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3440. Reschedule Meetings for Maximum Free Time II 👍

  • Time: $O(n)$
  • Space: $O(n)$
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class Solution {
 public:
  int maxFreeTime(int eventTime, vector<int>& startTime, vector<int>& endTime) {
    const int n = startTime.size();
    const vector<int> gaps = getGaps(eventTime, startTime, endTime);
    int ans = 0;
    vector<int> maxLeft(n + 1);   // maxLeft[i] := max(gaps[0..i])
    vector<int> maxRight(n + 1);  // maxRight[i] := max(gaps[i..n])

    maxLeft[0] = gaps[0];
    maxRight[n] = gaps[n];

    for (int i = 1; i < n + 1; ++i)
      maxLeft[i] = max(gaps[i], maxLeft[i - 1]);

    for (int i = n - 1; i >= 0; --i)
      maxRight[i] = max(gaps[i], maxRight[i + 1]);

    for (int i = 0; i < n; ++i) {
      const int currMeetingTime = endTime[i] - startTime[i];
      const int adjacentGapsSum = gaps[i] + gaps[i + 1];
      const bool canMoveMeeting =
          currMeetingTime <= max(i > 0 ? maxLeft[i - 1] : 0,  //
                                 i + 2 < n + 1 ? maxRight[i + 2] : 0);
      ans = max(ans, adjacentGapsSum + (canMoveMeeting ? currMeetingTime : 0));
    }

    return ans;
  }

 private:
  vector<int> getGaps(int eventTime, const vector<int>& startTime,
                      const vector<int>& endTime) {
    vector<int> gaps{startTime[0]};
    for (int i = 1; i < startTime.size(); ++i)
      gaps.push_back(startTime[i] - endTime[i - 1]);
    gaps.push_back(eventTime - endTime.back());
    return gaps;
  }
};

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class Solution {
  public int maxFreeTime(int eventTime, int[] startTime, int[] endTime) {
    final int n = startTime.length;
    final int[] gaps = getGaps(eventTime, startTime, endTime);
    int ans = 0;
    int[] maxLeft = new int[n + 1];  // maxLeft[i] := max(gaps[0..i])
    int[] maxRight = new int[n + 1]; // maxRight[i] := max(gaps[i..n])

    maxLeft[0] = gaps[0];
    maxRight[n] = gaps[n];

    for (int i = 1; i < n + 1; ++i)
      maxLeft[i] = Math.max(gaps[i], maxLeft[i - 1]);

    for (int i = n - 1; i >= 0; --i)
      maxRight[i] = Math.max(gaps[i], maxRight[i + 1]);

    for (int i = 0; i < n; ++i) {
      final int currMeetingTime = endTime[i] - startTime[i];
      final int adjacentGapsSum = gaps[i] + gaps[i + 1];
      final boolean canMoveMeeting =
          currMeetingTime <= Math.max(i > 0 ? maxLeft[i - 1] : 0, //
                                      i + 2 < n + 1 ? maxRight[i + 2] : 0);
      ans = Math.max(ans, adjacentGapsSum + (canMoveMeeting ? currMeetingTime : 0));
    }

    return ans;
  }

  private int[] getGaps(int eventTime, int[] startTime, int[] endTime) {
    int[] gaps = new int[startTime.length + 1];
    gaps[0] = startTime[0];
    for (int i = 1; i < startTime.length; ++i)
      gaps[i] = startTime[i] - endTime[i - 1];
    gaps[startTime.length] = eventTime - endTime[endTime.length - 1];
    return gaps;
  }
}

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class Solution:
  def maxFreeTime(
      self,
      eventTime: int,
      startTime: list[int],
      endTime: list[int]
  ) -> int:
    n = len(startTime)
    gaps = ([startTime[0]] +
            [startTime[i] - endTime[i - 1] for i in range(1, len(startTime))] +
            [eventTime - endTime[-1]])
    ans = 0
    maxLeft = [gaps[0]] + [0] * n  # maxLeft[i] := max(gaps[0..i])
    maxRight = [0] * n + [gaps[n]]  # maxRight[i] := max(gaps[i..n])

    for i in range(1, n + 1):
      maxLeft[i] = max(gaps[i], maxLeft[i - 1])

    for i in range(n - 1, -1, -1):
      maxRight[i] = max(gaps[i], maxRight[i + 1])

    for i, (start, end) in enumerate(zip(startTime, endTime)):
      currMeetingTime = end - start
      adjacentGapsSum = gaps[i] + gaps[i + 1]
      canMoveMeeting = currMeetingTime <= max(
          maxLeft[i - 1] if i > 0 else 0,
          maxRight[i + 2] if i + 2 < n + 1 else 0
      )
      ans = max(ans, adjacentGapsSum +
                (currMeetingTime if canMoveMeeting else 0))

    return ans