The challenge
A Hamming number is a positive integer of the form 2i3j5k, for some non-negative integers i, j, and k.
Write a function that computes the _n_th smallest Hamming number.
Specifically:
- The first smallest Hamming number is 1 = 235
- The second smallest Hamming number is 2 = 2135
- The third smallest Hamming number is 3 = 2315
- The fourth smallest Hamming number is 4 = 2235
- The fifth smallest Hamming number is 5 = 2351
The 20 smallest Hamming numbers are given in example test fixture.
The solution in Java code
Option 1:
public class Hamming {
public static long hamming(int n) {
long[] h = new long[n];
h[0] = 1;
long x2 = 2, x3 = 3, x5 = 5;
int i = 0, j = 0, k = 0;
for (int index = 1; index < n; index++) {
h[index] = Math.min(x2, Math.min(x3, x5));
if (h[index] == x2) x2 = 2 * h[++i];
if (h[index] == x3) x3 = 3 * h[++j];
if (h[index] == x5) x5 = 5 * h[++k];
}
return h[n - 1];
}
}
Option 2:
import java.util.Arrays;
import java.util.TreeSet;
public class Hamming {
public static long hamming(int n) {
if (n <= 0) return -1;
TreeSet<Long> ts = new TreeSet<>(Arrays.asList(2L, 3L, 5L));
long smallest = 1;
for (int i = 1; i < n; i++) {
smallest = ts.pollFirst();
ts.add(smallest * 2);
ts.add(smallest * 3);
ts.add(smallest * 5);
}
return smallest;
}
}
Option 3:
import java.util.PriorityQueue;
public class Hamming {
public static long hamming(int n) {
PriorityQueue<Long> minheap = new PriorityQueue<Long>();
minheap.add(2L);
minheap.add(3L);
minheap.add(5L);
long curr = 1;
for (int i = 1; i < n; i++) {
curr = minheap.poll();
while (minheap.peek() == curr) {curr = minheap.poll();}
minheap.add(curr*2);
minheap.add(curr*3);
minheap.add(curr*5);
}
return curr;
}
}
Test cases to validate our solution
import org.junit.*;
import static org.junit.Assert.*;
public class HammingTests {
@Test
public void Test1() {
Assert.assertEquals("hamming(1) should be 1", 1, Hamming.hamming(1));
Assert.assertEquals("hamming(2) should be 2", 2, Hamming.hamming(2));
Assert.assertEquals("hamming(3) should be 3", 3, Hamming.hamming(3));
Assert.assertEquals("hamming(4) should be 4", 4, Hamming.hamming(4));
Assert.assertEquals("hamming(5) should be 5", 5, Hamming.hamming(5));
Assert.assertEquals("hamming(6) should be 6", 6, Hamming.hamming(6));
Assert.assertEquals("hamming(7) should be 8", 8, Hamming.hamming(7));
Assert.assertEquals("hamming(8) should be 9", 9, Hamming.hamming(8));
Assert.assertEquals("hamming(9) should be 10", 10, Hamming.hamming(9));
Assert.assertEquals("hamming(10) should be 12", 12, Hamming.hamming(10));
Assert.assertEquals("hamming(11) should be 15", 15, Hamming.hamming(11));
Assert.assertEquals("hamming(12) should be 16", 16, Hamming.hamming(12));
Assert.assertEquals("hamming(13) should be 18", 18, Hamming.hamming(13));
Assert.assertEquals("hamming(14) should be 20", 20, Hamming.hamming(14));
Assert.assertEquals("hamming(15) should be 24", 24, Hamming.hamming(15));
Assert.assertEquals("hamming(16) should be 25", 25, Hamming.hamming(16));
Assert.assertEquals("hamming(17) should be 27", 27, Hamming.hamming(17));
Assert.assertEquals("hamming(18) should be 30", 30, Hamming.hamming(18));
Assert.assertEquals("hamming(19) should be 32", 32, Hamming.hamming(19));
}
}
