2761. Prime Pairs With Target Sum
You are given an integer n. We say that two integers x and y form a prime number pair if:
1 <= x <= y <= nx + y == nxandyare 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
ArrayMathEnumerationNumber Theory
Hints
Hint 1
Pre-compute all the prime numbers in the range [1, n] using a sieve, and store them in a data structure where they can be accessed in O(1) time.
Hint 2
For x in the range [2, n/2], we can use the pre-computed list of prime numbers to check if both x and n - x are primes. If they are, we add them to the result.
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