## The challenge

Create a function that returns an array containing the first `l` digits from the `n`th diagonal of Pascal’s triangle.

`n = 0` should generate the first diagonal of the triangle (the ‘ones’). The first number in each diagonal should be 1.

If `l = 0`, return an empty array. Assume that both `n` and `l` will be non-negative integers in all test cases.

## The solution in Java code

Option 1:

 `````` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 `````` ``````public class PascalDiagonals { public static long[] generateDiagonal(int n, int l) { long[] result = new long[l]; if(l > 0) { result[0] = 1; } for(int i = 1; i < l; i++) { result[i] = ( result[i-1] * (n + i) / i); } return result; } } ``````

Option 2:

 `````` 1 2 3 4 5 6 7 8 9 10 11 12 `````` ``````public class PascalDiagonals { public static long[] generateDiagonal(int n, int l) { long[] result = new long[l]; if (l > 0) { result[0] = 1; for (int i = 1; i < l; ++i) result[i] = result[i-1] * (n + i) / i; } return result; } } ``````

Option 3:

 `````` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 `````` ``````public class PascalDiagonals { public static long[] generateDiagonal(int n, int l) { if (l == 0) return new long[0]; long[] diagonal = new long[l]; long[] temp = null; long[][] result = new long[n + l][]; for (int i = 1; i <= n + l; i++) { long[] row = new long[i]; for (int j = 0; j < i; j++) { if (j == 0 || j == i - 1) row[j] = 1; else row[j] = temp[j - 1] + temp[j]; } result[i - 1] = row; temp = row; } for (int i = n, j = 0; i < n + l; i++, j++) { diagonal[j] = result[i][n]; } return diagonal; } } ``````

## Test cases to validate our solution

 `````` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 `````` ``````import org.junit.Test; import static org.junit.Assert.assertArrayEquals; import org.junit.runners.JUnit4; import java.util.Random; import java.util.Arrays; public class SolutionTest { @Test public void basicTests() { long[] expected = new long[] { 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 }; assertArrayEquals("All the ones", expected, PascalDiagonals.generateDiagonal(0, 10)); expected = new long[] { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 }; assertArrayEquals("Natural numbers", expected, PascalDiagonals.generateDiagonal(1, 10)); expected = new long[] { 1, 3, 6, 10, 15, 21, 28, 36, 45, 55 }; assertArrayEquals("Triangular numbers", expected, PascalDiagonals.generateDiagonal(2, 10)); expected = new long[] { 1, 4, 10, 20, 35, 56, 84, 120, 165, 220 }; assertArrayEquals("Tetrahedral numbers", expected, PascalDiagonals.generateDiagonal(3, 10)); expected = new long[] { 1, 5, 15, 35, 70, 126, 210, 330, 495, 715 }; assertArrayEquals("Pentatope numbers", expected, PascalDiagonals.generateDiagonal(4, 10)); } @Test public void edgeCases() { assertArrayEquals("Array length zero", new long[] {}, PascalDiagonals.generateDiagonal(10, 0)); long[] expected = new long[] { 1, 101, 5151, 176851, 4598126, 96560646 }; assertArrayEquals("Late row, short array", expected, PascalDiagonals.generateDiagonal(100, 6)); } @Test public void randomTests() { Random r = new Random(); for (int i = 0; i < 100; i++) { int n = r.nextInt(26) + 25; int l = r.nextInt(6) + 10; assertArrayEquals("Random " + i, generateDiagonal(n, l), PascalDiagonals.generateDiagonal(n, l)); } } private static long[] generateDiagonal(int n, int l) { long[] diagonal = new long[l]; Arrays.fill(diagonal, 1); for (int i = 1; i < l; i++) diagonal[i] = diagonal[i - 1] * (n + i) / i; return diagonal; } } ``````