pub type DistanceMatrix = Vec<Vec<usize>>;

pub fn print_table(table: &DistanceMatrix) {
    for row in table {
        for item in row {
            print!("{} ", item);
        }
        println!("");
    }
}

// Returns an initialized distance table of dimensions m+1 * n+1
// Where the first row is 0..n+1
// The First column is 0..m+1
// And the rest of the values are usize::MAX
pub fn get_distance_table(m: usize, n: usize) -> DistanceMatrix {
    let mut distances: Vec<Vec<usize>> = Vec::with_capacity(m + 1);

    // The first row
    distances.push((0..n + 1).collect());

    for i in 1..m + 1 {
        // initialize the whole row to sentinel
        distances.push(vec![usize::MAX; n + 1]);
        // update the first item in the row
        distances[i][0] = i;
    }

    distances
}