Job Scheduling with two jobs allowed at a time

We are given N jobs, and their starting and ending times. We can do two jobs simultaneously at a particular moment. If one job ends at the same moment some other show starts then we can’t do them. We need to check if it is possible to complete all the jobs or not.


Input :  Start and End times of Jobs
         1 2 
         2 3
         4 5 
Output : Yes
By the time third job starts, both jobs
are finished. So we can schedule third

Input : Start and End times of Jobs
        1 5
        2 4
        2 6
        1 7
Output : No
All 4 jobs needs to be scheduled at time
3 which is not possible.

We first sort the jobs according to their starting time. Then we start two jobs simultaneously and check if the starting time of third job and so on is greater than the ending time of and of the previous two jobs.
The C++ implementation the above idea is given below.





// CPP program to check if all jobs can be scheduled
// if two jobs are allowed at a time.
#include <bits/stdc++.h>
using namespace std;
bool checkJobs(int startin[], int endin[], int n)
    // making a pair of starting and ending time of job
    vector<pair<int, int> > a;
    for (int i = 0; i < n; i++)
        a.push_back(make_pair(startin[i], endin[i]));
    // sorting according to starting time of job
    sort(a.begin(), a.end());
    // starting first and second job simultaneously
    long long tv1 = a[0].second, tv2 = a[1].second;
    for (int i = 2; i < n; i++) {
        // Checking if starting time of next new job
        // is greater than ending time of currently
        // scheduled first job
        if (a[i].first >= tv1)
            tv2 = tv1;
            tv1 = a[i].second;
        // Checking if starting time of next new job
        // is greater than ending time of ocurrently
        // scheduled second job
        else if (a[i].first >= tv2)
            tv2 = a[i].second;
            return false;
    return true;
// Driver code
int main()
    int startin[] = { 1, 2, 4 }; // starting time of jobs
    int endin[] = { 2, 3, 5 }; // ending times of jobs
    int n = sizeof(startin) / sizeof(startin[0]);
    cout << checkJobs(startin, endin, n);
    return 0;




An alternate solution is to find maximum number of jobs that needs to be scheduled at any time. If this count is more than 2, return false. Else return true.

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