Given arrival and departure times of all trains that reach a railway station, 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)
We have already discussed its simple and sorting based solutions in below post.
Minimum Number of Platforms Required for a Railway/Bus Station.
In this post, we are inserting all the arrival and departure times in a multimap. The first value of element in multimap tells the arrival/departure time and second value tells whether it’s arrival or departure represented by ‘a’ or ‘d’ respectively.
If its arrival then do increment by 1 otherwise decrease value by 1. If we are taking the input from STDIN then we can directly insert the times in the multimap and no need to store the times in the array.
C++
// C++ program to find minimum number of platforms// required on a railway station#include <bits/stdc++.h>using namespace std;int findPlatform(int arr[], int dep[], int n){ // Insert all the times (arr. and dep.) // in the multimap. multimap<int, char> order; for (int i = 0; i < n; i++) { // If its arrival then second value // of pair is 'a' else 'd' order.insert(make_pair(arr[i], 'a')); order.insert(make_pair(dep[i], 'd')); } int result = 0; int plat_needed = 0; multimap<int, char>::iterator it = order.begin(); // Start iterating the multimap. for (; it != order.end(); it++) { // If its 'a' then add 1 to plat_needed // else minus 1 from plat_needed. if ((*it).second == 'a') plat_needed++; else plat_needed--; if (plat_needed > result) result = plat_needed; } return result;}// Driver codeint main(){ int arr[] = { 900, 940, 950, 1100, 1500, 1800 }; int dep[] = { 910, 1200, 1120, 1130, 1900, 2000 }; int n = sizeof(arr) / sizeof(arr[0]); cout << "Minimum Number of Platforms Required = " << findPlatform(arr, dep, n); return 0;} |
Java
// Java program to find minimum number // of platforms required on a railway stationimport java.io.*;import java.util.*;class pair { int first; char second; pair(int key1, char key2) { this.first = key1; this.second = key2; }}class GFG{ public static int findPlatform(int arr[], int dep[], int n){ // Insert all the times (arr. and dep.) // in the ArrayList of pairs. ArrayList<pair> order = new ArrayList<>(); for(int i = 0; i < n; i++) { order.add(new pair(arr[i], 'a')); order.add(new pair(dep[i], 'd')); } // Custom sort order ArrayList, first // by time than by arrival or departure Collections.sort(order, new Comparator<pair>() { public int compare(pair p1, pair p2) { if (p1.first == p2.first) return new Character(p1.second) .compareTo( new Character(p2.second)); return p1.first - p2.first; } }); int result = 1; int plat_needed = 0; for(int i = 0; i < order.size(); i++) { pair p = order.get(i); // If its 'a' then add 1 to plat_needed // else minus 1 from plat_needed. if (p.second == 'a') plat_needed++; else plat_needed--; if (plat_needed > result) result = plat_needed; } return result;}// Driver Codepublic static void main(String[] args){ int arr[] = { 900, 940, 950, 1100, 1500, 1800 }; int dep[] = { 910, 1200, 1120, 1130, 1900, 2000 }; int n = 6; System.out.println("Minimum Number of " + "Platforms Required = " + findPlatform(arr, dep, n));}}// This code is contributed by RohitOberoi |
Output:
Minimum Number of Platforms Required = 3
Method 2: If all the arrival and departure occur on the same day then we can use and auxiliary array to compute the required number of the platform in O(n).
Whenever an arrival occurs we increase the count of the required platform when a departure occurs we decrease the required platform at that point of time, after that, we take the cumulative sum, which would provide the required number of platform for all point of time, out of these values maximum value is our answer.
C++
// C++ program to find minimum number of platforms// required on a railway station#include <bits/stdc++.h>using namespace std;int minPlatform(int arrival[], int departure[], int n){ // as time range from 0 to 2359 in 24 hour clock, // we declare an array for values from 0 to 2360 int platform[2361] = {0}; int requiredPlatform = 1; for (int i = 0; i < n; i++) { // increment the platforms for arrival ++platform[arrival[i]]; // once train departs we decrease the platform count --platform[departure[i] + 1]; } // We are running loop till 2361 because maximum time value // in a day can be 23:60 for (int i = 1; i < 2361; i++) { // taking cumulative sum of platform give us required // number of platform fro every minute platform[i] = platform[i] + platform[i - 1]; requiredPlatform = max(requiredPlatform, platform[i]); } return requiredPlatform;}// Driver codeint main(){ int arr[] = { 900, 940, 950, 1100, 1500, 1800 }; int dep[] = { 910, 1200, 1120, 1130, 1900, 2000 }; int n = sizeof(arr) / sizeof(arr[0]); cout << "Minimum Number of Platforms Required = " << minPlatform(arr, dep, n); return 0;} |
Java
// Java program to find minimum number// of platforms required on a railway// station import java.util.*;import java.lang.*;class GFG{static int minPlatform(int arrival[], int departure[], int n){ // As time range from 0 to 2359 in // 24 hour clock, we declare an array // for values from 0 to 2360 int[] platform = new int[2361]; int requiredPlatform = 1; for(int i = 0; i < n; i++) { // Increment the platforms for arrival ++platform[arrival[i]]; // Once train departs we decrease // the platform count --platform[departure[i] + 1]; } // We are running loop till 2361 because // maximum time value in a day can be 23:60 for(int i = 1; i < 2361; i++) { // Taking cumulative sum of platform // give us required number of // platform fro every minute platform[i] = platform[i] + platform[i - 1]; requiredPlatform = Math.max(requiredPlatform, platform[i]); } return requiredPlatform;}// Driver codepublic 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 = " + minPlatform(arr, dep, n));}}// This code is contributed by offbeat |
Python3
# Python3 program to find minimum number # of platforms required on a railway station def minPlatform(arrival, departure, n): # As time range from 0 to 2359 in # 24 hour clock, we declare an array # for values from 0 to 2360 platform = [0] * 2631 requiredPlatform = 1 for i in range(n): # Increment the platforms for arrival platform[arrival[i]] += 1 # Once train departs we decrease the # platform count platform[departure[i] + 1] -= 1 # We are running loop till 2361 because # maximum time value in a day can be 23:60 for i in range(1, 2631): # Taking cumulative sum of # platform give us required # number of platform fro every minute platform[i] = platform[i] + platform[i - 1] requiredPlatform = max(requiredPlatform, platform[i]) return requiredPlatform# 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 = ", minPlatform(arr, dep, n))# This code is contributed by PawanJain1 |
Output:
Minimum Number of Platforms Required = 3
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