oj.uz

Submission #674789

# Submission time Handle Problem Language Result Execution time Memory
674789 2022-12-26T08:20:57 Z Giantpizzahead Let's Win the Election (JOI22_ho_t3) C++17
10 / 100
 165 ms 6292 KB 
/*
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, vector<double>(N+2, INF)));
    dp[0][0][1] = 0;
    rep(i, 0, N) {
        // Fill next row with infinity first
        rep(k, 0, i+2) rep(p, 1, i+3) 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) 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(6) << 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

# Verdict Execution time Memory Grader output
1 Correct 1 ms 212 KB Output is correct
2 Correct 1 ms 324 KB Output is correct
3 Correct 1 ms 212 KB Output is correct
4 Correct 1 ms 212 KB Output is correct
5 Correct 67 ms 6272 KB Output is correct
6 Correct 72 ms 6228 KB Output is correct
7 Correct 71 ms 6228 KB Output is correct
8 Correct 63 ms 6272 KB Output is correct
9 Correct 77 ms 6228 KB Output is correct
10 Correct 75 ms 6208 KB Output is correct

Subtask #2
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 212 KB Output is correct
2 Correct 1 ms 324 KB Output is correct
3 Correct 1 ms 212 KB Output is correct
4 Correct 1 ms 212 KB Output is correct
5 Correct 67 ms 6272 KB Output is correct
6 Correct 72 ms 6228 KB Output is correct
7 Correct 71 ms 6228 KB Output is correct
8 Correct 63 ms 6272 KB Output is correct
9 Correct 77 ms 6228 KB Output is correct
10 Correct 75 ms 6208 KB Output is correct
11 Correct 0 ms 212 KB Output is correct
12 Correct 165 ms 6272 KB Output is correct
13 Correct 129 ms 6228 KB Output is correct
14 Correct 94 ms 6276 KB Output is correct
15 Correct 160 ms 6228 KB Output is correct
16 Correct 123 ms 6276 KB Output is correct
17 Correct 87 ms 6228 KB Output is correct
18 Correct 160 ms 6292 KB Output is correct
19 Correct 122 ms 6276 KB Output is correct
20 Correct 90 ms 6280 KB Output is correct

Subtask #3
0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 212 KB Output is correct
2 Correct 0 ms 212 KB Output is correct
3 Correct 0 ms 212 KB Output is correct
4 Correct 0 ms 324 KB Output is correct
5 Correct 1 ms 212 KB Output is correct
6 Correct 1 ms 212 KB Output is correct
7 Correct 1 ms 340 KB Output is correct
8 Correct 0 ms 320 KB Output is correct
9 Incorrect 1 ms 212 KB Output isn't correct
10 Halted 0 ms 0 KB -

Subtask #4
0 / 12.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 212 KB Output is correct
2 Correct 0 ms 212 KB Output is correct
3 Correct 0 ms 212 KB Output is correct
4 Correct 0 ms 324 KB Output is correct
5 Correct 1 ms 212 KB Output is correct
6 Correct 1 ms 212 KB Output is correct
7 Correct 1 ms 340 KB Output is correct
8 Correct 0 ms 320 KB Output is correct
9 Incorrect 1 ms 212 KB Output isn't correct
10 Halted 0 ms 0 KB -

Subtask #5
0 / 33.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 212 KB Output is correct
2 Correct 0 ms 212 KB Output is correct
3 Correct 0 ms 212 KB Output is correct
4 Correct 0 ms 324 KB Output is correct
5 Correct 1 ms 212 KB Output is correct
6 Correct 1 ms 212 KB Output is correct
7 Correct 1 ms 340 KB Output is correct
8 Correct 0 ms 320 KB Output is correct
9 Incorrect 1 ms 212 KB Output isn't correct
10 Halted 0 ms 0 KB -

Subtask #6
0 / 11.0

# Verdict Execution time Memory Grader output
1 Incorrect 159 ms 6280 KB Output isn't correct
2 Halted 0 ms 0 KB -

Subtask #7
0 / 23.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 212 KB Output is correct
2 Correct 1 ms 324 KB Output is correct
3 Correct 1 ms 212 KB Output is correct
4 Correct 1 ms 212 KB Output is correct
5 Correct 67 ms 6272 KB Output is correct
6 Correct 72 ms 6228 KB Output is correct
7 Correct 71 ms 6228 KB Output is correct
8 Correct 63 ms 6272 KB Output is correct
9 Correct 77 ms 6228 KB Output is correct
10 Correct 75 ms 6208 KB Output is correct
11 Correct 0 ms 212 KB Output is correct
12 Correct 165 ms 6272 KB Output is correct
13 Correct 129 ms 6228 KB Output is correct
14 Correct 94 ms 6276 KB Output is correct
15 Correct 160 ms 6228 KB Output is correct
16 Correct 123 ms 6276 KB Output is correct
17 Correct 87 ms 6228 KB Output is correct
18 Correct 160 ms 6292 KB Output is correct
19 Correct 122 ms 6276 KB Output is correct
20 Correct 90 ms 6280 KB Output is correct
21 Correct 1 ms 212 KB Output is correct
22 Correct 0 ms 212 KB Output is correct
23 Correct 0 ms 212 KB Output is correct
24 Correct 0 ms 324 KB Output is correct
25 Correct 1 ms 212 KB Output is correct
26 Correct 1 ms 212 KB Output is correct
27 Correct 1 ms 340 KB Output is correct
28 Correct 0 ms 320 KB Output is correct
29 Incorrect 1 ms 212 KB Output isn't correct
30 Halted 0 ms 0 KB -