제출 #468318

#제출 시각아이디문제언어결과실행 시간메모리
468318Shogun3103Job Scheduling (CEOI12_jobs)C++17
100 / 100
511 ms26368 KiB
#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 jobs
pair<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";
    }
}
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