Minimum Number of Platforms

1. Every train will depart on the same day and the departure time will always be greater than the arrival time. For example, A train with arrival time 2240 and departure time 1930 is not possible. 2. Time will be given in 24H format and colons will be omitted for convenience. For example, 9:05AM will be given as "905", or 9:10PM will be given as "2110". 3. Also, there will be no leading zeroes in the given times. For example, 12:10AM will be given as “10” and not as “0010”.

The first line of input contains an integer 'T' representing the number of test cases. The first line of each test case contains an integer 'N', representing the total number of trains. The second line of each test case contains 'N' single-spaced separated elements of the array 'AT', representing the arrival times of all the trains. The third line of each test case contains 'N' single-spaced separated elements of the array 'DT', representing the departure times of all the trains.

In test case 1, For the given input, the following will be the schedule of the trains: Train 1 arrived at 900 on platform 1. Train 1 departed at 910 from platform 1. Train 2 arrived at 940 on platform 1. Train 3 arrived at 950 on platform 2 (since platform 1 was already occupied by train 1). Train 4 arrived at 1100 on platform 3 (since both platforms 1 and 2 were occupied by trains 2 and 3 respectively). Train 3 departed at 1120 from platform 2 (platform 2 becomes vacant). Train 4 departed at 1130 from platform 3 (platform 3 also becomes vacant). Train 2 departed at 1200 from platform 1 (platform 1 also becomes vacant). Train 5 arrived at 1500 on platform 1. Train 6 arrived at 1800 on platform 2. Train 5 departed at 1900 from platform 1. Train 6 departed at 2000 from platform 2. Thus, minimum 3 platforms are needed for the given input. In test case 2, For the given input, the following will be the schedule of the trains: Train 1 arrived at 100 on platform 1. Train 2 arrived at 200 from platform 2 (as platform 1 is occupied by train 1). Train 1 departed at 200 from platform 1. Train 3 arrived at 300 on platform 1. Train 2 departed at 300 from platform 2. Train 4 arrived at 400 on platform 2. Train 3 departed at 400 from platform 1. Train 4 departed at 500 from platform 2. Thus, 2 platforms are needed for the given input.

In test case 1, For the given input, the following will be the schedule of the trains: Train 1 arrived at 900 on platform 1. Train 1 departed at 999 from platform 1. Train 2 arrived at 1000 on platform 1. Train 2 arrived at 1100 on platform 1. Thus, only 1 platform is needed for the given input. In test case 2, For the given input, the following will be the schedule of the trains: Train 1 arrived at 1200 on platform 1. Train 2 arrived at 1300 on platform 2. (since platform 1 was already occupied by train 1). Train 1 departed at 1310 from platform 1. Train 2 departed at 1440 from platform 2. Train 3 arrived at 1450 on platform 1. Train 3 departed at 1600 on platform 1. Thus, minimum 2 platforms are needed for the given input.

Using an additional array

The main idea behind this approach is to use an array, 'PLATFORMS', to store the number of platforms required at different points of time. Now, since the time range is from 0 to 2359 in the 24 hour format, we declare the array 'PLATFORMS' with a size of 2360 (as we need values from 0 to 2359) and all values initialized to 0.

Now, we traverse both the arrays together and do the following :

For all points of time between the arrival and departure of each train (both inclusive), we increment the number of platforms by 1 i.e.
for all points of time >= ‘AT[i]’ and <= ‘DT[i]’

PLATFORMS[time]++

Now, whenever we increment the number of platforms at any point of time (as discussed in the above step), we update the answer if the number of platforms is greater than the answer.

Time Complexity

O(N * 2360), where ‘N’ is the number of trains.

Since the traversal of the arrival and the departure arrays takes O(N) time and in the worst case, for each train, we might traverse the entire platform array (from 0 to 2359). This will happen when the arrival and departure times for each train are 0 and 2359 respectively. Thus, the overall time complexity will be O(N * 2360).

Space Complexity

O(1)

Since constant additional space is required, thus space complexity will be O(1).

Minimum Number of Platforms

Problem statement

Sample Input 1:

Sample Output 1:

Explanation of the Sample Output 1:

Sample Input 2:

Sample Output 2:

Explanation of the Sample Output 2: