답안 #674748

#	제출 시각	아이디	문제	언어	결과	실행 시간	메모리
674748	2022-12-26T06:37:49 Z	Giantpizzahead	Let's Win the Election (JOI22_ho_t3)	C++17	10 / 100	158 ms	6288 KB

Main

/*
JOI 2022 Problem 3

Solution: DP.

Sort the states by increasing B[i].
Let dp[i][k][p] =
Minimum time required to get k votes and p people together (1 + # of collabs),
using only states 1 to i (one indexed).

Base case: dp[0][0][1] = 0

Assuming A and B are stored using zero indexing.
Transitions:
dp[i][k][p] = C
Get a collaborator: dp[i+1][k+1][p+1] = C + B[i] / p
Get a vote only: dp[i+1][k+1][p] = C + A[i] / p
Skip: dp[i+1][k][p] = C
To save memory, compress the first dimension.

Runtime: O(N^3 / 4)
Memory: O(N^2)

Notes:
Collaborators should be gotten first in the order (greedy to maximize total hours).
AKA given a solution with a fixed set (0, 1, 2) where 0=None, 1=Vote, 2=Collab:
The states with smallest B_i should be talked to first to get collabs.
In fact, all people should talk in the same place, since the total time wouldn't change
and this could only be beneficial.

Total time = Sum of the below
B_1 + B_2 / 2 + B_3 / 3 + ... for type 2
(A_1 + A_2 + ...) / (# of people)
Where the total number of states = K.

Say the # of people we want at the end is fixed. Then go for the states with smallest B_i
to satisfy that requirement, then smallest A_i for the vote requirement.
I think this is a valid greedy solution.

Say we have (1, 100), (90, 105)
105.5 would be the non-greedy...
So no, it's not a valid greedy. Perhaps DP is more applicable here...
*/

#include <bits/stdc++.h>
using namespace std;

#define rep(i, a, b) for (int i = (a); i < (b); i++)
#define sz(x) ((int) x.size())
#define all(x) x.begin(), x.end()
#define debug if (true) cerr
using ll = long long;
using pii = pair<int, int>;
using vi = vector<int>;

struct State {
    int a, b;
};

void tryTrans(double& a, double b) {
    a = min(a, b);
}

void solve() {
    int N; cin >> N;
    int K; cin >> K;
    vector<State> S(N);
    rep(i, 0, N) {
        cin >> S[i].a >> S[i].b;
    }
    sort(all(S), [](const State& s1, const State& s2) {
        int b1 = (s1.b == -1 ? 1e9 : s1.b);
        int b2 = (s2.b == -1 ? 1e9 : s2.b);
        return b1 < b2;
    });
    // rep(i, 0, N) cout << S[i].a << ' ' << S[i].b << '\n';

    // DP
    double INF = 1e18;
    vector<vector<vector<double>>> dp(2, vector<vector<double>>(N+1+1, vector<double>(N+2+1, INF)));
    dp[0][0][1] = 0;
    rep(i, 0, N) {
        // Fill next row with infinity first
        rep(k, 0, i+2+1) rep(p, 0, i+3+1) dp[1][k][p] = INF;
        // Main transitions
        rep(k, 0, i+1) {
            rep(p, 1, i+2) {
                double C = dp[0][k][p];
                if (C > INF/2) continue;
                // cout << "dp[" << i << "][" << k << "][" << p << "] = " << C << endl;
                // Get a collaborator
                if (S[i].b != -1) tryTrans(dp[1][k+1][p+1], C + (double) S[i].b / p);
                // Get a vote only
                tryTrans(dp[1][k+1][p], C + (double) S[i].a / p);
                // Skip
                tryTrans(dp[1][k][p], C);
            }
        }
        // Swap rows
        swap(dp[0], dp[1]);
    }

    // Calculate answer
    double answer = INF;
    rep(p, 1, N+2) answer = min(dp[0][K][p], answer);
    cout << fixed << setprecision(16) << answer << '\n';
}

int main() {
    ios::sync_with_stdio(0);
    cin.tie(0);
    cin.exceptions(cin.failbit);
    solve();
    return 0;
}

Subtask #1
5.0 / 5.0

#	결과	실행 시간	메모리	Grader output
1	Correct	1 ms	316 KB	Output is correct
2	Correct	1 ms	212 KB	Output is correct
3	Correct	0 ms	212 KB	Output is correct
4	Correct	1 ms	320 KB	Output is correct
5	Correct	63 ms	6288 KB	Output is correct
6	Correct	54 ms	6288 KB	Output is correct
7	Correct	50 ms	6288 KB	Output is correct
8	Correct	63 ms	6288 KB	Output is correct
9	Correct	51 ms	6228 KB	Output is correct
10	Correct	58 ms	6284 KB	Output is correct

Subtask #2
5.0 / 5.0

#	결과	실행 시간	메모리	Grader output
1	Correct	1 ms	316 KB	Output is correct
2	Correct	1 ms	212 KB	Output is correct
3	Correct	0 ms	212 KB	Output is correct
4	Correct	1 ms	320 KB	Output is correct
5	Correct	63 ms	6288 KB	Output is correct
6	Correct	54 ms	6288 KB	Output is correct
7	Correct	50 ms	6288 KB	Output is correct
8	Correct	63 ms	6288 KB	Output is correct
9	Correct	51 ms	6228 KB	Output is correct
10	Correct	58 ms	6284 KB	Output is correct
11	Correct	0 ms	320 KB	Output is correct
12	Correct	152 ms	6288 KB	Output is correct
13	Correct	113 ms	6228 KB	Output is correct
14	Correct	84 ms	6288 KB	Output is correct
15	Correct	153 ms	6228 KB	Output is correct
16	Correct	110 ms	6284 KB	Output is correct
17	Correct	75 ms	6228 KB	Output is correct
18	Correct	150 ms	6284 KB	Output is correct
19	Correct	121 ms	6228 KB	Output is correct
20	Correct	91 ms	6288 KB	Output is correct

Subtask #3
0 / 11.0

#	결과	실행 시간	메모리	Grader output
1	Correct	1 ms	324 KB	Output is correct
2	Correct	1 ms	320 KB	Output is correct
3	Correct	1 ms	212 KB	Output is correct
4	Correct	0 ms	212 KB	Output is correct
5	Correct	0 ms	320 KB	Output is correct
6	Correct	0 ms	212 KB	Output is correct
7	Correct	0 ms	324 KB	Output is correct
8	Correct	1 ms	212 KB	Output is correct
9	Incorrect	1 ms	324 KB	Output isn't correct
10	Halted	0 ms	0 KB	-

Subtask #4
0 / 12.0

#	결과	실행 시간	메모리	Grader output
1	Correct	1 ms	324 KB	Output is correct
2	Correct	1 ms	320 KB	Output is correct
3	Correct	1 ms	212 KB	Output is correct
4	Correct	0 ms	212 KB	Output is correct
5	Correct	0 ms	320 KB	Output is correct
6	Correct	0 ms	212 KB	Output is correct
7	Correct	0 ms	324 KB	Output is correct
8	Correct	1 ms	212 KB	Output is correct
9	Incorrect	1 ms	324 KB	Output isn't correct
10	Halted	0 ms	0 KB	-

Subtask #5
0 / 33.0

#	결과	실행 시간	메모리	Grader output
1	Correct	1 ms	324 KB	Output is correct
2	Correct	1 ms	320 KB	Output is correct
3	Correct	1 ms	212 KB	Output is correct
4	Correct	0 ms	212 KB	Output is correct
5	Correct	0 ms	320 KB	Output is correct
6	Correct	0 ms	212 KB	Output is correct
7	Correct	0 ms	324 KB	Output is correct
8	Correct	1 ms	212 KB	Output is correct
9	Incorrect	1 ms	324 KB	Output isn't correct
10	Halted	0 ms	0 KB	-

Subtask #6
0 / 11.0

#	결과	실행 시간	메모리	Grader output
1	Incorrect	158 ms	6284 KB	Output isn't correct
2	Halted	0 ms	0 KB	-

Subtask #7
0 / 23.0

#	결과	실행 시간	메모리	Grader output
1	Correct	1 ms	316 KB	Output is correct
2	Correct	1 ms	212 KB	Output is correct
3	Correct	0 ms	212 KB	Output is correct
4	Correct	1 ms	320 KB	Output is correct
5	Correct	63 ms	6288 KB	Output is correct
6	Correct	54 ms	6288 KB	Output is correct
7	Correct	50 ms	6288 KB	Output is correct
8	Correct	63 ms	6288 KB	Output is correct
9	Correct	51 ms	6228 KB	Output is correct
10	Correct	58 ms	6284 KB	Output is correct
11	Correct	0 ms	320 KB	Output is correct
12	Correct	152 ms	6288 KB	Output is correct
13	Correct	113 ms	6228 KB	Output is correct
14	Correct	84 ms	6288 KB	Output is correct
15	Correct	153 ms	6228 KB	Output is correct
16	Correct	110 ms	6284 KB	Output is correct
17	Correct	75 ms	6228 KB	Output is correct
18	Correct	150 ms	6284 KB	Output is correct
19	Correct	121 ms	6228 KB	Output is correct
20	Correct	91 ms	6288 KB	Output is correct
21	Correct	1 ms	324 KB	Output is correct
22	Correct	1 ms	320 KB	Output is correct
23	Correct	1 ms	212 KB	Output is correct
24	Correct	0 ms	212 KB	Output is correct
25	Correct	0 ms	320 KB	Output is correct
26	Correct	0 ms	212 KB	Output is correct
27	Correct	0 ms	324 KB	Output is correct
28	Correct	1 ms	212 KB	Output is correct
29	Incorrect	1 ms	324 KB	Output isn't correct
30	Halted	0 ms	0 KB	-

답안 #674748

Compilation message

Subtask #1 5.0 / 5.0

Subtask #2 5.0 / 5.0

Subtask #3 0 / 11.0

Subtask #4 0 / 12.0

Subtask #5 0 / 33.0

Subtask #6 0 / 11.0

Subtask #7 0 / 23.0

Subtask #1
5.0 / 5.0

Subtask #2
5.0 / 5.0

Subtask #3
0 / 11.0

Subtask #4
0 / 12.0

Subtask #5
0 / 33.0

Subtask #6
0 / 11.0

Subtask #7
0 / 23.0