Right Answer: Depth-First Search (DFS) explores a graph branch as far as possible before backtracking. Breadth-First Search (BFS) explores all the neighbors of a node before moving to the next level of neighbors. DFS uses a stack (implicitly through recursion), while BFS uses a queue.
Right Answer: 1. **Understand the problem:** Clarify requirements, inputs, outputs, and constraints.
2. **Explore examples:** Work through concrete examples to grasp the problem's nuances.
3. **Break it down:** Decompose the problem into smaller, manageable subproblems.
4. **Design the algorithm:** Choose appropriate data structures and algorithmic techniques.
5. **Write pseudocode:** Outline the algorithm's steps in plain language.
6. **Implement the code:** Translate the pseudocode into a specific programming language.
7. **Test thoroughly:** Test with various inputs, including edge cases, to ensure correctness.
8. **Analyze complexity:** Determine the algorithm's time and space complexity.
9. **Optimize (if needed):** Identify bottlenecks and improve performance.
10. **Document:** Clearly explain the algorithm's purpose, logic, and usage.
1. **Operations:** What operations are frequently performed (search, insert, delete, etc.)?
2. **Data Characteristics:** What is the type of data (numbers, strings, objects) and its relationships (ordered, unique, hierarchical)?
3. **Memory Usage:** How much memory is available and how much will the data structure consume?
4. **Time Complexity:** What are the time complexities of the common operations for different data structures?
Right Answer: Divide-and-conquer algorithms work by:
1. **Divide:** Breaking the original problem into smaller, similar subproblems.
2. **Conquer:** Solving the subproblems recursively. If they're small enough, solve them directly.
3. **Combine:** Merging the solutions of the subproblems to get the solution to the original problem.
Right Answer: Brute force algorithms try all possible solutions, guaranteeing a result but potentially taking a very long time. Optimized algorithms use techniques like data structures or mathematical insights to reduce the number of steps needed, solving the problem faster, although they might be more complex to implement.
Right Answer: Regression analysis is a statistical method used to examine the relationship between one dependent variable and one or more independent variables. It is used to predict outcomes, identify trends, and understand the strength of relationships in data.
Right Answer: Classification analysis is a data analysis technique used to categorize data into predefined classes or groups. It works by using algorithms to learn from a training dataset, where the outcomes are known, and then applying this learned model to classify new, unseen data based on its features. Common algorithms include decision trees, logistic regression, and support vector machines.
Right Answer: The different types of data distributions include:
1. Normal Distribution
2. Binomial Distribution
3. Poisson Distribution
4. Uniform Distribution
5. Exponential Distribution
6. Log-Normal Distribution
7. Geometric Distribution
8. Beta Distribution
9. Chi-Squared Distribution
10. Student's t-Distribution
Right Answer: Descriptive statistics summarize and describe the main features of a dataset, using measures like mean, median, mode, and standard deviation. Inferential statistics use sample data to make predictions or inferences about a larger population, often employing techniques like hypothesis testing and confidence intervals.