Chess problem Horse

Does anyone has an idea how to do this one or is there a website where i can get info on how this can be done.

I need to write a program that can do this:

A classical chess problem: is it possible to make the horse visit every square once using its
usual chess moves?

Actually, to accomplish this task, there is a nice heuristic that states that player can start from
any square and should move the horse to the next legal but not-yet-visited square according
to the following rule: consider all the legal but not-yet-visited squares and pick the one that
would have the maximum number of legal moves next.

Have you tried the "internets". Maybe you could perform a search at a search engine?

Quzah.

Wikipedia - knights tour

There is a trick to doing this, iirc it was to always have the knight move to the square that has the fewest possible connecting knight moves. Turns the whole problem into the realm of networking and communication.

Quote:

Originally Posted by Cyberman86

Does anyone has an idea how to do this one or is there a website where i can get info on how this can be done.

I need to write a program that can do this:

A classical chess problem: is it possible to make the horse visit every square once using its
usual chess moves?

Actually, to accomplish this task, there is a nice heuristic that states that player can start from
any square and should move the horse to the next legal but not-yet-visited square according
to the following rule: consider all the legal but not-yet-visited squares and pick the one that
would have the maximum number of legal moves next.

Sounds like a 2 d array and changing all the contents to something in a specific way.

Does it sound hard to you?

Know how to declare a 2 d array?(the size of a chess board and wouldnt hurt to start all positions of the array to 0, except one of them (where the knight is starting))
perhaps after you post that code I'll try and help some more.

Quote:

Originally Posted by Cyberman86

A classical chess problem: is it possible to make the horse visit every square once using its usual chess moves?

A classical solution: yes!

Quote:

Actually, to accomplish this task, there is a nice heuristic that states that player can start from
any square and should move the horse to the next legal but not-yet-visited square according
to the following rule: consider all the legal but not-yet-visited squares and pick the one that
would have the maximum number of legal moves next.

That's a nice way of saying "when using brute force, always pick the most promising move" (known as the Minimax Algorithm), which implies that your algorithm knows a correct solution before making the first move.

If you actually want to compute a solution, I suggest using brute force.

Greets,
Philip

This is not a brute force algorithm.

In this approach, you count the connections to the possible squares the knight could move to, from it's current square.

Then you move to the square with the fewest connections that has not yet been visited. It is not required that you calculate the whole tour (although it becomes easy to do so). You can just calculate the knight's (one), next move.

I did this by hand, rather than by the computer, so I'm not ENTIRELY sure that no look-ahead was used, but certainly I didn't pre-plan the whole tour.

Quote:

Originally Posted by Adak

This is not a brute force algorithm.

I was talking about Cyberman's approach, not yours. Your approach looks promising, although there might be cases with complications (starting near the corner), but I'll have to do some examples first.

Greets,
Philip

It's called Warndorff's Algorithm.

Quote:

Originally Posted by strickyc

Sounds like a 2 d array and changing all the contents to something in a specific way.

Does it sound hard to you?

Know how to declare a 2 d array?(the size of a chess board and wouldnt hurt to start all positions of the array to 0, except one of them (where the knight is starting))
perhaps after you post that code I'll try and help some more.

Chess Problem:

Code:

In the main() function: 1. Declare a 8x8 two dimensional array (int chess[8][8];) to represent a chess board and set all its elements to -1 (i.e., no cells (squares) are visited, yet). 2. Ask user to enter i and j as the row and column numbers of the initial cell. (Since you are using C, make sure that user enters a number between 0 and 7 (inclusive) for row and column numbers). 3. Set chess[i][j] to 1 means that the horse visited that cell first. 4. Implement and call a function to determine in which order the horse visits the legal squares once according to our random selection strategy described below and returns the number of squares visited numofsquares = random_horse(chess, i, j); print(“Number of squares visited = %d\n”, numofsquares); 5. Implement and call a function print_board(chess); to print the values in chess board showing in which order the cells are visited In the int random_horse(int chess[][8], int i, int j) function: while(1) { a. Identify the legal but not-yet-visited squares b. If there is no such squares return chess[i][j]; c. Pick one of these cells randomly (say you picked chess[x][y]) d. Update order number (chess[x][y] = chess[i][j] + 1;) e. Move the horse to the selected cell (i=x; j=y;) } /* end of while */

I think Warndorff's Algorithm can't work all of the time, but I'm not sure whether my argument works:

Visiting every square exactly once is known to be NP-complete (Hamiltonian path), hence the optimal algorithm will have a runtime >= O(2^n) where n*n is the size of the board. In Warndorff's Algorithm, the knight visits every square exactly once (i.e. there are n*n iterations) and for each square, the knight checks at most 8 other squares (the maximum possible number of different knight moves). Hence, the overall runtime is O(n*n*8) = O(n^2). If Warndorff's algorithm always works, then we have discovered a polynomial time algorithm which solves a NP-complete problem, hence P=NP.

So there are three possible scenarios:
- I'm wrong
- P=NP
- Warndorff occasionally fails

Right now, I'd choose the last one. Ideas anyone?

Greets,
Philip

This is what i have so far, Not sure if it makes sense but i tried my best.

Code:

#include <stdio.h> #include <stdlib.h> #include <math.h> int main() { int random_horse(int chess[8][8], int i, int j) for (i=0; i<7; i++) for(j=0; j<7; j++) random_horse[i][j] = i+j; i=2; j=2; numofsquares = random_horse(chess, i, j); print(“Number of squares visited = %d\n”, numofsquares); while(1) i-1>=0 && j-2>=0 && chess [i-1][j-2]== -1) { pm[k][0] = i-1; pm[k][1] = j-2; k++; } { if(k==0) return chess[1][j]; rc = rand_int (0,k-1); x = pm[rc][0]; y = pm[rc][1]; chess[x][y] = chess[i][j] + 1; i=x; j=y; } return 0; }

Have you tried to compile your code? If you do, make sure you get rid of all the compiler errors. Do you have a specific question?

Greets,
Philip

Quote:

Originally Posted by Snafuist

Have you tried to compile your code? If you do, make sure you get rid of all the compiler errors. Do you have a specific question?

Greets,
Philip

i just want to know if the whole code makes sense according to the problem instructions, I'm a beginner and sometimes i can't tell if the code is following the problem.

Code:

In the main() function: 1. Declare a 8x8 two dimensional array (int chess[8][8];) to represent a chess board and set all its elements to -1 (i.e., no cells (squares) are visited, yet). 2. Ask user to enter i and j as the row and column numbers of the initial cell. (Since you are using C, make sure that user enters a number between 0 and 7 (inclusive) for row and column numbers). 3. Set chess[i][j] to 1 means that the horse visited that cell first. 4. Implement and call a function to determine in which order the horse visits the legal squares once according to our random selection strategy described below and returns the number of squares visited numofsquares = random_horse(chess, i, j); print(“Number of squares visited = %d\n”, numofsquares); 5. Implement and call a function print_board(chess); to print the values in chess board showing in which order the cells are visited In the int random_horse(int chess[][8], int i, int j) function: while(1) { a. Identify the legal but not-yet-visited squares b. If there is no such squares return chess[i][j]; c. Pick one of these cells randomly (say you picked chess[x][y]) d. Update order number (chess[x][y] = chess[i][j] + 1;) e. Move the horse to the selected cell (i=x; j=y;) } /* end of while */

@Snafuist: I've used Warndorff's algorithm by hand, and it worked fine. Can you give an example where it fails?

Solving the knights tour can be done without using Warndorff's algo, it's just that it's more difficult.

@Cyberman: You can't make a knights tour succeed very often, simply by choosing a random square for the knight to move to next.

That wouldn't be much of a puzzle would it?

Of course, you have to stick with the assignment you were given, just be aware that very few attempted tours by your program, will succeed.

The way to tell if your program meets the assignment requirements is to simply run it, and see if it does what the assignment requires, step by step. We can't check that any better than you can, and I'm certainly not going to try.

If you have a question about C (and not about your assignment), ask it.

Quote:

Originally Posted by Cyberman86

i just want to know if the whole code makes sense according to the problem instructions, I'm a beginner and sometimes i can't tell if the code is following the problem.

Code:

In the main() function: 1. Declare a 8x8 two dimensional array (int chess[8][8];) to represent a chess board and set all its elements to -1 (i.e., no cells (squares) are visited, yet). 2. Ask user to enter i and j as the row and column numbers of the initial cell. (Since you are using C, make sure that user enters a number between 0 and 7 (inclusive) for row and column numbers). 3. Set chess[i][j] to 1 means that the horse visited that cell first. 4. Implement and call a function to determine in which order the horse visits the legal squares once according to our random selection strategy described below and returns the number of squares visited numofsquares = random_horse(chess, i, j); print(“Number of squares visited = %d\n”, numofsquares); 5. Implement and call a function print_board(chess); to print the values in chess board showing in which order the cells are visited In the int random_horse(int chess[][8], int i, int j) function: while(1) { a. Identify the legal but not-yet-visited squares b. If there is no such squares return chess[i][j]; c. Pick one of these cells randomly (say you picked chess[x][y]) d. Update order number (chess[x][y] = chess[i][j] + 1;) e. Move the horse to the selected cell (i=x; j=y;) } /* end of while */

No it doesnt make since. Just think of your problem once sentence at a time.
so for starts

Code:

int main() { //step 2: int xcoord; int ycoord; step 1: int chessBoard[8][8] = {{-1,-1,-1,-1,-1,-1,-1,-1}, {-1,-1,-1,-1,-1,-1,-1,-1}, {-1,-1,-1,-1,-1,-1,-1,-1}, {-1,-1,-1,-1,-1,-1,-1,-1}, {-1,-1,-1,-1,-1,-1,-1,-1}, {-1,-1,-1,-1,-1,-1,-1,-1}, {-1,-1,-1,-1,-1,-1,-1,-1}, {-1,-1,-1,-1,-1,-1,-1,-1}}; step 2: printf("Enter the x coord for the peice to be set\n"); scanf("%d", &xcoord); printf("Enter the y coord for the peice to be set\n"); scanf("%d", &ycoord); /* since your didn't plan your program out ahead of time you need to go back and add the variables as your create them.*/ step 3: chessBoard[xcoord-1][ycoord-1] = 1; }

have fun.

Programming is problem solveing.
btw I know its easier to use for to set all the elements to -1; he can do that :P

Quote:

Originally Posted by Cyberman86

This is what i have so far, Not sure if it makes sense but i tried my best.

Code:

#include <stdio.h> #include <stdlib.h> #include <math.h> int main() { int random_horse(int chess[8][8], int i, int j) this is a function? you havent declared any variables to pass to the funtion. also you cant declare a funtion inside of main. they can only be created before or after main. If you do it after main you must also include a function header before main. I think you should listen to your instructor and read the book that came with the class. is it to late to drop the class and change your major? for (i=0; i<7; i++) for(j=0; j<7; j++) //? whats going on here?why assign the 8,8 position of the checker board to 16? random_horse[i][j] = i+j; i=2; //wtf is this? j=2; /wtf is this? numofsquares = random_horse(chess, i, j); //what is this suppose to be doing? print(“Number of squares visited = %d\n”, numofsquares); // where in the hell did you declare numberofsquares and //where in the hell did you add anything to it? while(1) i-1>=0 && j-2>=0 && chess [i-1][j-2]== -1) // you have absoluty no idea do you? { pm[k][0] = i-1; // pm[k][1] = j-2; // k++; } { if(k==0) return chess[1][j]; rc = rand_int (0,k-1); x = pm[rc][0]; y = pm[rc][1]; chess[x][y] = chess[i][j] + 1; i=x; j=y; } return 0; }

really looking at your code makes me want to shoot myself.

^^^ ROFL! :D :D :D

I thought something like this was enough to give him a start:

It still needs to be finished, but I know the logic has a bug in it, already.

If the OP finishes the knights possible moves and gets the logic fixed, he'll be good to go, I believe.

/* knight's tour by Adak May 1, 2009

status: just started

In the main() function:
1. Declare a 8x8 two dimensional array (int chess[8][8];) to represent a chess
board and set all its elements to -1 (i.e., no cells (squares) are visited, yet).

2. Ask user to enter i and j as the row and column numbers of the initial cell. (Since
you are using C, make sure that user enters a number between 0 and 7 (inclusive)
for row and column numbers).

3. Set chess[i][j] to 1 means that the horse visited that cell first.

4. Implement and call a function to determine in which order the horse visits the legal
squares once according to our random selection strategy described below and
returns the number of squares visited
numofsquares = random_horse(chess, i, j);
print(“Number of squares visited = %d\n”, numofsquares);

5. Implement and call a function print_board(chess); to print the values in chess
board showing in which order the cells are visited

In the int random_horse(int chess[][8], int i, int j) function:
while(1) {
a. Identify the legal but not-yet-visited squares
b. If there is no such squares return chess[i][j];
c. Pick one of these cells randomly (say you picked chess[x][y])
d. Update order number (chess[x][y] = chess[i][j] + 1;)
e. Move the horse to the selected cell (i=x; j=y;)
} /* end of while */

*/

Code:

#include <stdio.h> #include <stdlib.h> void print_board(int chess[][8]); int random_horse(int chess[][8], int i, int j); int main(void) { int r,c, i, j, numofsquares; int chess[8][8]; for(r = 0; r < 8; r++) for(c = 0; c < 8; c++) chess[r][c] = =1; i = -1; while(i < 0 || i > 7) { printf("\nEnter your starting row [0-7] "); scanf("%d", &i); } j = -1; while(j < 0 || j > 7) { printf("\nEnter your starting column [0-7] "); scanf("%d", &j); } chess[i][j] = 1; numofsquares = random_horse(chess, i, j); print_board(chess); printf("Number of squares visited = %d\n", numofsquares); printf("\n\n\t\t\t press enter when ready "); i = getchar(); return 0; } int random_horse(int chess[][8], int i, int j) { int r = i; int c = j; int k, kmoves, moves, validmoves, n, sqr; int valid[8] = { 0 }; moves = kmoves = 0; /* Log: -1 = sqr has not been visited by the knight >0= sqr has been visited by the knight -2= sqr is a legal next move by the knight array rows are in ascending order on the screen 0 1 2 */ while(1) { //check the 8 (max) possible knight moves if((r > 1) && (c < 7) && (chess[r-2][c+1] == -1)) //1:30 o'clock move ok? chess[r-2][c+1] = -2; if((r > 0) && (c < 6) && (chess[r-1][c+2] == -1)) //2:30 move chess[r-1][c+2] = -2; if((r < 7) && (c < 6) && (chess[r+1][c+2] == -1)) //3:30 move chess[r+1][c+2] = -2; if((r < 6) && (c < 7) && (chess[r+2][c+1] == -1)) //5:30 move chess[r+2][c+1] = -2; //etc., for all 8 possible moves. for(r = 0, k = 0; r < 8; r++) { for(c = 0; c < 8; c++) { if(chess[r][c] == -2) { validmoves++; if(!r) sqr = c; else sqr = r * 10 + c; valid[k] = sqr; ++k; } } } if(!moves) { return chess[i][j]; } n = rand() % validmoves; if(valid[n] < 8) { r = 0; c = valid[n]; } else { r = valid[n] / 10; c = valid[n] % 10; } chess[r][c] = kmoves; ++kmoves; print_board(chess); moves = getchar(); //resets moves = 0; for(i = 0; i < 8; i++) valid[i] = 0; validmoves = 0; } } void print_board(int chess[][8]) { int i, r, c; printf("\n\n"); for(r = 0; r < 8; r++) { for(i = 0; i < 9; i++) { if(i < 8) printf("|---"); else printf("|"); } printf("\n"); for(c = 0; c < 8; c++) { printf("| %d ", chess[r][c]); if(c % 7 == 0 && c > 0) printf("|\n"); } } for(i = 0; i < 9; i++) { if(i < 8) printf("|---"); else printf("|"); } printf("\n"); }

Edit:
A bit of smoothing out was needed, even for a rough idea.

No need to post it here, but the above is on the right track.

The random choice does not allow it to ever complete a full knights tour of all 64 squares, unless you add
more logic, as noted in my posts earlier in the thread.

Quote:

Originally Posted by Adak

^^^ ROFL! :D :D :D

I think looking at your code makes him want to change his major.

^^^ Does that qualify as a Public Service? :p :p

I tried to steer the code toward the assignment, and keep it clear. There is a simpler way to test for a knights move, but I couldn't remember it. If he tried to grok it, the OP would really just get nauseous, anyway. :)

I modified my own version to check all 64 starting squares. The highest number of moves it found was only 53.

I also looked more into Warndorff's algorithm, and apparently it only works 100% of the time, if you use the Ira Pohl innovation, that when you have two moves with identical subsequent move possibilities, you must choose the move which, if it were made, would give the knight on the subsequent move, the fewest possible moves.

(so, check it just one ply deep, in cases where there's a tie).

Coincidentally, Ira Pohl was one of the authors of my very first book on C. :)