๐ŸŽฒ Randomized Algorithms

๐Ÿ”ฅ Vibe Coding Prompt

"Implement Randomized Quickselect to find the K-th smallest element. Compare fixed vs random pivot performance on sorted input."

๐Ÿ“‹ Course Outline

  1. Monte Carlo vs Las Vegas
  2. Randomized Quickselect / Quicksort
  3. Monte Carlo Methods
  4. Karger's Min Cut
  5. Probability Analysis

Key Points

  • Understand the core concepts thoroughly
  • Practice with hands-on code examples
  • Apply knowledge to real-world problems
  • Review and reinforce through exercises

Further Learning

  • Official documentation
  • Open source projects on GitHub
  • Community forums and discussions
  • Related courses and tutorials

Course Chapter Index

1

Monte Carlo vs. Las Vegas Algorithms โ€” Two Types of Randomization

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2

Randomized Quicksort โ€” Why Random Pivots Make Sorting Fast

3

Monte Carlo Methods โ€” Randomized Algorithms

4

Quickselect โ€” Find the K-th Smallest Element in Expected O(n) Time

5

Karger's Randomized Min-Cut Algorithm

6

Reservoir Sampling โ€” Random Sampling from a Stream of Unknown Size

7

Monte Carlo Tree Search โ€” Decision Making with Random Simulation

8

Probability Analysis of Randomized Algorithms