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There are n vehicles on an n x n grid. At the start they are ordered in the top row 1. The vehicles have to get to the bottom row such that the vehicle at (1,n) must get to (n, n − i + 1). On each time step, each of the vehicles can move one square up, down, left or right, or it can stay put. If the vehicle stays put, one adjacent vehicle (but not more than one) can hop over it. Two vehicles cannot occupy the same square.
Which of the following heuristics are admissible for the problem of moving all the vehicles to their destination?
i. sum from 1 to n (h1 ... hn)
ii. max(h1 ... hn)
iii. min(h1 ...hn)
I think that iii is the only correct one, but I'm not sure how to formulate my reasoning on why.
I am sure someone will come along with a very detailed answer, but as a favour to those who like me can be a bit overwhelmed by all things AI, an admissible heuristic is quite simply:
A heuristic that never overestimates the true cost of getting to the goal
Not to sound too uncharitable, but it sounds as if maybe the problems you've posted are from a homework problem or assignment. I wouldn't want to spoil your fun working out exactly which of those three heuristics are and aren't admissible - but hopefully that one sentence definition should help you along.
If you get confused, just remember: if once your vehicles have both reached their goals you find the actual cost was less than what the heuristic thought it would be then it's inadmissable.
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Suppose you have two strings. Each string has lines, seperated by a newline character. Now you want to compare both strings and then find the best method (shortest number of steps) by only adding or deleting lines of one string, to transform the second string in to the first string.
i.e.
string #2:
abc
def
efg
hello
123
and string #1:
abc
def
efg
adc
123
The best (shortest steps) solution to transform string #2 in to string #1 would be:
remove line at line position 3 ('hello')
add 'abc' after line
position 3
How would one write a generic algorithm to find the quickest, least steps, solutions for transforming one string to another, given that you can only add or remove lines?
This is a classic problem.
For a given set of allowed operations the edit distance between two strings is the minimal number of operations required to transform one into the other.
When the set of allowed operations consists of insertion and deletion only, it is known as the longest common subsequence edit distance.
You'll find everything you need to compute this distance in Longest common subsequence problem.
Note that to answer this question fully, one would have to thoroughly cover the huge subject of graph similarity search / graph edit distance, which I will not do here. I will, however, point you in directions where you can study the problem more thoroughly on your own.
... to find the quickest, least steps, solutions for transforming
one string to another ...
This is a quite common problem known as the (minimum) edit distance problem (or, originally, the specific 'The String-to-String Correction problem', by R. Wagner and M. Fischer), which is a non-trivial problem for the optimal (minimum = least steps) edit distance, which is what you ask for in your question.
See e.g.:
https://en.wikipedia.org/wiki/Edit_distance
https://web.stanford.edu/class/cs124/lec/med.pdf
The minimum edit distance problem for string similarity is in itself a subclass of the more general minimum graph edit distance problem, or graph similarity search (since any string or even sequenced object, as you have noted yourself, can be represented as a graph), see e.g. A survey on graph edit distance.
For details regarding this problem here on SO, refer to e.g. Edit Distance Algorithm and Faster edit distance algorithm.
This should get you started.
I'd tag this problem rather as a math problem (algorithmic instructions) rather than language specific problems, unless someone could guide you to an existing language (C) library for solving edit distance problems.
The fastest way would be to remove all sub-strings, then append (not insert) all new sub-strings; and to do "all sub-strings at once" if you can (possibly leading to a destPointer = sourcePointer approach).
The overhead of minimising the amount of sub-strings removed and inserted will be higher than removing and inserting/appending without checking if its necessary. It's like spending $100 to pay a consultant to determine if you should spend $5.
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I want to make an algorithm which will enable the conduct of A/B testing over a variable number of subjects with a variable number of properties per subject.
For example I have 1000 people with the following properties: they come from two departments, some are managers, some are women etc. these properties may increase/decrease according to the situation.
I want to make an algorithm which will split the population in two with the best representation possible in both A and B of all the properties. So i want two groups of 500 people with equal number of both departments in both, equal number of managers and equal number of women. More specifically, I would like to maintain the ratio of each property in both A and B. So if we have 10% managers I want 10% of sample A and Sample B to be managers.
Any pointers on where to begin? I am pretty sure that such an algorithm exists. I have a gut feeling that this may be unsolvable in some cases as there may be an odd number of managers AND women AND Dept. 1.
Make a list of permutations of all a/b variables.
Dept1,Manager,Male
Dept1,Manager,Female
Dept1,Junior,Male
...
Dept2,Junior,Female
Go through all the people and assign them to their respective permutation. Maybe randomise the order of the people first just to be sure there is no bias in the order they are added to each permutation.
Dept1,Manager,Male-> Person1, Person16, Person143...
Dept1,Manager,Female-> Person7, Person10, Person83...
Have a second process that goes through each permutation and assigns half the people to one test group and half to the other. You will need to account for odd numbers of people in the group, but that should be fairly easy to factor in, obviously a larger sample size will reduce the impact of this odd number on the final results.
The algorithm for splitting the groups is simple - take each group of people who have all dimensions in common and assign half to the treatment and half to the control. You don't need to worry about odd numbers of people, whatever statistical test you are using will account for that. If some dimension is so skewed (i.e., there are only 2 females in your entire sample), it may be wise throw the dimension out.
Simple A/B tests usually use a t-test or g-test, but in your case, you'd be better of using an ANOVA to determine the significance of the treatment on each of the individual dimensions.
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I'm actually working on a board game which is a variant of the TIC-TAC-TOE game. The specifics of the game are the followings :
1. The game is played on a nxn board, with n variable.
2. A player wins if he succeeds in placing k alignments the first, k is variable.
3. An alignment is constituted of l marks (X or O) in a horizontal, vertical or diagonal. l is fixed.
4. If the nxn grid is full (no player can add a mark either X or O) and no player succeeded in placing k alignments so the game is drawn.
I'm using an minmax with alpha-beta prunning algorithm. This is my first program with artificial intelligence and I don't know exactly how to create the evaluation function to be used by the algorithm. I saw some examples on the net which use a material weighting to evaluate a position but I can't apply that in my case. Actually, I'm using a radom evaluation function which returns a value between -100 and 100.
float Conf_eval(Configuration c)
{
return (rand()%201)-100;
}
Any idea on how can I evaluate a given board configuration ?
This is thoroughly discussed in the book Artificial Intelligence - A Modern Approach
There are also excellent implementations available (this is java, there is also python, you can Google for more) based on the book series. Including for tic-tac-toe (and alpha-beta pruning agents).
If you're using the min-max algorithm with alpha-beta prunning, you can use a sorted "Actions" list to perform better in addition to your heuristic function (a trivial utility-function would be assigning 1 to a victory, 0 to a tie and -1 to a loss - these are all leaf nodes of the min-max expanded tree).
To sort the actions you can, for say, prefer actions that add your symbol(X, O) to a clear-to-victory path. This should eventually lead to better prunning.
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i need some help with a math task our professor gave us. Any suggestions would help.
The problem is:
There are N cannibals and M missinaries. All missionaries have a strenght attribute, which can be 1 or any positive whole number. Strenght indicates how many cannibals he can fight off.
Basically: there are two sides of the river, there is a 2-slot boat, and you have to transfer all the guys to the other side, without letting the cannibals eat the missionaries.
How would you write a program for this? What would be the transferring-grouping algorythm?
Thanks in anticipation,
Mark.
Model your problem as a states graph.
In here, a state is ({L,R}n,{L,R}m,{L,R}) Where:
First n entries: one for each missionary - where he is: left/right bank of the river
next,m entries: one for each canibal- where he is: left/right bank of the river
Last entry is for the boat
These are your vertices - you should also trim the invalid states - where strength of missionaries is not enough in one (or more) side. It is easy to calculate it for each state.
Your edges are:
E = { (S1,S2) | Can move in one boat ride from S1 to S2 }
All is left to do - use some shortest path algorithm to find the shortest path from: (L,L,....,L) to (R,R,...,R).
You can use BFS for this task, or even bi-directional search - or an informed algorithm (with admissible heuristic) such as A* Algorithm.
PS. The 'graph' is just conceptual, in practice you will have a function next:S->2^S, that given a state - returns all valid successors of this state (states that you can get to them using one edge on the graph from S). This will allow you to "generate the graph" on the fly.
Your next(S) function should be something like (high level pseudo code, without optimizations):
next(S):
let x be the bank where the boat is, and y the other bank
for each person p1 on bank x:
S' = S where boat and p1 moved from x to y
if S' is valid according to strength limitations, yield S'
for each p2 != p1 on bank x:
S' = S where boat and p1 and p2 moved from x to y
if S' is valid according to strength limitations, yield S'
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Below is a lecture slide about AI. I think it's a pseudo code about something.
But I don't know what these symbols mean. I even can't get the main points of this slide.
Please help me. Thank you :)
It's not pseudocode. Please check out Norvig and Russell, "Artificial Intelligence: A Modern Approach". This looks like effects of an action for a reflex agent but you need at least the previous slide and probably the previous few slides to determine that. It could also deal with the frame problem in some way.
At any rate, presumably given an action with a precondition p and an effect e and a state s, the set of effects are the four logic statements: x , not x, x and not x. The first two logic statements say x when x has the value 1 in the effect e, etc. The third and fourth logic statements say x if in the set of logic clauses phi then x has the value 1 in effect e and the state s entails (|=) the set of logic clauses phi.
So a pair precondition,effect is executable in a state s if and only if s entails p and the set of effects in s is consistent.
But as I said more information is actually needed.