| # | 제출 시각 | 아이디 | 문제 | 언어 | 결과 | 실행 시간 | 메모리 |
|---|---|---|---|---|---|---|---|
| 674281 | thienbao1602 | Job Scheduling (CEOI12_jobs) | C++17 | 0 ms | 0 KiB |
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CEOI 2012 - Job SchedulingAuthor: Chuyang WangLanguage: C++Edit This PagePrerequisitesSilver - Binary SearchView Problem StatementTable of ContentsExplanationImplementationOfficial Analysis
Explanation
To find the minimum possible solution, we can use binary search on the number of machines needed for finishing the jobs within the given deadline. With $M$ requests, the number of needed machines must lie in the range $[1, M]$ as in the worst case where all the requests are given on the last day, we still have $D + 1$ days to process these requests.
For each number of machines being tested, we can check its feasibility in linear time if the given job requests are already sorted in ascending order with respect to the request date. We iterate through each day $i$ from $1$ to $N$ and add requests to the schedule in the sorted order. If there is no available machine left on a certain day $i$ while there are still requests not processed, we move to next day $i+1$ and process these requests. If the day $i$ exceeds the delay limit for the current job being processed, i.e. the request date of the job added with the permitted delay is strictly less than the current day $i$, we can stop iterating as it is not possible to use the giving number of machines to process all the jobs within the deadline. Otherwise, if we have processed all job requests, the number of machines being tested is feasible, and we also found a schedule for these jobs.
Implementation
Time Complexity: $\mathcal{O}(N \log N)$
Copy#include <bits/stdc++.h>using namespace std;
#define all(x) begin(x), end(x)#define mp make_pair
using pi = pair<int, int>;using vi = vector<int>;
int N, D, M;
// test if it is possible to finish the jobs using given # of machines// return: first: possible or not, second: if possible, the schedule for the jobspair<bool, vector<vi>> isFeasible(const vector<pi> &jobs, int machineCount){ vector<vi> schedule(N); int reqNum = 0; // we simulate from day 1 until the last day N // we move to the next day if all the machines are used or // there is no more job requests left on or before this day for (int day = 1; day <= N; day++) { for (int j = 0; j < machineCount; j++) { // if all jobs before and on this day are finished, // we can go to the next day, even if there are usable machines left // we can determine that since the vector jobs is sorted if (jobs[reqNum].first > day) break; // if the current date is before the deadline for the job // we can add this job to the schedule and move to the next job request if (jobs[reqNum].first + D >= day) schedule[day - 1].push_back(jobs[reqNum++].second); // otherwise, it is not feasible due to deadline else return mp(false, schedule);
// if we have processed all the requests, we have found a feasible sol if (reqNum == M) return mp(true, schedule); } } // if not all the requests can be processed within the given N days, // then it is not feasible return mp(false, schedule);}
int main(){ cin.tie(0)->sync_with_stdio(false);
cin >> N >> D >> M; vector<pi> jobs(M); for (int i = 0; i < M; i++) { int day; cin >> day; // first: request date, second: index [1..M] jobs[i] = mp(day, i + 1); } // we sort the jobs by the request date in ascending order // sothat we can test them using isFeasible() in linear time whether they // can be done in given time using a certain amount of machines sort(all(jobs));
vector<vi> result; // binary search on the number of machines for the minimum possible solution // left and right bound, l and r int l = 1, r = M; while (l < r) { int machineNum = (l + r) / 2; // test if the jobs would finish within the deadline // using the current # of machines, machineNum pair<bool, vector<vi>> curResult = isFeasible(jobs, machineNum); // if it's possible, we set the right bound as the tested machine number // and save the current schedule if (curResult.first) { r = machineNum; result = curResult.second; } // otherwise, we set the left bound to be the tested number + 1 // and test the next machineNum again else l = machineNum + 1; }
cout << l << "\n"; for (int i = 0; i < N; i++) { for (int &idx : result[i]) cout << idx << " "; cout << 0 << "\n"; }}Join the USACO Forum!Stuck on a problem, or don't understand a module? Join the USACO Forum and get help from other competitive programmers!Join Forum