Lu, Yukuan

Outline：

• Norms
• Analysis
• Functions
• Derivatives
• Linear Algebra

ref: Optimization Methods

Outline:

• Mathematical Optimization
• Least-squares
• Linear Programming
• Convex Optimization
• Nonlinear Optimization
• Summary

Outline:

• UAG的DFS树

• UAG的DFS框架

• UAG的DFS应用

  • 容错连通

    • 寻找割点

    • 寻找桥

Ref:

• 算法设计与分析(Algorithm design and analysis) by 黄宇

Outline:

• BFS

  • skeleton

  • 证明: $v.dis=\delta (s,v)$

  • BFS树

  • 应用

• DFS

  • s → all

Ref:

• 算法设计与分析(Algorithm design and analysis) by 黄宇

Outline:

• 找前k大元素
• 找离medium最近的k个元素
• Weighted medium
• 找unique

Ref:

• 算法设计与分析(Algorithm design and analysis) by 黄宇

Outline：

• NPC = P ？
• NPC判定问题
• 规约： 等价

Ref:

• 算法设计与分析(Algorithm design and analysis) by 黄宇

Outline:

• BestFS
• MCE

Ref:

• 算法设计与分析(Algorithm design and analysis) by 黄宇

Outline:

• Decision Problem
• The class P
• The class NP
• Reduction between problems
• NP-Complete Problems
• Other advanced topics

Ref:

• 算法设计与分析(Algorithm design and analysis) by 黄宇

Outline:

• Basic Idea of Dynamic Programming(DP)
  • Smart scheduling of subproblems
• Minimum Cost Matrix Multiplication
  • BF1, BF2
  • A DP solution
• Weighted Binary Search Tree
  • The "same" DP with matrix multiplication
• From the DP perspective
  • All-pairs shortest paths SSSP over DAG
• More DP problems
  • Edit distance
  • Highway restaurants; Separating Sequence of words
  • Changing coins
• Elements of DP

Ref:

• 算法设计与分析(Algorithm design and analysis) by 黄宇

Outline:

• Single-Sources shortest paths( SSSP )

  • Dijkstra algorithm by example
  • Priority queue-based implementation
  • Proof of correctness

• All-pairs shortest paths( APSP )

  • Shortest path and transitive closure
  • Warshall algorithm for transitive closure
    • BF1, BF2, BF3 => Warshall algorithm
    • Floyd algorithm for shortest paths

Ref:

• 算法设计与分析(Algorithm design and analysis) by 黄宇