algorithms

name	algorithms
description	Master algorithm design, common patterns, optimization techniques, and problem-solving strategies. Learn to solve any computational challenge efficiently.
sasmp_version	1.3.0
bonded_agent	02-algorithms-expert
bond_type	PRIMARY_BOND

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

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Problem-Solving Framework

1. Understand: Read problem, identify constraints, find examples
2. Plan: Recognize pattern, think brute force, optimize
3. Code: Write clean code, handle edge cases
4. Optimize: Improve time/space complexity
5. Verify: Test, verify analysis

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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

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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

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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)

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Interview Tips

• Communicate your approach
• Discuss time/space trade-offs
• Code cleanly on the first try
• Test with examples
• Optimize if time permits