LeetCode-in-Java

2761. Prime Pairs With Target Sum

Medium

You are given an integer n. We say that two integers x and y form a prime number pair if:

• 1 <= x <= y <= n
• x + y == n
• x and y are prime numbers

Return the 2D sorted list of prime number pairs [xi, yi]. The list should be sorted in increasing order of xi. If there are no prime number pairs at all, return an empty array.

Note: A prime number is a natural number greater than 1 with only two factors, itself and 1.

Example 1:

Input: n = 10

Output: [[3,7],[5,5]]

Explanation:

In this example, there are two prime pairs that satisfy the criteria.

These pairs are [3,7] and [5,5], and we return them in the sorted order as described in the problem statement.

Example 2:

Input: n = 2

Output: []

Explanation:

We can show that there is no prime number pair that gives a sum of 2, so we return an empty array.

Constraints:

• 1 <= n <= 106

Solution

import java.util.ArrayList;
import java.util.HashSet;
import java.util.List;

public class Solution {
    private static final HashSet<Integer> PRIMES = new HashSet<>();
    private static final List<Integer> LIST = new ArrayList<>();

    public List<List<Integer>> findPrimePairs(int n) {
        List<List<Integer>> answer = new ArrayList<>();
        for (int a : LIST) {
            int other = n - a;
            if (other < n / 2 || a > n / 2) {
                break;
            }
            if (PRIMES.contains(other)) {
                answer.add(List.of(a, other));
            }
        }
        return answer;
    }

    static {
        int m = 1000001;
        boolean[] visited = new boolean[m];
        for (int i = 2; i < m; i++) {
            if (!visited[i]) {
                PRIMES.add(i);
                LIST.add(i);
                int j = i;
                while (j < m) {
                    visited[j] = true;
                    j += i;
                }
            }
        }
    }
}

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