Find if k bookings possible with given arrival and departure times

A hotel manager has to process N advance bookings of rooms for the next season. His hotel has K rooms. Bookings contain an arrival date and a departure date. He wants to find out whether there are enough rooms in the hotel to satisfy the demand.

The idea is to sort the arrays and keep track of overlaps.

Examples:

Input :  Arrivals :   [1 3 5]
         Departures : [2 6 8]
         K : 1
Output : False
Hotel manager needs at least two
rooms as the second and third 
intervals overlap.


The idea is store arrival and departure times in an auxiliary array with an additional marker to indicate whether time is arrival or departure. Now sort the array. Process the sorted array, for every arrival increment active bookings. And for every departure, decrement. Keep track of maximum active bookings. If count of active bookings at any moment is more than k, then return false. Else return return true.

Below is the c++ code for above approach.

#include <bits/stdc++.h>
using namespace std;

bool areBookingsPossible(int arrival[], 
           int departure[], int n, int k)
{
    vector<pair<int, int> > ans;

    // create a common vector both arrivals
    // and departures.
    for (int i = 0; i < n; i++) {
        ans.push_back(make_pair(arrival[i], 1));
        ans.push_back(make_pair(departure[i], 0));
    }

    // sort the vector
    sort(ans.begin(), ans.end());

    int curr_active = 0, max_active = 0;

    for (int i = 0; i < ans.size(); i++) {

        // if new arrival, increment current
        // guests count and update max active 
        // guests so far
        if (ans[i].second == 1) {
            curr_active++;
            max_active = max(max_active, 
                            curr_active);
        }

        // if a guest departs, decrement 
        // current guests count.
        else
            curr_active--;
    }

    // if max active guests at any instant 
    // were more than the available rooms, 
    // return false. Else return true.
    return (k >= max_active);
}

int main()
{
    int arrival[] = { 1, 3, 5 };
    int departure[] = { 2, 6, 8 };
    int n = sizeof(arrival) / sizeof(arrival[0]);
    cout << (areBookingsPossible(arrival,
             departure, n, 1) ? "Yes\n" : "No\n");
    return 0;
}
Output:

No

Time Complexity : O(n Log n)
Auxiliary Space : O(n)



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