Say I have some set of arrays with variable size, e.g. [a, b, c] and [1, 2]
The cartesian product would be:
[
[a, 1],
[a, 2],
[b, 1],
[b, 2],
[c, 1],
[c, 2]
]
As the number of initial arrays increase the size of the cartesian product quickly gets very large.
Is it possible to figure out what value would be in a given cell (i, j), for any number of initial arrays without having to generate the whole truth table?
(In the truth table above (0, 0) => a, (0, 1) => 1 )
Thanks to @Sebastian and @Damien for answering the question in the comments.
Here's how I implemented the function in Java:
public static class CartesianValueFactory {
private final Object[][] dimensions;
public CartesianValueFactory(Object[][] dimensions) {
this.dimensions = dimensions;
}
public Object valueAt(long row, int column) {
long index = row;
for (int nextColumn = column + 1; nextColumn < dimensions.length; nextColumn++) {
index = index / dimensions[nextColumn].length;
}
if (column == 0) {
return dimensions[column][(int) index];
} else {
return dimensions[column][(int) index % dimensions[column].length];
}
}
}