#algorithms

What does it mean for an algorithm to be generalizable? Why is this important?

An algorithm should be general enough so that it 'works for all problems of a specific form' as well as for a variety of input sets - this property can also be referred to as the robustness of the algorithm. The algorithm should also produce a correct result even when the set of inputs presents an edge case. The property of generalizability is related to another important property of 'doability of operations' since the algorithm must work for any appropriate type of input.

What are the requirements for a good algorithm?

The algorithm needs to be well-ordered, clear, unambiguous, effective, finite, and generalizable.

List at least 2-3 strategies to debug code that isn't working properly.

1. Add print statements at different points in your code to see what values variables hold, which functions are being called, and where errors might be occurring. 2. Use a debugger to step through your code line by line, inspect variables, and identify where errors are occurring. 3. Read error messages carefully to understand what went wrong. 4. Write pseudocode before writing actual code and test each part of the code as you write it.

List at least three strategies you can use to understand how a complicated algorithm works.

1. Break the algorithm down into smaller components. Errors may be more easily identified when observing tractable parts. 2. If the algorithm is implemented in code, add "print" statements along the way to see what values certain variables take at different stages in the algorithm. 3. Trace the algorithm. Tracing an algorithm means walking through it step-by-step, manually calculating the output for a given input. This can help you understand how the algorithm processes information, how it makes decisions, and how it arrives at the final output. You can also experiment with the algorithm using different inputs. 4. Identify the algorithm's inputs and outputs. Then, test the algorithm against edge cases or unusual inputs. 5. Find out more about the algorithm by reading the algorithm's documentation, looking for examples of the algorithm in action, and discussing the algorithm with others. 6. Create visual representations of the algorithm. Visualizations such as flow charts or diagrams can help you understand how the different parts of the algorithm are interconnected. This can help you identify patterns, identify inputs and outputs, and see how the algorithm processes information.

What is a Brute force algorithm?

A brute force algorithm involves a systematic approach to try every possible solution to a problem until the best one is found. Brute force algorithms are not guaranteed to always find the globally optimal solution, particularly for problems with large input sizes because the computer might not have the capacity to get to the correct solution in a specific amount of time. One example is finding the shortest path between two points in a graph. A brute force approach would involve trying every possible path between the two points. Note that this can quickly become infeasible for large graphs. In such cases, a more efficient algorithm such as Dijkstra's algorithm or A* search algorithm may be used instead.

What is a Divide-and-conquer algorithm?

A divide-and-conquer algorithm is one that breaks a problem down into smaller subproblems that can be solved independently. These subproblems are then combined to form a solution to the original problem. An example of a problem that can be solved using a divide-and-conquer algorithm is sorting a list of numbers using merge sort.

What is a Greedy algorithm?

A greedy algorithm is one that makes locally optimal choices at each step in the hope of finding a globally optimal solution. These algorithms are often used for optimization problems and can be more efficient than brute force algorithms. However, they are not always guaranteed to find the optimal solution, and may get stuck in local optima. An example of a problem that can be solved using a greedy algorithm is the knapsack problem, where a set of items with different values and weights must be selected to maximize the total value while staying within a weight limit.

Does an application of #algorithms require code?

Certainly not! Any time you are using a systematic process (with inputs, outputs, and steps) to solve a problem, you are using algorithmic thinking. Good algorithms can be written in simple natural language or pseudo code. They can also be visualized in a flowchart. Regardless of the format, a strong algorithm should meet the same features: well-ordered, clear, unambiguous, effective, finite, and generalizable.

What are different ways you can describe an algorithm's runtime?

Complexity: Mathematical notation of Big-O, Big-Ω, Big-Θ are used to describe the algorithm's time complexity as a function of the input size. Big-O describes the asymptotic upper bound, or the worst-case scenario time complexity. Big-Ω describes the asymptotic lower bound or the best-case scenario. Big-Θ describes both the upper and lower bounds or tight bounds of the time complexity. It provides a range within which the growth rate of the algorithm's runtime falls. Empirical analysis: This involves measuring the actual runtime of the algorithm for different input sizes and comparing it to the expected runtime based on the algorithm's time complexity analysis. Benchmarking: This involves comparing the runtime of the algorithm to other algorithms solving the same problem, under similar conditions.

What does it mean for an algorithm to have effectively computable operations? Why is this important?

Each step must be possible to perform otherwise the algorithm will be ineffective as it will get stuck and be unable to use the inputs to produce an output. This is also related to generalizability: the algorithm should be able to take in a wide range of inputs to transform without getting stuck.

What does it mean to test an algorithm? What are different ways you can test an algorithm?

Testing an algorithm is essential to make sure that it works effectively as desired (that it produces the desired outputs for all possible inputs). It's usually best to begin tests with very simple cases for which you know what the expected output should be: run the algorithm on an easy/simple input to ensure that the output matches expectations. The algorithm designer must then consider possible edge cases, failure modes, or ways to break the algorithm and continue more thoughtful tests to ensure the algorithm is robust enough to handle a wide variety of inputs. Upon testing the algorithms and identifying errors, you can engage in debugging, the process of finding and fixing errors or bugs in your code. You can use print statements and debuggers to step through your code and see what is happening at each step. This can help you identify and fix errors in your code.

What does it mean for an algorithm to be finite? Why is this important?

The algorithm contains a limited number of steps and each of them takes a finite amount of time to be executed. This way we guarantee that the algorithm always produces an output. One way to do this is to have a termination condition. For example, when working with 'while' loops we should avoid infinite loops. In some cases, it may be acceptable for an algorithm to run continually as long as it produces some output in finite time as it keeps running. An example of this could be a real-time monitoring system, where an output of a monitoring report is produced within finite time intervals.

What does it mean for an algorithm to be clear and unambiguous? Why is this important?

The steps must be clear both for the computer to understand what and how to execute the operations AND for the user/coder. Computers are often 'dumb' as they lack intuition. We need to provide them with specific details so that they are able to perform the task accurately. This is important because otherwise the algorithm may fail to produce a correct result. For the user/coder, clear and ambiguous code eases debugging and reproducing the code when read by someone else.

What are some different ways to measure an algorithm's efficiency? Why is this important?

There are many different ways to measure an algorithm's efficiency. The most common approaches are considering the (1) number of steps, (2) runtime, and (3) memory/space usage. However, we are not interested just in the number of steps, runtime, or memory usage. We are interested in how the number of steps scales with the input size. Perhaps it may be a linear relationship between them: if the input is an array of n integers, and we simply have a single loop through the list, then the number of steps is also n. If we have a nested for-loop that goes through the list twice, then the number of steps is n2; the number of steps scales in a quadratic behavior as input size increases. This is important because if we are testing an algorithm on a small input size and it runs very quickly, we need to know what would happen if we increase the input.

What is Regression testing?

This involves re-testing the algorithm after changes or updates have been made, to ensure that existing functionality has not been affected.

What is Integration testing?

This involves testing how different components or functions of the algorithm work together. Integration tests can uncover issues that may arise when different parts of the algorithm are combined.

What is unit testing?

This involves testing individual components or functions of the algorithm in isolation, using a set of inputs and expected outputs. Unit tests can be automated and run frequently during the development process.

What is Acceptance testing?

This involves testing the algorithm against a set of requirements or specifications provided by the client or end user. Acceptance tests are designed to ensure that the algorithm meets the desired functionality and performance criteria. Acceptance testing may be conducted in line with test-driven development, where tests are written before the code is written. This helps ensure that the code is working correctly and that it meets the desired functionality.

What is an algorithm?

Using recipes to solve problems.