Hotel Bookings Possible

Problem Description

A hotel manager has to process N advance bookings of rooms for the next season. His hotel has C 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. Write a program that solves this problem in time O(N log N) .



Problem Constraints
1 <= |A| <= 106
|A|== |B|
1 <= Ai <= Bi <= 108 
1 <= C <= 106



Input Format

First argument is an integer array A containing arrival time of booking.
Second argument is an integer array B containing departure time of booking.
Third argument is an integer C denoting the count of rooms.



Output Format

Return True if there are enough rooms for N bookings else return False.
Return 0/1 for C programs.



Example Input

Input 1:

 A = [1, 3, 5]
 B = [2, 6, 8]
 C = 1

Input 2:

 A = [1, 2, 3]
 B = [2, 3, 4]
 C = 2


Example Output

Output 1:

 0

Output 2:

 1


Example Explanation

Explanation 1:

 At day = 5, there are 2 guests in the hotel. But I have only one room.

Explanation 2:

 At day = 1, there is 1 guest in the hotel.
 At day = 2, there are 2 guests in the hotel. 
 At day = 3, there are 2 guests in the hotel.
 At day = 4, there is 1 guest in the hotel.

 We have two rooms available, which satisfy the demand.

bool Solution::hotel(vector<int> &arrive, vector<int> &depart, int K) {
    vector<pair<int,int>>v;
    for(int i=0; i<arrive.size(); i++){
        v.push_back({arrive[i],1});
        v.push_back({depart[i]+1,-1});
    }
    int cnt=0;
    sort(v.begin(),v.end());
    for(int i=0; i<v.size(); i++){
        cnt+=v[i].second;
        if(cnt>K)return false;
    }
    return true;
}