Maximize Count of Distinct Primes After Split

Maximize Count of Distinct Primes After Split - Problem

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.

Input & Output

Example 1 — Basic Case

$ Input: nums = [4,2,6,10], queries = [[1,3],[3,7]]

› Output: [1,2]

💡 Note: Query 1: nums becomes [4,3,6,10]. All possible splits give 1 distinct prime total (the prime 3 appears in either left or right part). Query 2: nums becomes [4,3,6,7]. Split at k=1 gives left=[4] (0 primes) and right=[3,6,7] (2 primes: 3,7) for total=2. Other splits also give total=2. Maximum is 2.

Example 2 — Small Array

$ Input: nums = [2,3], queries = [[0,5]]

› Output: [2]

💡 Note: After update: nums = [5,3]. Only one split possible at k=1: left=[5] (1 prime) + right=[3] (1 prime) = 2 total distinct primes.

Example 3 — No Primes

$ Input: nums = [4,6,8,9], queries = [[1,10]]

› Output: [0]

💡 Note: After update: nums = [4,10,8,9]. No matter how we split, there are no prime numbers, so the result is 0.

Constraints

2 ≤ nums.length ≤ 10³
1 ≤ queries.length ≤ 10³
1 ≤ nums[i], val ≤ 10⁶
0 ≤ idx < nums.length

Visualization

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Asked in

G Google 25 a Amazon 18 M Microsoft 15

This problem requires efficiently handling array updates and finding optimal splits to maximize distinct prime counts. The key insight is to precompute prefix and suffix prime counts after each update to avoid redundant calculations. Best approach uses prefix/suffix arrays with time O(q × n × √max_val) and space O(n).

Common Approaches

✓ Bfs

⏱️ Time: N/A Space: N/A

Dfs

⏱️ Time: N/A Space: N/A

Brute Force

⏱️ Time: O(q × n × m × √max_val) Space: O(1)

Update the array, then for each possible split position, count distinct primes in left and right parts. Choose the split that maximizes the sum of distinct prime counts.

Prefix/Suffix Precomputation

⏱️ Time: O(q × n × √max_val) Space: O(n)

For each query, precompute the count of distinct primes from left (prefix) and from right (suffix) for each position. Then combine these counts efficiently.

Algorithm Steps — Algorithm Steps

Code -

solution.c — C

Time & Space Complexity

Time Complexity

⏱️

✓ Linear Growth

Space Complexity

✓ Linear Space

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