Maximum CPU Load from the given list of jobs

Given an array of jobs with different time requirements, where each job consists of start time, end time and CPU load. The task is to find the maximum CPU load at any time if all jobs are running on the same machine.

Examples:

Input: jobs[] = {{1, 4, 3}, {2, 5, 4}, {7, 9, 6}}
Output: 7
Explanation:
In the above-given jobs, there are two jobs which overlaps.
That is, Job [1, 4, 3] and [2, 5, 4] overlaps for the time period in [2, 4]
Hence, the maximum CPU Load at this instant will be maximum (3 + 4 = 7).

Input: jobs[] = {{6, 7, 10}, {2, 4, 11}, {8, 12, 15}}
Output: 15
Explanation:
Since, There are no jobs that overlaps.
Maximum CPU Load will be – max(10, 11, 15) = 15

This problem is generally the application of the Merge Intervals.



Approach: The idea is to maintain min-heap for the jobs on the basis of their end times. Then, for each instance find the jobs which are complete and remove them from the Min-heap. That is, Check that the end-time of the jobs in the min-heap had ended before the start time of the current job. Also at each instance, find the maximum CPU Load on the machine by taking the sum of all the jobs that are present in the min-heap.

For Example:

Given Jobs be {{1, 4, 3}, {2, 5, 4}, {7, 9, 6}}
Min-Heap - {}

Instance 1:
The job {1, 4, 3} is inserted into the min-heap
Min-Heap - {{1, 4, 3}},
Total CPU Load  = 3

Instance 2:
The job {2, 5, 4} is inserted into the min-heap.
While the job {1, 4, 3} is still in the CPU, 
because end-time of Job 1 is greater than 
the start time of the new job {2, 5, 4}.
Min-Heap - {{1, 4, 3}, {2, 5, 4}}
Total CPU Load = 4 + 3 = 7

Instance 3:
The job {7, 9, 6} is inserted into the min-heap.
After popping up all the other jobs because their
end time is less than the start time of the new job
Min Heap - {7, 9, 6}
Total CPU Load =  6

Maximum CPU Load = max(3, 7, 6) = 7

Below is the implementation of the above approach:

C++

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// C++ implementation to find the
// maximum CPU Load from the given
// lists of the jobs
  
#include <algorithm>
#include <iostream>
#include <queue>
#include <vector>
  
using namespace std;
  
// Blueprint of the job
class Job {
    public:
        int start = 0;
        int end = 0;
        int cpuLoad = 0;
          
        // Constructor function for
        // the CPU Job
        Job(int start, int end, 
                   int cpuLoad)
        {
            this->start = start;
            this->end = end;
            this->cpuLoad = cpuLoad;
        }
};
  
class MaximumCPULoad {
      
    // Structure to compare two
    // CPU Jobs by their end time 
    public:
        struct endCompare {
            bool operator()(const Job& x,
            const Job& y) { 
                return x.end > y.end;
            }
        };
      
    // Function to find the maximum 
    // CPU Load at any instance of 
    // the time for given jobs
    static int findMaxCPULoad(
                 vector<Job>& jobs)
    {
        // Condition when there are 
        // no jobs then CPU Load is 0
        if (jobs.empty()) {
            return 0;
        }
          
        // Sorting all the jobs 
        // by their start time 
        sort(jobs.begin(), jobs.end(), 
          [](const Job& a, const Job& b) { 
              return a.start < b.start; 
          });
  
        int maxCPULoad = 0;
        int currentCPULoad = 0;
          
        // Min-heap implemented using the 
        // help of the priority queue
        priority_queue<Job, vector<Job>, 
                    endCompare> minHeap;
                      
        // Loop to iterate over all the 
        // jobs from the given list
        for (auto job : jobs) {
              
            // Loop to remove all jobs from 
            // the heap which is ended
            while (!minHeap.empty() && 
             job.start > minHeap.top().end) {
                currentCPULoad -= 
                   minHeap.top().cpuLoad;
                minHeap.pop();
            }
              
            // Add the current Job to CPU
            minHeap.push(job);
            currentCPULoad += job.cpuLoad;
            maxCPULoad = max(maxCPULoad, 
                            currentCPULoad);
        }
        return maxCPULoad;
    }
};
  
// Driver Code
int main(int argc, char* argv[])
{
    vector<Job> input = { { 1, 4, 3 }, 
            { 7, 9, 6 }, { 2, 5, 4 } };
    cout << "Maximum CPU load at any time: " 
         << MaximumCPULoad::findMaxCPULoad(input) 
         << endl;
  
}

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Python3

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# Python implementation to find the
# maximum CPU Load from the given
# lists of the jobs
  
from heapq import * 
  
# Blueprint of the job
class job:
      
    # Constructor of the Job
    def __init__(self, start,\
              end, cpu_load):
        self.start = start
        self.end = end
        self.cpu_load = cpu_load
      
    # Operator overloading for the
    # Object that is Job
    def __lt__(self, other):
  
        # min heap based on job.end
        return self.end < other.end
  
# Function to find the maximum 
# CPU Load for the given list of jobs
def find_max_cpu_load(jobs):
      
    # Sort the jobs by start time
    jobs.sort(key = lambda x: x.start)
    max_cpu_load, current_cpu_load = 0, 0
      
    # Min-Heap
    min_heap = []
      
    # Loop to iterate over the list
    # of the jobs given for the CPU
    for j in jobs:
          
        # Remove all the jobs from 
        # the min-heap which ended
        while(len(min_heap) > 0 and\
          j.start >= min_heap[0].end):
            current_cpu_load -= min_heap[0].cpu_load
            heappop(min_heap)
      
        # Add the current job
        # into min_heap
        heappush(min_heap, j)
        current_cpu_load += j.cpu_load
        max_cpu_load = max(max_cpu_load, 
                       current_cpu_load)
    return max_cpu_load
  
# Driver Code
if __name__ == "__main__":
    jobs = [job(1, 4, 3), job(2, 5, 4),\
                         job(7, 9, 6)]
                           
    print("Maximum CPU load at any time: " +\
               str(find_max_cpu_load(jobs)))

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Output:

Maximum CPU load at any time: 7

Performance Analysis:

  • Time complexity: O(N*logN)
  • Auxillary Space: O(N)

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