(Analysis by Nick Wu)

Imagine that we have already selected the smallest diamond that will be shown. We can then count exactly how many diamonds are no smaller than that one, but can also appear in the display case along with that diamond.

There are up to a thousand possible sizes for the smallest diamond, and at most one thousand diamonds to inspect, giving us roughly one million operations, which will be fast enough.

Here is my Java code demonstrating this solution.

import java.io.*;
import java.util.*;
public class diamond {
public static void main(String[] args) throws IOException {
PrintWriter pw = new PrintWriter(new BufferedWriter(new FileWriter("diamond.out")));
// read in N and K
int n = Integer.parseInt(st.nextToken());
int k = Integer.parseInt(st.nextToken());
// read in sizes of all the diamonds
int[] list = new int[n];
for(int i = 0; i < n; i++) {
}
int ans = 0;
for(int i = 0; i < n; i++) {
// list[i] will be the size of the smallest diamond in the case
int amt = 0;
for(int j = 0; j < n; j++) {
// loop over all diamonds, see if this diamond can be arranged with the selected one
if(list[j] >= list[i] && list[j] <= list[i] + k) {
amt++;
}
}