithm.
Pseudocode: A plain-language description of an algorithm's steps, not tied to any programming language.
Tracing: Following an algorithm step by step with a specific input, recording the values of variables and the output at each step.
Conditional: A statement that allows the algorithm to divert execution through different routes based on a condition.
Termination: The property that an algorithm eventually stops after producing an output.

闪卡

What is an algorithm?

An algorithm is a finite sequence of precise, rigorous instructions used to solve a class of specific problems or perform a computation.

What is the difference between an algorithm and a heuristic?

An algorithm has well-defined correct or optimal results, while a heuristic is an approach to solving problems without such well-defined results, often used when no truly correct answer exists.

What are the three common ways to express an algorithm?

Flowcharts, pseudocode, and structured English (or natural language) are common ways to express algorithms.

What is a flowchart?

A flowchart is a diagram that uses standard symbols to visually represent the steps and decisions in an algorithm.

What is pseudocode?

Pseudocode is a simplified, informal way of writing an algorithm using plain language and some programming-like constructs, without strict syntax rules.

Why is precision important in an algorithm?

Precision is important because an algorithm must be unambiguous and exact so that it can be followed correctly by a computer or human, avoiding confusion.

What does it mean to trace an algorithm?

Tracing an algorithm means manually stepping through each instruction with sample inputs to check the output and verify correctness.

What is the standard symbol for a start/end in a flowchart?

A rounded rectangle (or oval) is used to represent the start and end of a flowchart.

What is the standard symbol for a process/instruction in a flowchart?

A rectangle is used to represent a process or instruction, such as a calculation or assignment.

What is the standard symbol for a decision in a flowchart?

A diamond is used to represent a decision point, where the flow can branch based on a condition.

What is the standard symbol for input/output in a flowchart?

A parallelogram is used to represent input or output operations.

What are the arrows in a flowchart used for?

Arrows indicate the flow of control, showing the sequence in which steps are executed.

What is a conditional in an algorithm?

A conditional is a statement that allows the algorithm to take different paths based on whether a condition is true or false.

What is the purpose of a loop in an algorithm?

A loop repeats a set of instructions multiple times until a condition is met or for a fixed number of iterations.

What is the difference between a variable and a constant in pseudocode?

A variable can change its value during execution, while a constant has a fixed value that does not change.

What does the term 'terminate' mean in the context of an algorithm?

An algorithm terminates when it stops after a finite number of steps, producing an output.

What is the origin of the word 'algorithm'?

The word 'algorithm' comes from the Latinization of the name of Persian mathematician al-Khwarizmi, 'Algoritmi'.

Name one ancient algorithm and its origin.

The Euclidean algorithm, described in Euclid's Elements (c. 300 BC), is an ancient algorithm for finding the greatest common divisor.

What is the Sieve of Eratosthenes?

It is an ancient algorithm for finding all prime numbers up to a given limit, described by Nicomachus.

What is a finite sequence of instructions?

It is a set of steps that has a definite beginning and end, with a limited number of steps.

What is the role of input in an algorithm?

Input is the data provided to the algorithm at the start, which it processes to produce output.

What is output in an algorithm?

Output is the result produced by the algorithm after processing the input.

What is an example of a non-deterministic algorithm?

A randomized algorithm that incorporates random input is non-deterministic, as its behavior may vary between runs.

What is the purpose of using flowcharts and pseudocode in algorithm design?

They help in planning, communicating, and testing algorithms before implementation in a programming language.

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