Submission #860633

# Submission time Handle Problem Language Result Execution time Memory
860633 2023-10-13T15:01:14 Z E869120 Uplifting Excursion (BOI22_vault) C++14
0 / 100
0 ms 348 KB
#include <bits/stdc++.h>
using namespace std;
 
vector<long long> SolveDP(long long N, long long LIM, vector<long long> List, vector<long long> Init) {
    vector<long long> dp(LIM + 1, -(1LL << 60));
    if (Init.size() == 0) dp[0] = 0;
    else {
        for (int i = 0; i < (int)Init.size(); i++) dp[i] = Init[i];
    }
 
    // DP Start
    for (int i = 0; i < N; i++) {
        vector<long long> ndp(LIM + 1, -(1LL << 60));
        long long kazu = i + 1;
        for (int j = 0; j < kazu; j++) {
            vector<pair<long long, long long>> maxi;
            int cur = 0;
            for (int k = j; k <= LIM; k += kazu) {
                long long val = dp[k] - (k / kazu);
                while (maxi.size() >= cur + 1) {
                    if (maxi[maxi.size() - 1].second <= val) maxi.pop_back();
                    else break;
                }
                maxi.push_back(make_pair(1LL * k, val));
                if (maxi[cur].second >= -(1LL << 59)) ndp[k] = maxi[cur].second + (k / kazu);
                while (cur < (int)maxi.size() && maxi[cur].first <= k - 1LL * kazu * List[i]) cur += 1;
            }
        }
        dp = ndp;
    }
 
    // Return
    return dp;
}
 
void Solve_Subtask2(long long M, long long L, vector<long long> A) {
    // Step 1. Calculate
    vector<long long> A1;
    vector<long long> A2;
    for (int i = M - 1; i >= 0; i--) A1.push_back(A[i]);
    for (int i = M + 1; i <= 2 * M; i++) A2.push_back(A[i]);
    vector<long long> DP1 = SolveDP(M, 700000, A1, vector<long long>{});
    vector<long long> DP2 = SolveDP(M, 700000, A2, vector<long long>{});
 
    // Step 2. Output
    long long Answer = -(1LL << 60);
    for (long long i = 0; i <= 700000LL - abs(L); i++) {
        long long idx1 = i;
        long long idx2 = i + abs(L); if (L < 0) swap(idx1, idx2);
        Answer = max(Answer, DP1[idx1] + DP2[idx2]);
    }
    if (Answer < 0LL) cout << "impossible" << endl;
    else cout << Answer + A[M] << endl;
}

void Solve_Subtask5(long long M, long long L, vector<long long> A) {
    if (L < 0) { cout << "Impossible" << endl; return; }

    // Step 1. Greedy
    vector<long long> L1(M, 0);
    vector<long long> L2(M, 0);
    long long rem = L - M * M;
    long long ans = 0;
    for (int i = 0; i < M; i++) {
        if (rem < 0) continue;
        L1[i] = min(A[M + 1 + i], rem / (i + 1));
        ans += L1[i];
        rem -= 1LL * (i + 1) * L1[i];
    }
    for (int i = 0; i < M; i++) L2[i] = A[i] - L1[i];
    if (rem > M) { cout << "impossible" << endl; return; }

    // Step 2. DP
    vector<long long> dp = SolveDP(M, M * M + rem, L2, vector<long long>{});
    if (dp[M * M + rem] == -(1LL << 60)) { cout << "impossible" << endl; }
    else cout << dp[M * M + rem] + ans + A[M] << endl;
}

void Solve_Subtask3(long long M, long long L, vector<long long> A) {
    long long Baseln = (M + 1) * M * M / 2LL;
    vector<long long> L1(M + 1, 0);
    vector<long long> L2(M + 1, 0);
    vector<long long> L3(M, 0);
    vector<long long> L4(M, 0);
    vector<long long> M1(M + 1, 0);
    vector<long long> M2(M + 1, 0);
    vector<pair<long long, long long>> Cand1; Cand1.push_back(make_pair(0, 0));
    vector<pair<long long, long long>> Cand2; Cand2.push_back(make_pair(0, 0));
 
    // Step 1. Set Up
    for (int i = 0; i <= M - 1; i++) {
        int idx = M - i;
        long long Threshold = M;
        L1[idx - 0] = A[i] - min(A[i], Threshold);
        L3[idx - 1] = min(A[i], Threshold);
    }
    for (int i = M + 1; i <= 2 * M; i++) {
        int idx = i - M;
        long long Threshold = M;
        L2[idx - 0] = A[i] - min(A[i], Threshold);
        L4[idx - 1] = min(A[i], Threshold);
    }
 
    // Step 2. Base DP
    vector<long long> dp1 = SolveDP(M, Baseln, L3, vector<long long>{});
    vector<long long> dp2 = vector<long long>(Baseln + 1, -(1LL << 60));
    for (int i = 0; i <= Baseln; i++) dp2[Baseln - i] = dp1[i];
    vector<long long> dp3 = SolveDP(M, Baseln * 2, L4, dp2);
 
    // Step 3. Get Theoritical Value
    long long a1 = 0;
    long long a2 = 0;
    for (int i = 1; i <= M; i++) a1 += 1LL * i * L1[i];
    for (int i = 1; i <= M; i++) a2 += 1LL * i * L2[i];
    if (a2 - a1 > L) a2 = a1 + L;
    else a1 = a2 - L;
    if (a1 + Baseln < 0 || a2 + Baseln < 0) {
        cout << "impossible" << endl;
        return;
    }
 
    // Step 4. Get Candiates for L1
    long long rem1 = a1 + Baseln;
    long long cnt1 = 0;
    for (int i = 1; i <= M; i++) {
        M1[i] = min(L1[i], rem1 / i);
        rem1 -= 1LL * i * M1[i];
        cnt1 += M1[i];
    }
    for (int i = M; i >= 1; i--) {
        for (long long j = 0; j < M1[i]; j++) {
            Cand1.push_back(make_pair((a1 + Baseln) - rem1, cnt1));
            rem1 += 1LL * i;
            cnt1 -= 1LL;
            if (rem1 > 2LL * Baseln) break;
        }
        if (rem1 > 2LL * Baseln) break;
    }
 
    // Step 5. Get Candidates for L2
    long long rem2 = a2 + Baseln;
    long long cnt2 = 0;
    for (int i = 1; i <= M; i++) {
        M2[i] = min(L2[i], rem2 / i);
        rem2 -= 1LL * i * M2[i];
        cnt2 += M2[i];
    }
    for (int i = M; i >= 1; i--) {
        for (long long j = 0; j < M2[i]; j++) {
            Cand2.push_back(make_pair((a2 + Baseln) - rem2, cnt2));
            rem2 += 1LL * i;
            cnt2 -= 1LL;
            if (rem2 > 2LL * Baseln) break;
        }
        if (rem2 > 2LL * Baseln) break;
    }
    // cout << "L1 = "; for (int i = 1; i <= M; i++) cout << L1[i] << " "; cout << endl;
    // cout << "L2 = "; for (int i = 1; i <= M; i++) cout << L2[i] << " "; cout << endl;
    // cout << "Cand1 = "; for (int i = 0; i < Cand1.size(); i++) cout << "(" << Cand1[i].first << "," << Cand1[i].second << ") "; cout << endl;
    // cout << "Cand2 = "; for (int i = 0; i < Cand2.size(); i++) cout << "(" << Cand2[i].first << "," << Cand2[i].second << ") "; cout << endl;
 
    // Step 6. Brute Force
    long long Answer = -(1LL << 60);
    for (pair<long long, long long> v1 : Cand1) {
        for (pair<long long, long long> v2 : Cand2) {
            long long diff = L - (v2.first - v1.first);
            if (diff < -Baseln || diff > Baseln) continue;
            if (dp3[diff + Baseln] == -(1LL << 60)) continue;
            Answer = max(Answer, v1.second + v2.second + dp3[diff + Baseln]);
        }
    }
 
    // Step 7. Output
    if (Answer == -(1LL << 60)) cout << "impossible" << endl;
    else cout << Answer + A[M] << endl;
}
 
int main() {
    // Input
    long long M, L;
    cin >> M >> L;
    vector<long long> A(2 * M + 1, 0);
    for (int i = 0; i <= 2 * M; i++) cin >> A[i];
 
    // Judge if Subtask 2
    bool Subtask2 = true;
    if (M > 100) Subtask2 = false;
    for (int i = 0; i <= 2 * M; i++) {
        if (A[i] > 100) Subtask2 = false;
    }
    Subtask2 = false;

    // Judge if Subtask 5
    bool Subtask5 = true;
    for (int i = 0; i <  M; i++) {
        if (A[i] > 0) Subtask5 = false;
    }
 
    // Execution
    if (Subtask2 == true) Solve_Subtask2(M, L, A);
    else if (Subtask5 == true) Solve_Subtask5(M, L, A);
    else Solve_Subtask3(M, L, A);
    return 0;
}

Compilation message

vault.cpp: In function 'std::vector<long long int> SolveDP(long long int, long long int, std::vector<long long int>, std::vector<long long int>)':
vault.cpp:20:36: warning: comparison of integer expressions of different signedness: 'std::vector<std::pair<long long int, long long int> >::size_type' {aka 'long unsigned int'} and 'int' [-Wsign-compare]
   20 |                 while (maxi.size() >= cur + 1) {
      |                        ~~~~~~~~~~~~^~~~~~~~~~
# Verdict Execution time Memory Grader output
1 Correct 0 ms 348 KB Output is correct
2 Correct 0 ms 348 KB Output is correct
3 Incorrect 0 ms 348 KB Output isn't correct
4 Halted 0 ms 0 KB -
# Verdict Execution time Memory Grader output
1 Correct 0 ms 348 KB Output is correct
2 Correct 0 ms 348 KB Output is correct
3 Incorrect 0 ms 348 KB Output isn't correct
4 Halted 0 ms 0 KB -
# Verdict Execution time Memory Grader output
1 Incorrect 0 ms 348 KB Output isn't correct
2 Halted 0 ms 0 KB -
# Verdict Execution time Memory Grader output
1 Incorrect 0 ms 348 KB Output isn't correct
2 Halted 0 ms 0 KB -
# Verdict Execution time Memory Grader output
1 Incorrect 0 ms 348 KB Output isn't correct
2 Halted 0 ms 0 KB -
# Verdict Execution time Memory Grader output
1 Correct 0 ms 348 KB Output is correct
2 Correct 0 ms 348 KB Output is correct
3 Incorrect 0 ms 348 KB Output isn't correct
4 Halted 0 ms 0 KB -
# Verdict Execution time Memory Grader output
1 Incorrect 0 ms 348 KB Output isn't correct
2 Halted 0 ms 0 KB -
# Verdict Execution time Memory Grader output
1 Correct 0 ms 348 KB Output is correct
2 Correct 0 ms 348 KB Output is correct
3 Incorrect 0 ms 348 KB Output isn't correct
4 Halted 0 ms 0 KB -
# Verdict Execution time Memory Grader output
1 Incorrect 0 ms 348 KB Output isn't correct
2 Halted 0 ms 0 KB -
# Verdict Execution time Memory Grader output
1 Correct 0 ms 348 KB Output is correct
2 Correct 0 ms 348 KB Output is correct
3 Incorrect 0 ms 348 KB Output isn't correct
4 Halted 0 ms 0 KB -