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algorithms-cs-expert

Expert-level algorithms and complexity theory covering sorting, searching, graph algorithms, dynamic programming, greedy algorithms, NP-completeness, and algorithm design paradigms.

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luokai0/ai-agent-skills-by-luo-kai
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Algorithms CS Expert

Before Starting

  1. Which algorithm category?
  2. Time or space optimization priority?
  3. Exact or approximate solution needed?

Core Expertise Areas

Sorting Algorithms

Comparison sorts: quicksort O(n log n) avg, mergesort O(n log n) worst, heapsort O(n log n). Non-comparison: counting sort O(n+k), radix sort O(nk), bucket sort O(n) avg. Stability: mergesort and timsort stable, quicksort and heapsort not stable. In-place: heapsort and quicksort in-place, mergesort requires O(n) extra space.

Graph Algorithms

BFS: shortest path in unweighted graphs, O(V+E), uses queue. DFS: topological sort, cycle detection, SCC, O(V+E), uses stack or recursion. Dijkstra: shortest path weighted non-negative, O(E log V) with priority queue. Bellman-Ford: handles negative weights, detects negative cycles, O(VE). Floyd-Warshall: all-pairs shortest path, O(V3), dynamic programming. Minimum spanning tree: Kruskal (sort edges + union-find), Prim (greedy + priority queue).

Dynamic Programming

Optimal substructure: optimal solution contains optimal solutions to subproblems. Overlapping subproblems: same subproblems solved multiple times without memoization. Top-down memoization: recursive with cache. Bottom-up tabulation: iterative filling of DP table. Classic problems: LCS, LIS, knapsack, matrix chain, edit distance, coin change.

Complexity Theory

Big-O classes: O(1) constant, O(log n) logarithmic, O(n) linear, O(n log n), O(n2), O(2n). P vs NP: P decidable in polynomial time, NP verifiable in polynomial time. NP-complete: NP-hard and in NP. First: SAT. Others via reduction. Common NP-complete: SAT, 3-SAT, vertex cover, clique, TSP decision, subset sum.

Best Practices

  • Analyze both time and space complexity
  • Consider average, worst, and best case separately
  • Prove correctness before optimizing
  • Use amortized analysis for data structure operations
  • Reduce unknown problems to known ones

Common Pitfalls

PitfallFix
Off-by-one in DP tableCarefully define base cases and indices
Dijkstra on negative edgesUse Bellman-Ford instead
Ignoring integer overflowUse long or BigInteger for large inputs
Wrong complexity analysisAccount for all loops and recursive calls

Related Skills

  • data-structures-expert
  • algorithms-expert
  • compiler-expert

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