Module 3: Solving Problems with UPER

UPER is an acronym for a systematic problem-solving framework with four key steps:

1. Understand

Before attempting to solve any problem, make sure you fully grasp what is being asked.

• Restate the problem in your own words
• Identify inputs, outputs, and constraints
• Ask clarifying questions
• Look for edge cases and potential issues
• Break down complex problems into smaller components

Questions to ask: What are the inputs? What are the expected outputs? What are the constraints? Are there any edge cases to consider?

2. Plan

Once you understand the problem, develop a strategy to solve it before writing any code.

• Brainstorm potential approaches
• Consider different algorithms and data structures
• Write pseudocode to outline your solution
• Consider time and space complexity
• Start with a simple solution before optimizing

Questions to ask: What algorithm fits this problem? Can I use existing patterns? How will I handle edge cases?

3. Execute

Implement your planned solution with clear, maintainable code.

• Follow your pseudocode and strategy
• Write clean, well-structured code
• Test your solution with various inputs
• Debug any issues that arise
• Implement error handling as needed

Focus on: Writing clean code, testing as you go, and handling exceptional cases.

4. Reflect

After implementing your solution, evaluate its effectiveness and consider improvements.

• Test the solution with different inputs
• Analyze time and space complexity
• Consider alternative approaches
• Refactor and optimize your code
• Document your solution and learnings

Questions to ask: Does my solution work for all cases? How can it be improved? What did I learn from this problem?

Problem: Finding the Maximum Value in an Array

Understand

We need to find the largest number in an array of integers. The input is an array of integers, and the output is a single integer representing the maximum value in the array.

Plan

We can solve this by:

• Initializing a variable to track the maximum value
• Iterating through each element in the array
• Comparing each element with our current maximum
• Updating the maximum if we find a larger value

Pseudocode:

function findMax(array):
    if array is empty:
        return error or null
    max = array[0]
    for each element in array:
        if element > max:
            max = element
    return max
                

Execute

Java implementation:

public int findMaximum(int[] numbers) {
    if (numbers.length == 0) {
        throw new IllegalArgumentException("Array cannot be empty");
    }
    
    int max = numbers[0];
    for (int i = 1; i < numbers.length; i++) {
        if (numbers[i] > max) {
            max = numbers[i];
        }
    }
    return max;
}
                

Reflect

Our solution has a time complexity of O(n) as we need to visit each element once. The space complexity is O(1) as we only use a single variable regardless of input size. The solution handles the edge case of an empty array by throwing an exception.

• UPER Practice Repository
• Problem Solving Guide
• Algorithm Practice Problems

• Apply UPER to solve coding challenges
• Break down complex problems into smaller tasks
• Implement solutions using systematic approaches
• Review and optimize existing solutions