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2447. Number of Subarrays With GCD Equal to K 👍

  • Time: $O(n\log(\min(\texttt{nums})))$
  • Space: $O(n)$
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class Solution {
 public:
  int subarrayGCD(vector<int>& nums, int k) {
    int ans = 0;
    unordered_map<int, int> gcds;

    for (const int num : nums)
      if (num % k == 0) {
        unordered_map<int, int> nextGcds{{num, 1}};
        for (const auto& [prevGcd, count] : gcds)
          nextGcds[gcd(prevGcd, num)] += count;
        ans += nextGcds[k];
        gcds = std::move(nextGcds);
      } else {
        // The GCD streak stops, so fresh start from the next number.
        gcds.clear();
      }

    return ans;
  }
};

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class Solution {
  public int subarrayGCD(int[] nums, int k) {
    int ans = 0;
    Map<Integer, Integer> gcds = new HashMap<>();

    for (final int num : nums)
      if (num % k == 0) {
        Map<Integer, Integer> nextGcds = new HashMap<>();
        nextGcds.put(num, 1);
        for (Map.Entry<Integer, Integer> entry : gcds.entrySet()) {
          final int prevGcd = entry.getKey();
          final int count = entry.getValue();
          nextGcds.merge(gcd(prevGcd, num), count, Integer::sum);
        }
        ans += nextGcds.getOrDefault(k, 0);
        gcds = nextGcds;
      } else {
        // The GCD streak stops, so fresh start from the next number.
        gcds.clear();
      }

    return ans;
  }

  private int gcd(int a, int b) {
    return b == 0 ? a : gcd(b, a % b);
  }
}

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class Solution:
  def subarrayGCD(self, nums: list[int], k: int) -> int:
    ans = 0
    gcds = collections.Counter()

    for num in nums:
      if num % k == 0:
        nextGcds = collections.defaultdict(int)
        nextGcds[num] += 1
        for prevGcd, count in gcds.items():
          nextGcds[math.gcd(prevGcd, num)] += count
        ans += nextGcds.get(k, 0)
        gcds = nextGcds
      else:
        # The GCD streak stops, so fresh start from the next number.
        gcds.clear()

    return ans