Task: Bell numbers





Java: import java.util.ArrayList;
import java.util.List;

public class Bell {
    private static class BellTriangle {
        private List<Integer> arr;

        BellTriangle(int n) {
            int length = n * (n + 1) / 2;
            arr = new ArrayList<>(length);
            for (int i = 0; i < length; ++i) {
                arr.add(0);
            }

            set(1, 0, 1);
            for (int i = 2; i <= n; ++i) {
                set(i, 0, get(i - 1, i - 2));
                for (int j = 1; j < i; ++j) {
                    int value = get(i, j - 1) + get(i - 1, j - 1);
                    set(i, j, value);
                }
            }
        }

        private int index(int row, int col) {
            if (row > 0 && col >= 0 && col < row) {
                return row * (row - 1) / 2 + col;
            } else {
                throw new IllegalArgumentException();
            }
        }

        public int get(int row, int col) {
            int i = index(row, col);
            return arr.get(i);
        }

        public void set(int row, int col, int value) {
            int i = index(row, col);
            arr.set(i, value);
        }
    }

    public static void main(String[] args) {
        final int rows = 15;
        BellTriangle bt = new BellTriangle(rows);

        System.out.println("First fifteen Bell numbers:");
        for (int i = 0; i < rows; ++i) {
            System.out.printf("%2d: %d\n", i + 1, bt.get(i + 1, 0));
        }

        for (int i = 1; i <= 10; ++i) {
            System.out.print(bt.get(i, 0));
            for (int j = 1; j < i; ++j) {
                System.out.printf(", %d", bt.get(i, j));
            }
            System.out.println();
        }
    }
}







Ada: with Ada.Text_IO; use Ada.Text_IO;
procedure Main is
	type Bell_Triangle is array(Positive range <>, Positive range <>) of Natural;
	
	
	procedure Print_Rows (Row : in Positive; Triangle : in Bell_Triangle) is
		begin
			if Row in Triangle'Range(1) then
				for I in Triangle'First(1) .. Row loop
					Put_Line (Triangle (I, 1)'Image);
				end loop;
			end if;
	end Print_Rows;
	
	procedure Print_Triangle (Num : in Positive; Triangle : in Bell_Triangle) is
		begin
			if Num in Triangle'Range then
				for I in Triangle'First(1) .. Num loop
					for J in Triangle'First(2) .. Num loop
						if Triangle (I, J) /= 0 then
							Put (Triangle (I, J)'Image);
						end if;
					end loop;
					New_Line;
				end loop;
			end if;
	end Print_Triangle;
	
	procedure Bell_Numbers is
		Triangle : Bell_Triangle(1..15, 1..15) := (Others => (Others => 0));
		Temp     : Positive := 1;
		begin
			
			Triangle (1, 1) := 1;
			
			for I in Triangle'First(1) + 1 .. Triangle'Last(1) loop
				Triangle (I, 1) := Temp;
				
				for J in Triangle'First(2) .. Triangle'Last(2) - 1 loop
					if Triangle (I - 1, J) /= 0 then
						Triangle (I, J + 1) := Triangle (I, J) + Triangle (I - 1, J);
					else
						Temp := Triangle (I, J);
						exit;
					end if;
				end loop;
			end loop;
			
			Put_Line ("First 15 Bell numbers:");
			Print_Rows (15, Triangle);
			
			New_Line;
			
			Put_Line ("First 10 rows of the Bell triangle:");
			Print_Triangle (10, Triangle);
	end Bell_Numbers;
begin
	Bell_Numbers;
end Main;