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; ` `} ` |

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**Output:**

No

Time Complexity : O(n Log n)

Auxiliary Space : O(n)

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