三数之和的多种可能

/*
 * Problem: Given an integer array arr and an integer target, return the number of tuples (i, j, k)
 * such that i < j < k and arr[i] + arr[j] + arr[k] == target.
 * The result should be returned modulo 10^9 + 7.
 */

import java.util.*;
import java.util.stream.Collectors;

public class SolutionStream {
    public int threeSumMulti(int[] arr, int target) {
        final int MOD = 1000000007;
        Map<Integer, Long> countMap = Arrays.stream(arr)
                                             .boxed()
                                             .collect(Collectors.groupingBy(e -> e, Collectors.counting()));
        long result = 0;
        List<Integer> keys = new ArrayList<>(countMap.keySet());
        for (int i = 0; i < keys.size(); i++) {
            for (int j = i; j < keys.size(); j++) {
                int x = keys.get(i);
                int y = keys.get(j);
                int z = target - x - y;
                if (countMap.containsKey(z)) {
                    long countX = countMap.get(x);
                    long countY = countMap.get(y);
                    long countZ = countMap.get(z);
                    if (x == y && y == z) {
                        result += countX * (countX - 1) * (countX - 2) / 6;
                    } else if (x == y && y != z) {
                        result += countX * (countX - 1) / 2 * countZ;
                    } else if (x < y && y < z) {
                        result += countX * countY * countZ;
                    }
                    result %= MOD;
                }
            }
        }
        return (int) result;
    }
}