Algorithms Q&A - Recent questions in Informed Search

Solve this grid world.

Tue, 06 May 2025 15:13:38 +0000

Solve the final V* values for the given grid world. All given values are exit states. Fill in all missing cells. Don’t use value iteration. Show all your work/logic/steps, etc.

Assume: Gamma = 0.9. Noise Model: [0.8, 0.1, 0.1], that is, 80% chance of going in the intended direction and 10% in each of perpendicular ones.

Using pen and paper is preferable.

Admissible Heuristic for Chutes and Ladders

Tue, 06 May 2025 15:12:07 +0000

You are a player of Chutes and Ladders. You are going from cell 1 to cell 100, using standard 6 faced dice. There are “chutes” and “ladders” that hurt and help, respectively.
Explain an algorithm to calculate an admissible heuristic starting square i.

Weird N Puzzle

Tue, 04 Mar 2025 16:03:53 +0000

You are given a weirdly shaped n puzzle (sliding puzzle).

The best way to imagine the shape is that think of 10 x 10 n puzzle (a rather large one), and that some tiles in the center are just fixed - they don't move. (See Slack for an example).

For this problem, what is a good heuristic, from an A Star algorithm perspective? Clearly Manhattan Distance still works, but is that the best?

I have all the (unsorted) cards

Tue, 04 Mar 2025 15:50:53 +0000

You are given 52 playing cards, organized in 4 columns and 13 rows. However, these are all Aces, in 4 different colors: red, blue, green and yellow. These are all jumbled up. You are supposed to organize them such that each column has one color of Aces only. You can decide which color you want to go in which column. The only move that you can move is to swap/exchange two cards that horizontally or vertically adjacent. That is, just vertical or horizontal movement, like the n-puzzle, and no diagonal moves.

Analyze the problem, and present an algorithm for this. Present your heuristic. No need to explain how A-Star works itself. Describe without using any pseudocode.

Solve the V* values for this grid world MDP - 3 x 4

Sun, 16 Apr 2023 19:47:18 +0000

Estimate the final V* values for a given grid world. Discount, noise, terminal states are all given. You are given a 3x4 grid world and you want to find V* values. There is a discount rate of 0.9 and noise of 0.8, 0.1, 0.1. The first column has all terminal states with value -1 and the last column has terminal states with value 1. There is no living reward.

-1			1
-1			1
-1			1

A* algorithm for fruit sorting

Sun, 19 Mar 2023 16:44:14 +0000

You are given 10 apples of different sizes, 10 bananas of different sizes and 10 oranges of different sizes, organized in a 3x10 array. You want to organize them so that fruits go from top to bottom in ascending order of size. Any fruit can be used in any column that you like. The only move allowed is to swap two fruits horizontally or vertically. You want to use A* algorithm to minimize the number of moves for this. Explain your approach.

Stationary Distribution for this conditional probability table

Sat, 04 Apr 2020 13:35:39 +0000

What is the stationary distribution for the following conditional probability table?

What is the code level difference between graph search and tree search?

Mon, 03 Feb 2020 16:54:34 +0000

What is the code level difference between graph search and tree search?

Solve this GridWorld

Mon, 13 May 2019 20:24:23 +0000

Calculate the final V* values for the given grid world. Fill in all missing cells. All given values are terminal states. Use value iteration/policy iteration, any method that you like.

Assume 50% discount (that is, gamma = 0.5). Assume 0.8, 0.1, 0.1 noise, that is, probability of going to the intended direction is 0.8, and probability of going left/right is 0.1 each.

GridWorld
10	10	10	10	10
10				10
10				10
10				10
10	10	10	10	10

Admissible Heuristic for n-puzzle if multiple tiles can be slided at once

Tue, 07 May 2019 10:51:24 +0000

In the context of n-puzzle, consider a variation that we can slide multiple tiles in one row or column, if they are touching each other. The cost of this slide operation is the same as that of sliding one tile.

Design an admissible and useful heuristic for this problem.

8 puzzle that can be solved or not?

Tue, 30 Apr 2019 22:49:15 +0000

Some of 8 puzzles can be solved if it is transferred from the #12345678. But there are 9! states. How to rule out many of the wrong states use rules that 8 puzzles have potential, like odd and even, the right rule is #12345678, every line only three place and so on.

Is Harmonic Mean of admissible heuristics an admissible heuristic?

Tue, 09 Apr 2019 02:25:06 +0000

Given a family of admissible heuristic functions h1, h2, .. hn. Is the Harmonic Mean, H = n / (1/h1 + 1/h2 + ... 1/hn) an admissible function? How would you define this function if one of the h functions is zero?

Converting ternary constraint into binary constraints

Sat, 09 Feb 2019 15:59:04 +0000

Show how a single ternary constraint such as "x + y = z" can be turned into three binary constraints by using an auxiliary variable.

Manhattan Distances, but Linear Interference...

Sat, 02 Feb 2019 16:11:04 +0000

Manhattan Distance does not take into account linear conflicts. For example:

- - 3,1 needs to be changed to - 1, -, 3

[Only first row is being shown here, and the blank is assumed to be at the top left corner.]

Manhattan Distance is 4, but tiles 1 and 3 interfere with each other while moving.

So, how can we improve this heuristic?

Give an example of a task environment that is..

Fri, 25 Jan 2019 18:48:48 +0000

Give an example of a task environment that is..

Episodic and Discrete
Continuous and Episodic
Continuous, Non-Deterministic and Non-Episodic.

For each of the combinations above, give an example of a task environment.

Admissible Heuristic for n-Queens Problem

Sat, 24 Mar 2018 11:44:41 +0000

Given all queens are in their own columns, and a move is defined as picking up a queen and moving to any other row in the same column, what is an admissible heuristic for this problem?

[We note that by the structure of the problem, we always have a queen in each column.]

In the context of informed search, what is the difference between complete, optimal and optimally efficient algorithm?

Mon, 19 Mar 2018 02:35:55 +0000

In the context of informed search, what is the difference between complete, optimal and optimally efficient algorithm?

Is A* complete?

Is A* optimal?

Is A* optimally efficient?

N-Queens Count all conflicts in O(n) time

Sat, 03 Mar 2018 02:26:23 +0000

Count all the conflicts in a given n-Queen state. It is easy to do in O(n²) time. Give an O(n) time algorithm to count all conflicts.