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Problem solution · C++

Count Prime Gap Balanced Subarrays

Count Prime Gap Balanced Subarrays: a C++ solution using sliding window or two pointers. Learn the idea, check the complexity, and read the full code, with credit to Kamyu LeetCode Solutions.

Technique
Sliding window or two pointers
Source
Kamyu LeetCode Solutions
Length
61 lines
Start with the idea.

Try the problem first. If you get stuck, read the approach below, then write your own solution. The full code is at the bottom.

Approach

Sliding window or two pointers

For Count Prime Gap Balanced Subarrays, the implementation maintains a moving interval and updates only the information that enters or leaves the window.

  1. Choose the invariant that makes a window valid or useful.
  2. Advance the right boundary and add the new element.
  3. Move the left boundary only as needed while maintaining the invariant and updating the answer.

Code notes

  • 61 lines of C++ from the credited upstream file count-prime-gap-balanced-subarrays.cpp.
  • The implementation visibly relies on sequence storage, work queue.
  • 6 loop blocks detected.

Complexity

Confirm that neither pointer moves backwards; if so, the scan is usually linear apart from the window’s data-structure operations.

Check the problem constraints before deciding whether this complexity will pass.

Source

Code and credit

This code comes from Kamyu LeetCode Solutions by kamyu104 and is used under the MIT licence.

Open problem ↗Original source ↗
Full codeCount Prime Gap Balanced Subarrays · C++C++
Use this to learn the idea, then write your own version.
// Time:  precompute: O(r), r = max(nums)//        runtime:    O(n)// Space: O(r) // number theory, mono deque, two pointers, sliding windowvector<int> linear_sieve_of_eratosthenes(int n) {  // Time: O(n), Space: O(n)    vector<int> spf(n + 1, -1);    vector<int> primes;    for (int i = 2; i <= n; ++i) {        if (spf[i] == -1) {            spf[i] = i;            primes.emplace_back(i);        }        for (const auto& p : primes) {            if (i * p > n || p > spf[i]) {                break;            }            spf[i * p] = p;        }    }    return spf;}; const int MAX_NUMS = 5 * 1e4;const auto& SPF = linear_sieve_of_eratosthenes(MAX_NUMS);class Solution {public:    int primeSubarray(vector<int>& nums, int k) {        deque<int> idxs, max_dq, min_dq;        int result = 0;        for (int right = 0, left = 0; right < size(nums); ++right) {            if (SPF[nums[right]] == nums[right]) {                idxs.emplace_back(right);                while (!empty(max_dq) && nums[max_dq.back()] <= nums[right]) {                    max_dq.pop_back();                }                max_dq.emplace_back(right);                while (!empty(min_dq) && nums[min_dq.back()] >= nums[right]) {                    min_dq.pop_back();                }                min_dq.emplace_back(right);                for (; nums[max_dq[0]] - nums[min_dq[0]] > k; ++left) {                    if (max_dq[0] == left) {                        max_dq.pop_front();                    }                    if (min_dq[0] == left) {                        min_dq.pop_front();                    }                    if (idxs[0] == left) {                        idxs.pop_front();                    }                }            }            if (size(idxs) >= 2) {                result += (idxs[size(idxs) - 2]) - left + 1;            }        }        return result;    }};

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