3569 - Maximize Count of Distinct Primes After Split.

Hard

You are given an integer array nums having length n and a 2D integer array queries where queries[i] = [idx, val].

For each query:

• Update nums[idx] = val.

• Choose an integer k with 1 <= k < n to split the array into the non-empty prefix nums[0..k-1] and suffix nums[k..n-1] such that the sum of the counts of distinct prime values in each part is maximum.

Note: The changes made to the array in one query persist into the next query.

Return an array containing the result for each query, in the order they are given.

Example 1:

Input: nums = 2,1,3,1,2, queries = [1,2,3,3]

Output: 3,4

Explanation:

• Initially nums = [2, 1, 3, 1, 2].

• After 1^st query, nums = [2, 2, 3, 1, 2]. Split nums into [2] and [2, 3, 1, 2]. [2] consists of 1 distinct prime and [2, 3, 1, 2] consists of 2 distinct primes. Hence, the answer for this query is 1 + 2 = 3.

• After 2^nd query, nums = [2, 2, 3, 3, 2]. Split nums into [2, 2, 3] and [3, 2] with an answer of 2 + 2 = 4.

• The output is [3, 4].

Example 2:

Input: nums = 2,1,4, queries = [0,1]

Output: 0

Explanation:

• Initially nums = [2, 1, 4].

• After 1^st query, nums = [1, 1, 4]. There are no prime numbers in nums, hence the answer for this query is 0.

• The output is [0].

Constraints:

• <code>2 <= n == nums.length <= 5 * 10⁴</code>

• <code>1 <= queries.length <= 5 * 10⁴</code>

• <code>1 <= numsi<= 10⁵</code>

• 0 <= queries[i][0] < nums.length

• <code>1 <= queries1<= 10⁵</code>