11544 - Recruiter's Problem

[baodog]

I keep get wa on this one. Is there some tricky i/o?
I notice only 1/9 got ac on contest, and 16% on judge.
Thanks. I just use max flow mincost (see below).
I use 10*cand*cand*cand+pref*((n-cand)*(n-cand)+1) as the cost, where cand is candidate id-1,
and pref is the order of preference for each task. (0..k-1 for p_0,..p_k-1).
Is this correct?

Code: Select all

AC

[LayCurse]

How about this case?

Input:
1
10 10
1 1 1 1 1 1 1 1 1 1
1 2
1 3
1 4
1 5
1 6
1 7
1 8
1 9
2 1 10
10 1 2 3 4 5 6 7 8 9 10

Output:
Case #1:
10 applicant(s) can be hired.
1 2
2 3
3 4
4 5
5 6
6 7
7 8
8 9
9 1
10 10

[baodog]

Thanks! I can get right answer now using BigNum for cost and
multiplying the spacing by k each time going from n-1 to 0,
but getting TLE. What is your approach? Thanks!

[sunny]

I didn't use min-cost-max-flow. Solved it by normal max-flow.

Suppose edges are ordered by worker #1's most preferred job,2nd most preferred job,....worker#2's most preferred,2nd most preferred and so on.
To determine the assignment, I removed each edge in increasing order and saw if it reduces the network flow by 1. If it
does assign that worker to that job and proceed to the next worker.
Running flow for every edge got TLE. I ran flow when the chosen edge was not in the previous flow otherwise that edge should be in the assignment, no need to run flow again.

My solution is quite slow, it took 1.89 secs.

[SerailHydra]

Can one candidate be assigned to more than one project?

[baodog]

Hi,

After speeding up my BigNum, I keep get WA in 1.9 seconds.
I tried many many cases and it gives the correct result.
Does anyone have more tricky cases ? Thanks.
My setup is shown below, if you feel like reading it and finding a
counter example. I keep multiplying the spacing by k and add 1, while going
backwards in candidates. Thanks!

Code: Select all

int main()
{
    int t,zz=0; cin2 >> t;
    int n,m;
    inf=0; REP(i,55) inf=(inf+1)*50;
    while(t--)
    {
        cin2 >> n >> m;
        memset( cap, 0, sizeof( cap ) );
        zz++;
        int s=n+m, t=n+m+1;
        REP(job,m) // spots
        {
            int r; cin2 >> r;
            cap[n+job][t]=r;
            cost[n+job][t]=0LL;
        }
        vector<vector<int> > jobs(n);
        REP(cand,n)
        {
            int k; cin2 >> k;
            while(k--) {int u; cin2>>u; u--; jobs[cand].push_back(u);}
        }
        vector<BigNum> space(n);
        space[n-1]=1;
        FORD(i,n-2,0)
        {
            space[i]=space[i+1]*((int)jobs[i+1].size())+1;
        }
        BigNum prev=0LL,best=0LL;
        REP(cand,n) // candidates
        {
            cap[s][cand]=1;
            cost[s][cand]=0LL;
            REP(i,jobs[cand].size())
            {
                int job=jobs[cand][i];
                cap[cand][n+job]=1;
                cost[cand][n+job]=prev+space[cand];
                prev=cost[cand][n+job]+0LL;
            }
        }
        cout << "Case #" << zz << ":" << endl;
        int flow = max_flow_min_cost(t+1, s, t);
        cout << flow << " applicant(s) can be hired." << endl;
        REP(i,n)
        {
            REP(j,m)
            {
                if(fnet[i][n+j])
                {
                    cout << i+1 << " " << j+1 << endl;
                    break;
                }
            }
        }
    }
    return 0;
}

[baodog]

>Suppose edges are ordered by worker #1's most preferred job,2nd most preferred job,....worker#2's most preferred,2nd most >preferred and so on.
>To determine the assignment, I removed each edge in increasing order and saw if it reduces the network flow by 1. If it
>does assign that worker to that job and proceed to the next worker.

Suppose just 1 worker, and 5 jobs. Remove any edge, and the flow is still 1.
This does not seem to work.

[sunny]

>Suppose just 1 worker, and 5 jobs. Remove any edge, and the flow is still 1.
>This does not seem to work.

When I process the jobs for a worker, actually I remove that worker form the network.

[baodog]

Thanks! I get it now, but I get TLE.

1) Do you clear the flows when you re-run network flow?
2) Do you use ford-fulkelson or dinic?

Thanks.

[sunny]

1) Yes. I think that's why my solution is slower. But I clear flows and re-run network flow if that job choice for the current worker was not in the previous computed flow. Otherwise just assign that worker to that job and go for the next worker.
2)Ford-fulkerson.

[LayCurse]

I got AC using almost same method with sunny.
I used dinic and runtime was 1.7s. (too slow)

> I removed each edge in increasing order
I think binary search may be more fast, but I do not try.
(Let first worker preferred 10 jobs. If max-flow with only first 5 edges for first worker less than max-flow with all edges, first worker should assign 6th prefer job or later or nothing. One max-flow calculation erase 5 edges in this case.)

[kengood]

can someone provide some testcases...?

2
50 50
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50
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50 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50
50 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50
50 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50
50 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50
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1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
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50 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50
50 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50
50 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50
50 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50
50 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50
50 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50
50 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50
50 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50
50 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

My program output:

Case #1:
50 applicant(s) can be hired.
1 1
2 2
3 2
4 3
5 3
6 3
7 4
8 4
9 4
10 4
11 5
12 5
13 5
14 5
15 5
16 6
17 6
18 6
19 6
20 6
21 6
22 7
23 7
24 7
25 7
26 7
27 7
28 7
29 8
30 8
31 8
32 8
33 8
34 8
35 8
36 8
37 9
38 9
39 9
40 9
41 9
42 9
43 9
44 9
45 9
46 10
47 10
48 10
49 10
50 10
Case #2:
50 applicant(s) can be hired.
1 1
2 2
3 3
4 4
5 5
6 6
7 7
8 8
9 9
10 10
11 11
12 12
13 13
14 14
15 15
16 16
17 17
18 18
19 19
20 20
21 21
22 22
23 23
24 24
25 25
26 26
27 27
28 28
29 29
30 30
31 31
32 32
33 33
34 34
35 35
36 36
37 37
38 38
39 39
40 40
41 41
42 42
43 43
44 44
45 45
46 46
47 47
48 48
49 49
50 50

[baodog]

I get same answers.