The challenge
Create a function that returns an array containing the first l digits from the nth 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:
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:
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:
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
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;
}
}
