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1851. Minimum Interval to Include Each Query 👍

  • Time: $O(\texttt{sort}(n) + \texttt{sort}(q) + q\log n)$
  • Space: $O(n + q)$
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struct T {
  int size;
  int right;
};

class Solution {
 public:
  vector<int> minInterval(vector<vector<int>>& intervals,
                          vector<int>& queries) {
    vector<int> ans(queries.size(), -1);
    auto compare = [](const T& a, const T& b) { return a.size > b.size; };
    priority_queue<T, vector<T>, decltype(compare)> minHeap(compare);
    vector<vector<int>> qs;

    for (int i = 0; i < queries.size(); ++i)
      qs.push_back({queries[i], i});

    ranges::sort(intervals);
    ranges::sort(qs);

    int i = 0;  // intervals' index
    for (const vector<int>& q : qs) {
      while (i < intervals.size() && intervals[i][0] <= q[0]) {
        minHeap.emplace(intervals[i][1] - intervals[i][0] + 1, intervals[i][1]);
        ++i;
      }
      while (!minHeap.empty() && minHeap.top().right < q[0])
        minHeap.pop();
      if (!minHeap.empty())
        ans[q[1]] = minHeap.top().size;
    }

    return ans;
  }
};

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class Solution {
  public int[] minInterval(int[][] intervals, int[] queries) {
    record T(int size, int right) {}
    int[] ans = new int[queries.length];
    Arrays.fill(ans, -1);
    Queue<T> minHeap = new PriorityQueue<T>((a, b) -> Integer.compare(a.size, b.size));
    Integer[] indices = new Integer[queries.length];

    for (int i = 0; i < queries.length; ++i)
      indices[i] = i;

    Arrays.sort(intervals, (a, b) -> Integer.compare(a[0], b[0]));
    Arrays.sort(indices, (a, b) -> Integer.compare(queries[a], queries[b]));

    int i = 0; // intervals' index
    for (final int index : indices) {
      while (i < intervals.length && intervals[i][0] <= queries[index]) {
        minHeap.offer(new T(intervals[i][1] - intervals[i][0] + 1, intervals[i][1]));
        ++i;
      }
      while (!minHeap.isEmpty() && minHeap.peek().right < queries[index])
        minHeap.poll();
      if (!minHeap.isEmpty())
        ans[index] = minHeap.peek().size;
    }

    return ans;
  }
}