# Summary

📗 Tuesday to Friday lectures: 1:00 to 2:15, Zoom Link
📗 Monday to Saturday office hours: Zoom Link
📗 Personal meeting room: always open, Zoom Link

📗 Math Homework: M9, M10,
📗 Programming Homework: P5,
📗 Examples and Quizzes: Q17, Q18, Q19, Q20,
📗 Discussions: D9, D10,

# Lectures

📗 Slides (will be posted before lecture, usually updated on Monday):
Blank Slides: Part 1: PDF, Part 2: PDF, Part 3: PDF, Part 4: PDF,
📗 The annotated lecture slides will not be posted this year: please copy down the notes during the lecture or from the Zoom recording.

📗 Notes

Image by DeepNorth via Wikipedia

# Other Materials

📗 Pre-recorded videos from 2020
Lecture 17 Part 1 (Uninformed Search): Link
Lecture 17 Part 2 (Breadth First Search): Link
Lecture 17 Part 3 (Depth First Search): Link
Lecture 18 Part 1 (Informed Search): Link
Lecture 18 Part 2 (Uniform Cost and Greedy): Link
Lecture 18 Part 3 (A Search): Link

Lecture 20 Part 1 (Hill Climbing): Link
Lecture 20 Part 2 (Simulated Annealing): Link
Lecture 20 Part 3 (Genetic Algorithm): Link


📗 Relevant websites
Sheep Game: Link
Sliding Puzzle: Link
Water Jugs: Link
All Search: Link
Google Map: Link
Robot Arm: (Game) Link, (2D) Link 2, (3D) Link 3
Professor Jerry Zhu's Slides (with Proofs etc): Link

Simulated Annealing Map: Link
SAT Solver: Link
Genetic Walkers: Link
Genetic Cars: Link
Genetic Eater: Link
Genetic Image: Link


📗 YouTube videos from previous summers
📗 Uninformed Search
How to get expansion path for BFS? Link
How to get expansion path for DFS? Link
How to get expansion path for IDS? Link
What is the shape of tree for IDS to search the quickest? Link
How to do backtracking for search problems? Link
How to compute time complexity for multi-branch trees? Link
How to find the best case time complexity? Link (Part 4)
What is the shape of the tree that minimizes the time complexity of IDS? Link (Part 8)
What is the minimum number of nodes searched given the goal depth? Link (Part 4)
How to find the number of states expanded during search for a large tree? Link (Part 12)
How to find all possible configurations of the 3-puzzle? Link (Part 1)
How to find the time complexity on binary search tree with large number of nodes? Link (Part 2, Part 3)
How to find the shape of a search tree such that IDS is the quickest? Link (Part 1)

📗 Informed Search
How to get expansion path for UCS? Link
How to get expansion path for BFGS? Link
How to get expansion path for A? Link
How to get expansion path for A*? Link
How to check if a heuristic is admissible? Link
How to find the expansion sequence for uniform cost search? Link
Which functions of two admissible heuristic are still admissible? Link
How to do A search on a maze? Link (Part 2)

📗 Hill Climbing
How to do hill climbing on 2D state spaces? Link
How to do hill climbing for SAT problems? Link
What is the number of flips needed to move from one binary sequence to another? Link (Part 7)
What is the local minimum of a linear function with three variables? Link (Part 14)
How to use hill climbing to solve the graph coloring problem? Link (Part 7)
How to do hill climbing on 3D state spaces? Link (Part 1)
How to find the shortest sequence of flipping consecutive entries to reach a specific configuration? Link

📗 Simulated Annealing
How to find the probability of moving in simulated annealing? Link
Which temperature would minimize the probability of moving in simulated annealing? Link (Part 2)

📗 Genetic Algorithm
How to find reproduction probabilities? Link
How to find the state with the highest reproduction probability given the argmax-argmin fitness functions? Link (Part 1, Part 2)
How to compute reproduction probabilities? Link

# Keywords and Notations

📗 Local Search
📗 Hill Climbing (Valley Finding), probability of moving from \(s\) to a state \(s'\) \(p = 0\) if \(f\left(s'\right) \geq f\left(s\right)\) and \(p = 1\) if \(f\left(s'\right) < f\left(s\right)\), where \(f\left(s\right)\) is the cost of the state \(s\).
📗 Simulated Annealing, probability of moving from \(s\) to a worse state \(s'\) = \(p = e^{- \dfrac{\left| f\left(s'\right) - f\left(s\right) \right|}{T\left(t\right)}}\) if \(f\left(s'\right) \geq f\left(s\right)\) and \(p = 1\) if \(f\left(s'\right) < f\left(s\right)\), where \(T\left(t\right)\) is the temperature as time \(t\).
📗 Genetic Algorithm, probability of get selected as a parent in cross-over: \(p_{i} = \dfrac{F\left(s_{i}\right)}{\displaystyle\sum_{j=1}^{n} F\left(s_{j}\right)}\), \(i = 1, 2, ..., N\), where \(F\left(s\right)\) is the fitness of state \(s\).

📗 Adversarial Search
📗 Sequential Game (Alpha Beta Pruning): prune the tree if \(\alpha \geq \beta\), where \(\alpha\) is the current value of the MAX player and \(\beta\) is the current value of the MIN player.
📗 Simultaneous Move Game (rationalizable): remove an action \(s_{i}\) of player \(i\) if it is strictly dominated \(F\left(s_{i}, s_{-i}\right) < F\left(s'_{i}, s_{-i}\right)\), for some \(s'_{i}\) of player \(i\) and for all \(s_{-i}\) of the other players.
📗 Simultaneous Move Game (Nash equilibrium): \(\left(s_{i}, s_{-i}\right)\) is a (pure strategy) Nash equilibrium if \(F\left(s_{i}, s_{-i}\right) \geq F\left(s'_{i}, s_{-i}\right)\) and \(F\left(s_{i}, s_{-i}\right) \geq F\left(s_{i}, s'_{-i}\right)\), for all \(s'_{i}, s'_{-i}\).