This problem requires updating an array and tracking distinct prime numbers after each modification. Using a sieve to preprocess primes and a data structure to maintain counts allows each query to be processed efficiently. The approach balances math insights with array manipulation for optimal performance under tight constraints.
Problem Statement
Given an integer array nums of length n and a 2D array queries where each query is [index, value], update nums[index] to value for each query. After each update, compute the maximum number of distinct prime numbers that can exist in the updated array.
Note that changes made in one query persist for subsequent queries. Your goal is to return an array of results representing the count of distinct primes after each update.
Examples
Example 1
Input: nums = [2,1,3,1,2], queries = [[1,2],[3,3]]
Output: [3,4]
Example 2
Input: nums = [2,1,4], queries = [[0,1]]
Output: [0]
Constraints
- 2 <= n == nums.length <= 5 * 104
- 1 <= queries.length <= 5 * 104
- 1 <= nums[i] <= 105
- 0 <= queries[i][0] < nums.length
- 1 <= queries[i][1] <= 105
Solution Approach
Preprocess Primes with a Sieve
Generate all primes up to the maximum possible value in nums using the Sieve of Eratosthenes. This allows constant-time primality checks for each number during updates.
Maintain Frequency Counts
Track the frequency of each prime in the current array. When an element is updated, adjust counts for any primes involved to quickly determine the number of distinct primes without rescanning the array.
Process Queries Efficiently
Iterate through queries, update nums, adjust prime frequencies, and record the current distinct prime count after each change. This ensures each query runs in near O(1) time relative to primes affected.
Complexity Analysis
| Metric | Value |
|---|---|
| Time | Depends on the final approach |
| Space | Depends on the final approach |
Time complexity depends on preprocessing primes (O(maxNum log log maxNum)) and processing each query efficiently using frequency maps. Space complexity is dominated by storing prime flags and counts, both O(maxNum).
What Interviewers Usually Probe
- Are you using preprocessing to check primality efficiently?
- How do you track distinct primes after each update without rescanning the array?
- Can you handle multiple queries while maintaining correctness under persistent changes?
Common Pitfalls or Variants
Common pitfalls
- Failing to preprocess primes, leading to repeated slow primality checks.
- Updating counts incorrectly, which can produce wrong distinct prime results.
- Not persisting previous updates before processing the next query.
Follow-up variants
- Compute the sum of distinct primes after each update instead of the count.
- Find distinct primes in a sliding window after multiple updates.
- Allow deletions and insertions in nums, requiring dynamic prime tracking.
How GhostInterview Helps
- Automatically identifies primes in nums and updates frequency counts per query.
- Provides optimized handling of array updates while maintaining distinct prime counts.
- Highlights edge cases where updates overwrite previously counted primes.
Topic Pages
Related GhostInterview Pages
- LeetCode Interview Copilot - Use GhostInterview as a live solver when you want direct help with LeetCode-style coding questions.
- Coding Interview Assistant - See how GhostInterview supports array, string, linked list, graph, and tree interview workflows.
- How GhostInterview Works - Review the screenshot, reasoning, and answer flow before using the solver in a live interview.
FAQ
What is the main challenge in Maximize Count of Distinct Primes After Split?
The challenge is efficiently tracking distinct primes after each update while handling persistent changes to the array.
Should I recompute primes from scratch after each query?
No, preprocessing all primes using a sieve allows constant-time checks and avoids redundant computation.
How does the array plus math pattern apply here?
Array manipulation handles updates, while number theory and the sieve help quickly identify and count distinct primes.
Can segment trees help in this problem?
Yes, segment trees can maintain prime frequency counts for range queries or batch updates if needed.
What is a common mistake when updating counts?
Forgetting to decrement the count of primes from the old value before incrementing for the new value can lead to incorrect results.
Need direct help with Maximize Count of Distinct Primes After Split instead of spending more time grinding it?
Download GhostInterview when you want a LeetCode solver, not another long practice loop. Capture Maximize Count of Distinct Primes After Split from a screenshot, get the answer path and complexity, and use supported stealth workflows that stay outside captured layers.
Capture the prompt fast instead of rewriting the problem by hand.
Get the solution path, trade-offs, and complexity summary in one pass.
Stay outside captured layers on supported screen-share workflows.
Stay in the same pattern family
The problem requires finding the minimum stability factor of an array by utilizing binary search and math-based optimizations.
Open problem page#3574 Maximize Subarray GCD ScoreMaximize Subarray GCD Score focuses on maximizing a subarray's score by using at most k doubling operations on an array of integers.
Open problem page#3589 Count Prime-Gap Balanced SubarraysCount the number of prime-gap balanced subarrays in an integer array using sliding window techniques and running state updates.
Open problem page