Hi guys, hopefully this is an easy one for you.
Given a grid of nxn squares, where each square has an id, the first(top left) square has id 0 (so a 5x5 grid will have ids 0-24) like below:
grid.png
I need to generate all diagonal solutions of length Y. So if Y is 3, then some of the solutions will be:
grid1.png
and
grid2.png
and
grid3.png
but obviously NOT
grid4.png
Any ideas how these solutions can be generated?
This is what Iv got so far (dimension = 5, inARow = 3):
public ArrayList<int[]> getSolutions(int dimension, int inARow) {
ArrayList<int[]> solutions = new ArrayList<int[]>();
//create row solutions
for(int i=0; i<dimension*dimension; i = i+dimension) {
for(int j=i; j<=i+dimension - inARow; j++){
int[] row = new int[inARow];
int counter = 0;
for(int k=j; k<j+inARow; k++){
row[counter++] = k;
}
solutions.add(row);
}
}
//create column solutions
for(int i=0;i<dimension;i++){
for(int j=i; j<(dimension*dimension)-(dimension*inARow)+dimension;j=j+dimension){
int[] col = new int[inARow];
int counter = 0;
for(int k=j;k<j+(dimension*inARow);k=k+dimension){
col[counter++] = k;
}
solutions.add(col);
}
}
//create diagonals
for(int i=0; i<dimension*dimension; i++){
for(int j=i; j<i+(dimension * inARow); j = j+dimension+1){
System.out.println(j);
}
}
return solutions;
This gives me all the diagonal solutions but also gives me the bad ones like 3,9,15. Im having trouble eliminating those.
Anti-diagonals are also solutions so 2,6,10 would also be a solution but if I get normal diagonals working I can probably do the same for anti-diagonals.