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Find Jobs involved in Weighted Job Scheduling in C++
Suppose we have a list of N jobs where each job has three parameters. 1. Start Time 2. Finish Time 3. Profit We have to find a subset of jobs associated with maximum profit so that no two jobs in the subset overlap.
So, if the input is like N = 4 and J = {{2, 3, 55},{4, 6, 25},{7, 20, 150},{3, 150, 250}} , then the output will be [(2, 3, 55),(3, 150, 250)] and optimal profit 305
To solve this, we will follow these steps −
Define a function find_no_conflict(), this will take an array jobs, index,
left := 0, right := index - 1
while left <= right, do −
mid := (left + right) / 2
if jobs[mid].finish <= jobs[index].start, then −
if jobs[mid + 1].finish <= jobs[index].start, then −
left := mid + 1
return mid
return mid
Otherwise
right := mid - 1
return -1
From the main method, do the following −
sort the array job_list based on finish time
make a table for jobs called table of size n
table[0].value := job_list[0].profit
insert job_list[0] at the end of table[0]
for initialize i := 1, when i < n, update (increase i by 1), do −
include_profit := job_list[i].profit
l := find_no_conflict(job_list, i)
if l is not equal to - 1, then −
include_profit := include_profit + table[l].value
if include_profit > table[i - 1].value, then −
table[i].value := include_profit
table[i].job := table[l].job
insert job_list[i] at the end of of table[i]
Otherwise
table[i] := table[i - 1]
display jobs from table
display Optimal profit := table[n - 1].value
Example (C++)
Let us see the following implementation to get better understanding −
#include <bits/stdc++.h>
using namespace std;
class Job {
public:
int start, finish, profit;
};
struct job_with_weight {
vector<Job> job;
int value;
};
bool jobComparator(Job s1, Job s2) {
return (s1.finish < s2.finish);
}
int find_no_conflict(Job jobs[], int index) {
int left = 0, right = index - 1;
while (left <= right) {
int mid = (left + right) / 2;
if (jobs[mid].finish <= jobs[index].start) {
if (jobs[mid + 1].finish <= jobs[index].start)
left = mid + 1;
else
return mid;
}
else
right = mid - 1;
}
return -1;
}
int get_max_profit(Job job_list[], int n) {
sort(job_list, job_list + n, jobComparator);
job_with_weight table[n];
table[0].value = job_list[0].profit;
table[0].job.push_back(job_list[0]);
for (int i = 1; i < n; i++) {
int include_profit = job_list[i].profit;
int l = find_no_conflict(job_list, i);
if (l != - 1)
include_profit += table[l].value;
if (include_profit > table[i - 1].value){
table[i].value = include_profit;
table[i].job = table[l].job;
table[i].job.push_back(job_list[i]);
}
else
table[i] = table[i - 1];
}
cout << "[";
for (int i=0; i<table[n-1].job.size(); i++) {
Job j = table[n-1].job[i];
cout << "(" << j.start << ", " << j.finish << ", " << j.profit << "),";
}
cout << "]\nOptimal profit: " << table[n - 1].value;
}
int main() {
Job arr[] = {{2, 3, 55},{4, 6, 25},{7, 20, 150},{3, 150, 250}};
int n = sizeof(arr)/sizeof(arr[0]);
get_max_profit(arr, n);
}Input
{{2, 3, 55},{4, 6, 25},{7, 20, 150},{3, 150, 250}}Output
[(2, 3, 55),(3, 150, 250),] Optimal profit: 305
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