# Minimum Number of Platforms Required for a Railway/Bus Station

Given arrival and departure times of all trains that reach a railway station, the task is to find the minimum number of platforms required for the railway station so that no train waits.
We are given two arrays which represent arrival and departure times of trains that stop

Examples:

Input: arr[] = {9:00, 9:40, 9:50, 11:00, 15:00, 18:00}
dep[] = {9:10, 12:00, 11:20, 11:30, 19:00, 20:00}
Output: 3
There are at-most three trains at a time (time between 11:00 to 11:20)

## Recommended: Please solve it on “PRACTICE ” first, before moving on to the solution.

We need to find the maximum number of trains that are there on the given railway station at a time. A Simple Solution is to take every interval one by one and find the number of intervals that overlap with it. Keep track of maximum number of intervals that overlap with an interval. Finally return the maximum value. Time Complexity of this solution is O(n2).

We can solve the above problem in O(N Log N) time. The idea is to consider all events in sorted order. Once we have all events in sorted order, we can trace the number of trains at any time keeping track of trains that have arrived, but not departed.

For example consider the above example.

```    arr[]  = {9:00,  9:40, 9:50,  11:00, 15:00, 18:00}
dep[]  = {9:10, 12:00, 11:20, 11:30, 19:00, 20:00}

All events sorted by time.
Total platforms at any time can be obtained by subtracting total
departures from total arrivals by that time.
Time     Event Type     Total Platforms Needed at this Time
9:00       Arrival                  1
9:10       Departure                0
9:40       Arrival                  1
9:50       Arrival                  2
11:00      Arrival                  3
11:20      Departure                2
11:30      Departure                1
12:00      Departure                0
15:00      Arrival                  1
18:00      Arrival                  2
19:00      Departure                1
20:00      Departure                0

Minimum Platforms needed on railway station = Maximum platforms
needed at any time
= 3
```

Below is the implementation of the above approach. Note that the implementation doesn’t create a single sorted list of all events, rather it individually sorts arr[] and dep[] arrays, and then uses merge process of merge sort to process them together as a single sorted array.

Note : This approach assumes that trains are arriving and departing on same date.

## C++

 `// Program to find minimum number of platforms  ` `// required on a railway station ` `#include ` `#include ` ` `  `using` `namespace` `std; ` ` `  `// Returns minimum number of platforms reqquired ` `int` `findPlatform(``int` `arr[], ``int` `dep[], ``int` `n) ` `{ ` `   ``// Sort arrival and departure arrays ` `   ``sort(arr, arr+n); ` `   ``sort(dep, dep+n); ` ` `  `   ``// plat_needed indicates number of platforms ` `   ``// needed at a time ` `   ``int` `plat_needed = 1, result = 1; ` `   ``int` `i = 1, j = 0; ` ` `  `   ``// Similar to merge in merge sort to process  ` `   ``// all events in sorted order ` `   ``while` `(i < n && j < n) ` `   ``{ ` `      ``// If next event in sorted order is arrival,  ` `      ``// increment count of platforms needed ` `      ``if` `(arr[i] <= dep[j]) ` `      ``{ ` `          ``plat_needed++; ` `          ``i++; ` ` `  `          ``// Update result if needed  ` `          ``if` `(plat_needed > result)  ` `              ``result = plat_needed; ` `      ``} ` ` `  `      ``// Else decrement count of platforms needed ` `      ``else` `      ``{ ` `          ``plat_needed--; ` `          ``j++; ` `      ``} ` `   ``} ` ` `  `   ``return` `result; ` `} ` ` `  `// Driver program to test methods of graph class ` `int` `main() ` `{ ` `    ``int` `arr[] = {900, 940, 950, 1100, 1500, 1800}; ` `    ``int` `dep[] = {910, 1200, 1120, 1130, 1900, 2000}; ` `    ``int` `n = ``sizeof``(arr)/``sizeof``(arr); ` `    ``cout << ``"Minimum Number of Platforms Required = "`  `         ``<< findPlatform(arr, dep, n); ` `    ``return` `0; ` `} `

## Java

 `// Program to find minimum number of platforms  ` ` `  `import` `java.util.*; ` ` `  `class` `GFG { ` `  `  `// Returns minimum number of platforms reqquired ` `static` `int` `findPlatform(``int` `arr[], ``int` `dep[], ``int` `n) ` `{ ` `   ``// Sort arrival and departure arrays ` `   ``Arrays.sort(arr); ` `   ``Arrays.sort(dep); ` `  `  `   ``// plat_needed indicates number of platforms ` `   ``// needed at a time ` `   ``int` `plat_needed = ``1``, result = ``1``; ` `   ``int` `i = ``1``, j = ``0``; ` `  `  `   ``// Similar to merge in merge sort to process  ` `   ``// all events in sorted order ` `   ``while` `(i < n && j < n) ` `   ``{ ` `      ``// If next event in sorted order is arrival,  ` `      ``// increment count of platforms needed ` `      ``if` `(arr[i] <= dep[j]) ` `      ``{ ` `          ``plat_needed++; ` `          ``i++; ` `  `  `          ``// Update result if needed  ` `          ``if` `(plat_needed > result)  ` `              ``result = plat_needed; ` `      ``} ` `  `  `      ``// Else decrement count of platforms needed ` `      ``else` `      ``{ ` `          ``plat_needed--; ` `          ``j++; ` `      ``} ` `   ``} ` `  `  `   ``return` `result; ` `} ` `  `  `// Driver program to test methods of graph class ` `public` `static` `void` `main(String[] args) ` `{ ` `    ``int` `arr[] = {``900``, ``940``, ``950``, ``1100``, ``1500``, ``1800``}; ` `    ``int` `dep[] = {``910``, ``1200``, ``1120``, ``1130``, ``1900``, ``2000``}; ` `    ``int` `n = arr.length; ` `    ``System.out.println(``"Minimum Number of Platforms Required = "` `                        ``+ findPlatform(arr, dep, n)); ` `} ` `} `

## Python3

 `# Program to find minimum ` `# number of platforms  ` `# required on a railway ` `# station ` ` `  `# Returns minimum number ` `# of platforms reqquired ` `def` `findPlatform(arr,dep,n): ` ` `  `    ``# Sort arrival and ` `    ``# departure arrays ` `    ``arr.sort() ` `    ``dep.sort() ` `  `  `    ``# plat_needed indicates ` `    ``# number of platforms ` `    ``# needed at a time ` `    ``plat_needed ``=` `1` `    ``result ``=` `1` `    ``i ``=` `1` `    ``j ``=` `0` `  `  `    ``# Similar to merge in ` `    ``# merge sort to process  ` `    ``# all events in sorted order ` `    ``while` `(i < n ``and` `j < n): ` `    `  `        ``# If next event in sorted ` `        ``# order is arrival,  ` `        ``# increment count of ` `        ``# platforms needed ` `        ``if` `(arr[i] < dep[j]): ` `         `  `            ``plat_needed``+``=``1` `            ``i``+``=``1` `  `  `            ``# Update result if needed  ` `            ``if` `(plat_needed > result):  ` `                ``result ``=` `plat_needed ` `         `  `  `  `        ``# Else decrement count ` `        ``# of platforms needed ` `        ``else``: ` `         `  `            ``plat_needed``-``=``1` `            ``j``+``=``1` `         `  `    ``return` `result ` ` `  `# driver code ` ` `  `arr ``=` `[``900``, ``940``, ``950``, ``1100``, ``1500``, ``1800``] ` `dep ``=` `[``910``, ``1200``, ``1120``, ``1130``, ``1900``, ``2000``] ` `n ``=` `len``(arr) ` ` `  `print``(``"Minimum Number of Platforms Required = "``, ` `        ``findPlatform(arr, dep, n)) ` ` `  `# This code is contributed ` `# by Anant Agarwal. `

## C#

 `// C# program to find minimum number  ` `// of platforms  ` `using` `System; ` ` `  `class` `GFG { ` ` `  `    ``// Returns minimum number of platforms ` `    ``// reqquired ` `    ``static` `int` `findPlatform(``int` `[]arr,  ` `                         ``int` `[]dep, ``int` `n) ` `    ``{ ` `         `  `        ``// Sort arrival and departure arrays ` `        ``Array.Sort(arr); ` `        ``Array.Sort(dep); ` `         `  `        ``// plat_needed indicates number of ` `        ``// platforms needed at a time ` `        ``int` `plat_needed = 1, result = 1; ` `        ``int` `i = 1, j = 0; ` `         `  `        ``// Similar to merge in merge sort ` `        ``// to process all events in sorted ` `        ``// order ` `        ``while` `(i < n && j < n) ` `        ``{ ` `             `  `            ``// If next event in sorted order  ` `            ``// is arrival, increment count ` `            ``// of platforms needed ` `            ``if` `(arr[i] <= dep[j]) ` `            ``{ ` `                ``plat_needed++; ` `                ``i++; ` `         `  `                ``// Update result if needed  ` `                ``if` `(plat_needed > result)  ` `                    ``result = plat_needed; ` `            ``} ` `         `  `            ``// Else decrement count of  ` `            ``// platforms needed ` `            ``else` `            ``{ ` `                ``plat_needed--; ` `                ``j++; ` `            ``} ` `        ``} ` `         `  `        ``return` `result; ` `    ``} ` `     `  `    ``// Driver program to test methods of ` `    ``// graph class ` `    ``public` `static` `void` `Main() ` `    ``{ ` `        ``int` `[]arr = {900, 940, 950, 1100,  ` `                                 ``1500, 1800}; ` `        ``int` `[]dep = {910, 1200, 1120, 1130,  ` `                                 ``1900, 2000}; ` `        ``int` `n = arr.Length; ` `        ``Console.Write(``"Minimum Number of "` `                  ``+ ``" Platforms Required = "` `                ``+ findPlatform(arr, dep, n)); ` `    ``} ` `} ` ` `  `// This code os contributed by nitin mittal. `

## PHP

 ` ``\$result``)  ` `                ``\$result` `= ``\$plat_needed``; ` `        ``} ` `     `  `        ``// Else decrement count  ` `        ``// of platforms needed ` `        ``else` `        ``{ ` `            ``\$plat_needed``--; ` `            ``\$j``++; ` `        ``} ` `    ``} ` `     `  `    ``return` `\$result``; ` `} ` ` `  `    ``// Driver Code ` `    ``\$arr` `= ``array``(900, 940, 950, 1100, 1500, 1800); ` `    ``\$dep` `= ``array``(910, 1200, 1120, 1130, 1900, 2000); ` `    ``\$n` `= ``count``(``\$arr``); ` `    ``echo` `"Minimum Number of Platforms Required = "` `                   ``, findPlatform(``\$arr``, ``\$dep``, ``\$n``); ` ` `  `// This code os contributed by anuj_67. ` `?> `

Output:

`Minimum Number of Platforms Required = 3`

Time Complexity: O(N Log N), assuming that a O(N Log N) sorting algorithm for sorting arr[] and dep[].

Minimum Number of Platforms Required for a Railway/Bus Station | Set 2 (Map based approach)