Let's talk about how to approach an algorithm problem.

**Understand the Problem:** Before diving into the solution, it's crucial to thoroughly understand the problem statement. Read it carefully, identify the input and output requirements, and clarify any ambiguities or edge cases. If needed, provide examples or test cases to ensure you comprehend the problem correctly.

*Example: Given an array of integers, write a function that returns an array continaing the maximum and minimum values in the array.*

input: [74, 13, 234, 46, 909]

output: [909, 13]

**Break Down the Problem:** Once you understand the problem, break it down into smaller, manageable steps. This process is referred to as *problem decomposition*. Identify the key components or sub-problems that need to be solved. This approach helps you tackle complex problems more easily.

*Example: To find the maximum and minimum values in an array, we can follow these steps:*

- Initialize variables to store the maximum and minimum values.
- Iterate through the array.
- Compare each element with the current maximum and minimum values.
- Update the maximum and minimum values if a larger or smaller value is found.
- After the loop is completed, return an array containting the maximum and minimum numbers.

**Brute Force Approach:** Start with a simple, straightforward solution, even if it's not the most efficient. This approach, known as the brute force method, helps you understand the problem better and provides a baseline for optimization.

*Example: To find the maximum and minimum values in an array using a brute force approach, we can iterate through the array and compare each element with the current maximum and minimum values, updating them as needed.*

**Optimize and Refine:**
Did you miss any edge cases? What if you are handed an empty array? Here is a solution that adds that in as a check at the beginning:

**Explore Alternative Solutions:** After solving the problem, explore alternative solutions or approaches. This exercise helps you broaden your problem-solving skills and exposes you to different techniques and ways of thinking.

**Practice and Review:** Regularly practice algorithm problems from various sources, such as coding platforms, books, or online resources. Review solutions from others, understand their thought processes, and learn from their approaches.

**Analyze Time and Space Complexity:** While not essential in the beginning, it's good to start learning about time and space complexity analysis early on.
Understand the trade-offs between time and space, and consider whether your solution meets the required performance constraints. Understanding the efficiency of your solutions will become increasingly important as you progress to more complex problems.

## Similarities Across Algorithm Problems¶

As you practice more algorithm problems, especially at the beginner level, you'll start to notice recurring patterns and techniques that can be applied to solve similar types of problems. Here are some common patterns and techniques that you can start to look out for now:

### 1. Traversal Patterns:¶

- Linear traversal (iterating through arrays or strings)
- Breadth-first traversal (using a queue)
- Depth-first traversal (using recursion or a stack)

### 2. Searching Patterns:¶

- Linear search (iterating through an array or string to find a specific element)
- Binary search (for sorted arrays or lists)

### 3. Sorting Patterns:¶

- Bubble sort
- Insertion sort
- Selection sort

### 4. Manipulation Patterns:¶

- Reversing an array or string
- Removing duplicates from an array or string
- Merging or splitting arrays or strings

### 5. Mathematical Patterns:¶

- Finding the maximum or minimum value
- Calculating the sum or average of elements
- Checking for prime numbers or palindromes

### 6. Recursion Patterns:¶

- Recursively traversing data structures (e.g., trees, linked lists)
- Recursively solving problems by breaking them down into smaller sub-problems

### 7. Divide and Conquer Patterns:¶

- Splitting a problem into smaller sub-problems, solving them independently, and then combining the solutions

As you practice more problems, you'll start recognizing these patterns and techniques, which will help you approach new problems more efficiently. Additionally, you'll develop a better understanding of data structures like arrays, strings, linked lists, and trees, and how to manipulate and traverse them effectively.