I have a task to create a crossword, a specific one. All the answers are given, but their places are unknown. Program must read a file with board scheme like this :
0 1 0 0 0 0 0 0 1 0 0
0 1 0 1 1 1 1 1 1 1 1
0 1 0 1 0 0 1 0 1 0 1
0 S 1 1 0 1 1 1 1 0 1
0 1 0 0 1 0 1 0 1 0 0
1 1 1 1 1 1 1 S 1 1 0
0 0 0 0 1 0 1 0 0 0 0
0 0 0 0 1 0 0 0 0 0 0
treating each column/row of ones as one possible answer. Is there any way to parse through this file and marking answers without using gazilion if's for each field ?
Rest of the logics is as follows :
- on the base of the parsed file crossword is created.
- user selects answers from lists of possibilities
- user clicks on the first block of Answer and if length and letters of selected answer and Answer match - fields are updated
Game board should be stored in 2d array I guess, and each Answer should have indexes of fields in it ?
Crossword puzzle construction is NP-Complete in general (i.e nxn board of 1s and 0s and a given set from which to pick answers). Look at: http://en.wikipedia.org/wiki/List_of_NP-complete_problems which just mentions this. Garey and Johnson's classic book also has a mention of this, saying Exact cover by 3 sets can be reduced to it.
So, you probably will have to use some backtracking/heuristic to fill the grid.
Perhaps this project report of two students from Dartmouth college will be of some help: Crossword Puzzle Generator. It contains some heuristics which you might be able to use.
Of course, you seem to imply there is a human involved, but it is not clear if you can leverage that person to fill the grid and whether your problem is basically some UI programming problem in helping the user out.
Related
the board is like this:
1 2 3 4
5 6 7 0
0 0 0 0
0 0 0 0
the '0' represents that is empty, we can move the non-zero number to the '0'.
so how to get all of the state of the board using BFS?
for example, there are two state of the board:
1 2 3 4
0 0 0 0
5 6 7 0
0 0 0 0
1 2 3 0
4 0 0 0
5 0 0 0
6 7 0 0
The reason I ask this question is that I need to process all of the 15-puzzle state using Disjoint pattern database to solve the nearly most difficult state of 15-puzzle in 1 minutes.
15 14 13 12
11 10 9 8
7 6 5 4
3 1 2 0
I need to process all of the 15-puzzle state [..] to solve the nearly most difficult state of 15-puzzle in 1 minutes
Approach 1 - using a database and storing all states
For reasons given by Henry as well, and also supported by [1], solving this problem using a database would require generating the entire A_15 , storing all of it and then finding the shortest path, or some path between a given state and the solved state. This would require a lot of space and a lot of time. See this discussion for an outline of this approach.
Approach 2 - using a specialized depth-first search algorithm
Here is an implementation of this search strategy that uses the IDA algorithm.
Approach 3 - using computational group theory
Yet another way to handle this in a much shorter amount of time is to use GAP (which implements a variant of Schreier-Sims) in order to decompose a given word into a product of generators. There is an example in the docs that shows how to use it to solve the Rubik's cube, and it can be adapted to the 15-puzzle too [2].
[1] Permutation Puzzles - A Mathematical Perspective by Jamie Mulholland - see page 103 and 104 for solvability criteria, and the state space being |A_15| ~ 653 billion
[2] link2 - page 37
Okay, so here is the scenario:
I have a 2D integer array representing my graph / matrix. If there is a connection, there is a 1, if no connection then there is a 0. Pretty simple, however I am iterating back through the array to create a subset as given. So if I have a graph:
{ 0 1 1 1
1 0 1 1
1 1 0 1
1 1 1 0 }
and I pass the subset {3,1}
then I will be left with
{ 0 0 1 0
0 0 0 0
1 0 0 0
0 0 0 0 }
Now my question is how to go about counting the maximum vertices in the components? So the output I want is the maximum vertices of a single component. My problem is I don't understand how I'm suppose to tell the difference in components. It's easier for me to understand on paper, but I am stumped on how to interpret it through code. I will say I am doing this in Java.
Any insight would be helpful
Edit Note:
I am trying to use BFS or some other search method to count each vertex and its connections. Then iterate over each vertex that has yet to be seen or checked, and continue. Then output the number of max components
Lets say I have a graph with connections as above before the subset given. The subset will be removed, then we are left with pieces of a graph. I then need to iterate over those pieces to find which piece has the most connections.
Say I have 2 leaves {1,2} and I was given their binary codes (same length), meaning that I should construct the binary tree based on the binary codes. And after constructing the binary tree, if I traverse the tree, I should retrieve the same binary codes for leave 1 and 2.
The data format is as follow:
leave : binary code
1: 0 1 1 0 0 1 1 0 0 1 0 1 1 1 1 1 1 0 1 0 1 1 0 1
2: 0 1 0 0 0 1 0 0 0 1 0 1 1 1 1 1 1 0 1 0 0 1 0 1
For example, when the binary code is 0 1 1 0, I start from the root of the tree and I go left when I see 0 and right when I see 1 ...
Question: How can I construct a binary tree based on the binary code given ? (Please note that I am in fact dealing with 200000 leaves , and hence 200000 lines of binary code. So I need an efficient method to do this.)
You may want to look at this
http://www.cs.princeton.edu/courses/archive/spring01/cs126/assignments/prefix.html
this should hopefully give you insight on what you need to do to create the tree you want
Here's the problem: I'm given a matrix like
Input:
1 1 1
1 1 1
1 1 1
At each step, I need to find a "second" matrix of 1's and 0's with no two 1's on the same row or column. Then, I'll subtract the second matrix from the original matrix. I will repeat the process until I get a matrix with all 0's. Furthermore, I need to take the least possible number of steps.
I need to print all the "second" matrices in O(n) time. In the above example I can get to the null matrix in 3 steps by subtracting these three matrices in order:
Expected output:
1 0 0
0 1 0
0 0 1
0 0 1
1 0 0
0 1 0
0 1 0
0 0 1
1 0 0
I have coded an attempt, in which I am finding the first maximum value and creating the second matrices based on the index of that value. But for the above input I am getting 4 output matrices, which is wrong:
My output:
1 0 0
0 1 0
0 0 1
0 1 0
1 0 0
0 0 0
0 0 1
0 0 0
1 0 0
0 0 0
0 0 1
0 1 0
My solution works for most of the test cases but fails for the one given above. Can someone give me some pointers on how to proceed, or find an algorithm that guarantees optimality?
Test case that works:
Input:
0 2 1
0 0 0
3 0 0
Output
0 1 0
0 0 0
1 0 0
0 1 0
0 0 0
1 0 0
0 0 1
0 0 0
1 0 0
Summing of each row / column and taking the largest of those sums gives you the optimal number of matrix subtractions required to reduce to a null matrix.
For example:
1 2 4 0 = 7
2 2 0 1 = 5
0 0 1 0 = 1
3 0 2 1 = 6
= = = =
6 4 7 2
Which means that this matrix will take 7 optimal subtractions to empty.
I believe that counting backwards from this and removing from columns / row with that value will solve your problem (I am not sure of an efficient way of selecting these - brute force?).
You can also use your previous method to remove extra elements.
For example (using the above matrix).
Step 7:
We must subtract from row 1 & column 3.
0 0 1 0
0 0 0 0
0 0 0 0
0 0 0 0
Solves this, so now we can use your previous method to remove "bonus" elements.
0 0 1 0
1 0 0 0
0 0 0 0
0 0 0 1
Now apply the sum of each row / column again and continue for the next step.
Step 6:
1 2 3 0 = 6
1 2 0 1 = 4
0 0 1 0 = 1
3 0 2 0 = 5
= = = =
5 4 6 1
Next subtraction:
0 0 1 0
0 1 0 0
0 0 0 0
1 0 0 0
And so on.
Note: This still does not work very well with "all 1" matrices, as you get stuck on the problem of selecting 1 from every row and column (same as you did in your example).
But someone may be able to extend my solution.
Let Number of rows = Number of columns = N
for iteration=1:N
for row=1:N
cell(row,(row+iteration)%N) := 0
Number of iterations is N. In every iteration N one's will be changed to 0
I'm not entirely sure if this is what you are after, but could you create a list of available columns and mark them as used for each iteration.
For Example:
repeat until an empty matrix
mark all columns as available
for each row
find the maximum value in all available columns and store it's coordinates
mark that column as unavailable
print, decrement and clear the list of stored coordinates
This doesn't work, but it does show the algorithm that user1459032 is using.
1) If all you want to do is iterate through all the elements in your matrix...
2) then all you have to do is loop for (int i=0; i < rows*cols; i++) {} ...
3) And such a loop is ALREADY O(n) (i.e. it increases LINEARLY with the #/elements in your matrix)
I'm pretty sure that this is some kind of variant of the exact cover problem, which is known to be NP-complete. Your proposed algorithm is a simple greedy solution. The problem with greedy solutions is that they often work well enough to convince you that greed is good and then suddenly leave you high and dry looking for a better solution. (Consider the global economy, for example.) Anyway, Knuth's Dancing Links technique is a standard way of solving the problem (exact set cover, not global economy).
I'm trying to write an algorithm that finds the number of solutions in a given partially filled in Sudoku board. i.e. given
"1 6 4 0 0 0 0 0 2",
"2 0 0 4 0 3 9 1 0",
"0 0 5 0 8 0 4 0 7",
"0 9 0 0 0 6 5 0 0",
"5 0 0 1 0 2 0 0 8",
"0 0 8 9 0 0 0 3 0",
"8 0 9 0 4 0 2 0 0",
"0 7 3 5 0 9 0 0 1",
"4 0 0 0 0 0 6 7 9"
where 0s represent blank spots. I want to create 3 separate arrays of sets, one for each set of numbers in each column, row, and 3x3 square. I am trying the declaration:
horizontal = new HashSet<Integer>[9];
Where private HashSet[] horizontal is declared earlier, but this doesn't work. What is the correct declaration or can I not make declare an array of Sets?
The problem is the type parameter. You can't create generic arrays in Java. You can remove the type parameter and it will work, but you should get a warning about unchecked operations.
You might try this:
horizontal = new ArrayList<HashMap<Integer>>();
Access it with horizontal.get(1); and you can treat it the same way as a normal array. As #user599152 said, you can't create generic arrays. So you need to figure out another way. A list is probably your best bet.
An array of sets is a strange way to store the data. A 2d array or a 2d array of 2d arrays might be a much more intuitive way of modeling this. Possibly even a 2d array of some custom class ("SudokuCube") would also work better than an array of sets.