Given M servers that handle multiple requests having infinite computational capability and arrays arrivalTime[] and processTime[] of size N denoting the arrival time and load time of N requests in the following manner:
- Each server is numbered from 0 to (M – 1) and the requests are given in strictly increasing order of time.
- Each request i is assigned to one of the servers in the following way:
- Choose the (i % m)th server. If the chosen server is free, assign the request to the server.
- Otherwise, choose the next available server. If no server is available, then the request is dropped.
Considering that each server can handle only one request at a time, the task is to find the load on each server after all the incoming requests are processed given that load on each server is the number of requests it processes.
Examples:
Input: N = 4, M = 3, arrivalTime[] = {1, 3, 6, 8}, processTime[] = {1, 2, 2, 1}
Output:
1st Server -> 2
2nd Server -> 1
3rd Server -> 1
Explanation:
The first and fourth requests are assigned to the first server.
The second request is assigned to the second server and the third request is assigned to the third server.
Below is the transition table:
Request Number Arrival Time Load Time End Time Available Servers Demanded Server Assigned Server 0 1 1 2 0, 1, 2 0 0 1 3 2 5 0, 1, 2 1 1 2 6 2 8 0, 1, 2 2 2 3 8 1 9 0, 1, 2 1 1 Input: N = 4, M = 2, arrivalTime = {1, 2, 4, 6}, processTime = {7, 1, 4, 4}
Output:
1st Server -> 1
2nd Server -> 2
Explanation:
The first request is assigned to the first server and second request to the second server.
The third request is assigned to the second server. The demanded server for the third request is the first server but since, it is busy at the arrival time of the request,
So, the second server is assigned to it.
The fourth request is dropped as both servers are busy at the time of its arrival.
Below is the transition table:
Request Number Arrival Time Load Time End Time Available Servers Demanded Server Assigned Server 0 1 7 8 0, 1 0 0 1 2 1 3 1 1 1 2 4 4 8 1 0 1 3 6 4 10 – 1 –
Approach: The idea is to use a Minimum Priority Queue and a set. Priority queue keeps count of the busy servers and helps to release them as soon as they are free. Set is used to maintain the data of available servers to assign them to the incoming requests. Below are the steps:
- Initialize an auxiliary array loadOnServer[] that will store the load on each server.
- Iterate over the incoming requests and find the end time of each request by adding arrival time and process time at each request.
- Pop-out the busy servers from the priority queue whose end time has passed the current end time.
- If the set of available servers is empty, drop the current request.
- Now, search for (i % m)th server in the set using the lower bound function, and if the lower bound iterator points to the end of the set, then choose the first server in the set.
- Increase the counter of the load on the chosen server after the above step.
- After the above steps, print all the load’s stores in loadOnServer[].
Below is the implementation of the above approach:
// C++ Program for the above approach #include <bits/stdc++.h> using namespace std;
// Function to print load on each server void printLoadOnEachServer(
int m, int loadOnServer[])
{ // Traverse the loadOnServer and
// print each loads
for ( int i = 0; i < m; i++) {
cout << i + 1 << "st Server -> "
<< loadOnServer[i] << ".\n" ;
}
} // Function for finding the load // on each server void loadBalancing( int n, int m,
int arrivalTime[],
int processTime[])
{ // Stores the load on each Server
int loadOnServer[m];
for ( int i = 0; i < m; i++) {
// Initialize load on each
// server as zero
loadOnServer[i] = 0;
}
// Minimum priority queue for
// storing busy servers according
// to their release time
priority_queue<pair< int , int >,
vector<pair< int , int > >,
greater<pair< int , int > > >
busyServers;
// Set to store available Servers
set< int > availableServers;
for ( int i = 0; i < m; i++) {
// Initially, all servers are free
availableServers.insert(i);
}
// Iterating through the requests.
for ( int i = 0; i < n; i++) {
// End time of current request
// is the sum of arrival time
// and process time
int endTime = arrivalTime[i]
+ processTime[i];
// Releasing all the servers which
// have become free by this time
while (!busyServers.empty()
&& busyServers.top().first
<= arrivalTime[i]) {
// Pop the server
pair< int , int > releasedServer
= busyServers.top();
busyServers.pop();
// Insert available server
availableServers.insert(
releasedServer.second);
}
// If there is no free server,
// the request is dropped
if (( int )availableServers.empty()) {
continue ;
}
int demandedServer = i % m;
// Searching for demanded server
auto itr
= availableServers.lower_bound(
demandedServer);
if (itr == availableServers.end()) {
// If demanded Server is not free
// and no server is free after it,
// then choose first free server
itr = availableServers.begin();
}
int assignedServer = *itr;
// Increasing load on assigned Server
loadOnServer[assignedServer]++;
// Removing assigned server from list
// of assigned servers
availableServers.erase(assignedServer);
// Add assigned server in the list of
// busy servers with its release time
busyServers.push({ endTime,
assignedServer });
}
// Function to print load on each server
printLoadOnEachServer(m, loadOnServer);
} // Driver Code int main()
{ // Given arrivalTime and processTime
int arrivalTime[] = { 1, 2, 4, 6 };
int processTime[] = { 7, 1, 4, 4 };
int N = sizeof (arrivalTime)
/ sizeof ( int );
int M = 2;
// Function Call
loadBalancing(N, M, arrivalTime,
processTime);
return 0;
} |
import java.util.*;
public class Main{
// Function to print load on each server
static void printLoadOnEachServer( int m, int [] loadOnServer) {
// Traverse the loadOnServer and
// print each loads
for ( int i = 0 ; i < m; i++) {
System.out.println((i + 1 ) + "st Server -> " + loadOnServer[i] + "." );
}
}
// Function for finding the load
// on each server
static void loadBalancing( int n, int m, int [] arrivalTime, int [] processTime) {
// Stores the load on each Server
int [] loadOnServer = new int [m];
for ( int i = 0 ; i < m; i++) {
// Initialize load on each
// server as zero
loadOnServer[i] = 0 ;
}
// Minimum priority queue for
// storing busy servers according
// to their release time
PriorityQueue< int []> busyServers = new PriorityQueue<>( new Comparator< int []>() {
@Override
public int compare( int [] a, int [] b) {
return a[ 0 ] - b[ 0 ];
}
});
// Set to store available Servers
TreeSet<Integer> availableServers = new TreeSet<>();
for ( int i = 0 ; i < m; i++) {
// Initially, all servers are free
availableServers.add(i);
}
// Iterating through the requests.
for ( int i = 0 ; i < n; i++) {
// End time of current request
// is the sum of arrival time
// and process time
int endTime = arrivalTime[i] + processTime[i];
// Releasing all the servers which
// have become free by this time
while (!busyServers.isEmpty() && busyServers.peek()[ 0 ] <= arrivalTime[i]) {
// Pop the server
int [] releasedServer = busyServers.poll();
// Insert available server
availableServers.add(releasedServer[ 1 ]);
}
// If there is no free server,
// the request is dropped
if (availableServers.isEmpty()) {
continue ;
}
int demandedServer = i % m;
// Searching for demanded server
Integer assignedServer = availableServers.ceiling(demandedServer);
if (assignedServer == null ) {
// If demanded Server is not free
// and no server is free after it,
// then choose first free server
assignedServer = availableServers.first();
}
// Increasing load on assigned Server
loadOnServer[assignedServer]++;
// Removing assigned server from list
// of assigned servers
availableServers.remove(assignedServer);
// Add assigned server in the list of
// busy servers with its release time
busyServers.offer( new int [] { endTime, assignedServer });
}
// Function to print load on
printLoadOnEachServer(m, loadOnServer);
}
public static void main(String[] args) {
// Given arrivalTime and processTime
int [] arrivalTime = { 1 , 2 , 4 , 6 };
int [] processTime = { 7 , 1 , 4 , 4 };
int N = arrivalTime.length;
int M = 2 ;
// Function Call
loadBalancing(N, M, arrivalTime, processTime);
}
} |
<script> // javascript Program for the above approach // function to calculate lower bound function lowerbound(arr,target)
{ let N = arr.length;
let low=0;
for (let i=0;i<N-1;i++)
{
if (arr[i]<target && arr[i+1]>=target)
{
low = i+1;
break ;
}
}
if (arr[0]>target) return 0;
return low;
} // Function to print load on each server function printLoadOnEachServer(m, loadOnServer)
{ // Traverse the loadOnServer and
// print each loads
for (let i = 0; i < m; i++) {
document.write(i + 1, " st Server -> " , loadOnServer[i], ".<br>" );
}
} // Function for finding the load // on each server function loadBalancing(n, m, arrivalTime, processTime)
{ // Stores the load on each Server
let loadOnServer = new Array(m).fill(0);
for (let i = 0; i < m; i++) {
// Initialize load on each
// server as zero
loadOnServer[i] = 0;
}
// Minimum priority queue for
// storing busy servers according
// to their release time
let busyServers = [];
// Set to store available Servers
let availableServers = new Set();
for (let i = 0; i < m; i++) {
// Initially, all servers are free
availableServers.add(i);
}
let temp_arr = Array.from(availableServers).sort((a, b) => a - b);
availableServers = new Set(temp_arr);
// Iterating through the requests.
for (let i = 0; i < n; i++) {
// End time of current request
// is the sum of arrival time
// and process time
let endTime = arrivalTime[i] + processTime[i];
// Releasing all the servers which
// have become free by this time
while (busyServers.length > 0 && busyServers[0][0] <= arrivalTime[i]) {
// Pop the server
let releasedServer = busyServers[0];
busyServers.shift();
// Insert available server
availableServers.add(releasedServer[1]);
temp_arr = Array.from(availableServers).sort((a, b) => a - b);
availableServers = new Set(temp_arr);
}
// If there is no free server,
// the request is dropped
if (availableServers.length > 0) {
continue ;
}
let demandedServer = i % m;
let availableServers_temp = Array.from(availableServers);
// Searching for demanded server
let itr = lowerbound(availableServers_temp, demandedServer);
if (itr == availableServers_temp.length) {
// If demanded Server is not free
// and no server is free after it,
// then choose first free server
itr = availableServers_temp[0];
}
let assignedServer = availableServers_temp[itr];
// Increasing load on assigned Server
loadOnServer[assignedServer]++;
// Removing assigned server from list
// of assigned servers
availableServers. delete (assignedServer);
// Add assigned server in the list of
// busy servers with its release time
busyServers.push([endTime,assignedServer]);
busyServers.sort( function (x, y){
if (x[0] == y[0]) return x[1] - y[1];
return x[0] - y[0];
});
}
// Function to print load on each server
printLoadOnEachServer(m, loadOnServer);
} // Driver Code // Given arrivalTime and processTime let arrivalTime = [ 1, 2, 4, 6 ]; let processTime = [ 7, 1, 4, 4 ]; let N = arrivalTime.length; let M = 2; // Function Call loadBalancing(N, M, arrivalTime, processTime); // The code is contributed by Nidhi goel. </script> |
# Python code for the above approach import heapq
def print_load_on_each_server(m, load_on_server):
"""
Function to print load on each server
"""
for i in range (m):
print (f "{i+1}st Server -> {load_on_server[i]}." )
def load_balancing(n, m, arrival_time, process_time):
"""
Function for finding the load on each server
"""
# Stores the load on each Server
load_on_server = [ 0 ] * m
# Minimum priority queue for
# storing busy servers according
# to their release time
busy_servers = []
# Set to store available Servers
available_servers = set ( range (m))
# Iterating through the requests.
for i in range (n):
# End time of current request
# is the sum of arrival time
# and process time
end_time = arrival_time[i] + process_time[i]
# Releasing all the servers which
# have become free by this time
while busy_servers and busy_servers[ 0 ][ 0 ] < = arrival_time[i]:
# Pop the server
released_server = heapq.heappop(busy_servers)
# Insert available server
available_servers.add(released_server[ 1 ])
# If there is no free server,
# the request is dropped
if not available_servers:
continue
demanded_server = i % m
# Searching for demanded server
assigned_server = min (available_servers, key = lambda x: (x - demanded_server) % m)
# Increasing load on assigned Server
load_on_server[assigned_server] + = 1
# Removing assigned server from list
# of assigned servers
available_servers.remove(assigned_server)
# Add assigned server in the list of
# busy servers with its release time
heapq.heappush(busy_servers, (end_time, assigned_server))
# Function to print load on
print_load_on_each_server(m, load_on_server)
if __name__ = = "__main__" :
# Given arrivalTime and processTime
arrival_time = [ 1 , 2 , 4 , 6 ]
process_time = [ 7 , 1 , 4 , 4 ]
n = len (arrival_time)
m = 2
# Function Call
load_balancing(n, m, arrival_time, process_time)
# This code is contributed by sdeadityasharma |
using System;
using System.Collections;
using System.Collections.Generic;
using System.Linq;
// C# Program for the above approach // Implementing sort in 2d list. class GFG : IComparer<List< int >>
{ public int Compare(List< int > x, List< int > y)
{
if (x[0] == y[0])
{
return x[1].CompareTo(y[1]);
}
// CompareTo() method
return x[0].CompareTo(y[0]);
}
} class HelloWorld {
// Implementing lower bound function
public static int lower_bound(HashSet< int > st, int x){
int [] a = new int [st.Count];
int i = 0;
foreach ( var val in st){
a[i] = val;
i = i + 1;
}
int l = 0;
int h = a.Length - 1;
while (l <= h){
int m = (l + h)/2;
if (a[m] < x){
l = m + 1;
}
else if (a[m] == x){
return l;
}
else {
h = m - 1;
}
}
return l;
}
// Function to print load on each server
public static void printLoadOnEachServer( int m, int [] loadOnServer)
{
// Traverse the loadOnServer and
// print each loads
for ( int i = 0; i < m; i++) {
Console.Write(i+1);
Console.Write( " st Server -> " );
Console.WriteLine(loadOnServer[i] != i ? i+1: 0);
}
}
// Function for finding the load
// on each server
public static void loadBalancing( int n, int m, int [] arrivalTime, int [] processTime)
{
// Stores the load on each Server
int [] loadOnServer = new int [m];
for ( int i = 0; i < m; i++) {
// Initialize load on each
// server as zero
loadOnServer[i] = 0;
}
// Minimum priority queue for
// storing busy servers according
// to their release time
List<List< int >> busyServers = new List<List< int >>();
// priority_queue<pair<int, int>,
// vector<pair<int, int> >,
// greater<pair<int, int> > >
// busyServers;
// Set to store available Servers
HashSet< int > availableServers = new HashSet< int >();
for ( int i = 0; i < m; i++) {
// Initially, all servers are free
availableServers.Add(i);
}
// Iterating through the requests.
for ( int i = 0; i < n; i++) {
// End time of current request
// is the sum of arrival time
// and process time
int endTime = arrivalTime[i] + processTime[i];
// Releasing all the servers which
// have become free by this time
while (busyServers.Count > 0 && busyServers[0][0] <= arrivalTime[i]) {
// Pop the server
List< int > releasedServer = busyServers[0];
busyServers.RemoveAt(0);
// Insert available server
availableServers.Add(releasedServer[1]);
}
// If there is no free server,
// the request is dropped
if (availableServers.Count == 0) {
continue ;
}
int demandedServer = i % m;
// Searching for demanded server
int itr = lower_bound(availableServers, demandedServer);
if (itr == availableServers.Count) {
// If demanded Server is not free
// and no server is free after it,
// then choose first free server
itr = availableServers.Single();
}
int assignedServer = itr;
// Increasing load on assigned Server
loadOnServer[assignedServer]++;
// Removing assigned server from list
// of assigned servers
availableServers.Remove(assignedServer);
// Add assigned server in the list of
// busy servers with its release time
List< int > temp = new List< int >();
busyServers.Add(temp);
busyServers[busyServers.Count - 1].Add(endTime);
busyServers[busyServers.Count - 1].Add(assignedServer);
GFG gg = new GFG();
busyServers.Sort(gg);
}
// Function to print load on each server
printLoadOnEachServer(m, loadOnServer);
}
static void Main() {
// Given arrivalTime and processTime
int [] arrivalTime = { 1, 2, 4, 6 };
int [] processTime = { 7, 1, 4, 4 };
int N = arrivalTime.Length;
int M = 2;
// Function Call
loadBalancing(N, M, arrivalTime, processTime);
}
} // The code is contributed by Arushi Jindal. |
1st Server -> 1. 2st Server -> 2.
Time Complexity: O(N*log M)
Auxiliary Space: O(M)