SKILL.md
Algorithms Skill
Skill Metadata
skill_config:
version: "1.0.0"
category: problem-solving
prerequisites: [cs-foundations]
estimated_time: "8-12 weeks"
difficulty: intermediate-advanced
parameter_validation:
pattern:
type: string
enum: [search, sort, dp, greedy, backtrack, divide-conquer, graph]
required: true
language:
type: string
enum: [python, java, cpp, javascript]
default: python
retry_config:
max_attempts: 3
backoff_strategy: exponential
initial_delay_ms: 500
observability:
log_level: INFO
metrics: [pattern_usage, solution_complexity, hint_count]Quick Start
Become a master problem solver through systematic algorithm design.
Common Algorithm Patterns
Searching & Sorting (Week 1)
- Linear search O(n)
- Binary search O(log n)
- Merge sort O(n log n)
- Quick sort O(n log n) average
- Heap sort O(n log n)
Divide & Conquer (Week 2)
- Split problem into subproblems
- Solve recursively
- Combine results
- Analyze with recurrence relations
Dynamic Programming (Weeks 3-4)
- Identify overlapping subproblems
- Define state and transitions
- Memoization vs tabulation
- Classic problems: Fibonacci, knapsack, LCS
Greedy Algorithms (Week 5)
- Make optimal local choice
- Examples: Huffman coding, Dijkstra, activity selection
- When to use: optimal substructure + greedy choice property
Backtracking (Week 6)
- Explore all solutions
- Backtrack when dead end
- Pruning branches
- N-Queens, permutations, sudoku solver
Problem-Solving Framework
- Understand: Read problem, identify constraints, find examples
- Plan: Recognize pattern, think brute force, optimize
- Code: Write clean code, handle edge cases
- Optimize: Improve time/space complexity
- Verify: Test, verify analysis
Must-Know Problems
- Array Problems: Two sum, max subarray, product of array
- String Problems: Longest substring, pattern matching, anagrams
- Tree Problems: Traversal, BST, LCA, path sum
- Graph Problems: Shortest path, cycle detection, topological sort
- DP Problems: Fibonacci, knapsack, coin change, edit distance
- Math Problems: Prime numbers, GCD, power
Troubleshooting
| Issue | Root Cause | Resolution |
|---|---|---|
| TLE | Wrong complexity class | Find better algorithm |
| WA | Edge case missing | Test empty, single, max inputs |
| RE | Index out of bounds | Add bounds checking |
| Stack overflow | Deep recursion | Convert to iteration |
Complexity Quick Reference
| Problem | Best | Average | Worst |
|---|---|---|---|
| Merge sort | O(n log n) | O(n log n) | O(n log n) |
| Quick sort | O(n log n) | O(n log n) | O(n²) |
| Binary search | O(1) | O(log n) | O(log n) |
| Linear search | O(1) | O(n/2) | O(n) |
Interview Tips
- Communicate your approach
- Discuss time/space trade-offs
- Code cleanly on the first try
- Test with examples
- Optimize if time permits