ICPC

Problem Strategies

What do problems look like?

• Problem Structure:
• Scenario: A real-world or fictional scenario is presented with specific rules or constraints.
• Task: Defines what you need to compute, optimize, or solve.
• Input/Output: Testcase are given as input and the output in a specific format.
• Constraints: Includes limits on input size, time complexity, and space complexity.
• General Features:
• Often involve grids, paths, or sequences.
• May ask you to compare "actual" vs "optimal" (e.g., travel routes, costs, or operations).
• Goal: Understand what’s being asked and identify how the input relates to the task.

Interpreting Problems

• Carefully Read the Problem:
• Focus on key actions or movements (e.g., directions, steps, operations).
• Look for keywords that imply specific constraints (e.g., shortest, longest, maximum, minimum).
• Understand the Objective:
• Identify what you're calculating (e.g., distance, cost, number of moves).
• Simplify complex descriptions into smaller, solvable pieces.
• Break Down the Problem:
• Analyze if the problem can be split into smaller subproblems.
• Example: For a movement problem, separate turns from actual moves.
• Identify Constraints as Hints:
• Large input sizes imply the need for efficient algorithms (e.g., O(n log n) instead of O(n^2)).
• Time constraints suggest that brute force approaches may not work.

Formulating the Approach

• Simplify the Problem:
• Focus on the core mechanics: What actions truly impact the solution?
• Can you reduce it to simple counting, grid traversal, or mathematical operations?
• Plan the Process:
• Input Parsing: Understand how you will handle the input (e.g., multiple test cases, strings, lists)
• Core Logic: Identify what must be computed for each case (e.g., count moves, compare paths).
• Think of Edge Cases:
• Consider minimal and maximal inputs.
• Handle possible edge cases where no actions are performed or where all actions might seem unnecessary.

Efficient Problem Solving

• Recognize Patterns:
• Many problems have underlying patterns (e.g., sequences, grid traversal, number operations)
• Find commonalities or repetitions in the input to simplify the solution.
• Avoid Unnecessary Work:
• If some actions don't affect the result (e.g., unnecessary turns), ignore them to reduce complexity
• Use Optimal Algorithms:
• If the problem involves searching, sorting, or pathfinding, use efficient algorithms like binary search, Dijkstra’s, or BFS/DFS
• Validate Assumptions:
• Make sure your understanding of the problem matches the constraints and edge cases.
• Test your approach against small or edge inputs before scaling up

Parsing Input

Implementing the Solution

• Input Parsing:
• Use the efficient input techniques discussed
• Handle multiple test cases and various input formats (e.g., strings, integers, or lists).
• Write Logic:
• Break the input down into manageable parts (e.g., counting certain actions, evaluating steps)
• Implement the logic that directly addresses the problem’s requirements.
• Handle Edge Cases:
• Test your solution with corner cases (e.g., minimal input, maximum input, unexpected values)
• Optimize Where Necessary:
• If your initial solution isn’t fast enough, revisit your algorithm (e.g., improve time complexity or optimize input/output operations).

Testing and Debugging

• Test on Sample Data:
• Use provided test cases first. Understand why each case outputs what it does.
• Create Your Own Test Cases:
• Create extreme cases (e.g., max values, edge behaviors) to test your code’s robustness.
• Debugging:
• Use print statements or debugging tools to trace the execution flow.
• Break down the problem into parts and check each individually.
• Validate Against Constraints:
• Ensure your solution performs efficiently within the problem’s constraints (time and space).

Your Turn

http://socalcontest.org/history/2023/SCICPC-2023-2024-ProblemSet.pdf

• Get in your teams (if here) and try to solve Problem 7 using our problem strategies

Reminders

Competition Date: November 16th