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답안 #1050076

# 제출 시각 아이디 문제 언어 결과 실행 시간 메모리
1050076 2024-08-09T07:14:55 Z shiomusubi496 Uplifting Excursion (BOI22_vault) C++17
10 / 100
 16 ms 9768 KB 
#include <bits/stdc++.h>

#define rep(i, n) for (int i = 0; i < (int)(n); ++i)
#define rep2(i, a, b) for (int i = (int)(a); i < (int)(b); ++i)
#define rrep(i, n) for (int i = (int)(n) - 1; i >= 0; --i)
#define rrep2(i, a, b) for (int i = (int)(b) - 1; i >= (int)(a); --i)
#define all(v) begin(v), end(v)
#define rall(v) rbegin(v), rend(v)

using namespace std;

using ll = long long;

template<class T, class U> bool chmin(T& a, const U& b) { return a > b ? a = b, true : false; }
template<class T, class U> bool chmax(T& a, const U& b) { return a < b ? a = b, true : false; }

using namespace std;

constexpr ll inf = 1e18;

ll gcd(ll a, ll b) {
    a = abs(a); b = abs(b);
    while (b) {
        a %= b;
        swap(a, b);
    }
    return a;
}

int main() {
    int M; cin >> M;
    ll L; cin >> L;
    vector<ll> A(2 * M + 1);
    rep (i, 2 * M + 1) cin >> A[i];
    if (L < 0) {
        reverse(all(A));
        L = -L;
    }
    ll sml = 0, smr = 0;
    rep (i, 2 * M + 1) {
        if (i < M) sml += A[i] * (i - M);
        if (i > M) smr += A[i] * (i - M);
    }
    if (L < sml || smr < L) {
        puts("impossible");
        return 0;
    }
    vector<pair<int, ll>> B;
    vector<pair<int, ll>> C;
    rep (i, 2 * M + 1) {
        if (i == M) continue;
        if (A[i] == 0) continue;
        if (A[i] <= M) B.emplace_back(i - M, A[i]);
        else C.emplace_back(i - M, A[i]);
    }
    sml = smr = 0;
    for (auto [x, y] : B) {
        if (x < 0) sml += x * y;
        else smr += x * y;
    }
    auto calc_dp = [](vector<pair<int, ll>> B) -> vector<ll> {
        ll sml = 0, smr = 0;
        for (auto [x, y] : B) {
            if (x < 0) sml += x * y;
            else smr += x * y;
        }
        vector<ll> dp(smr - sml + 1, -inf);
        dp[0 - sml] = 0;
        for (auto [x, y] : B) {
            int ax = abs(x);
            vector<ll> memo;
            vector<ll> res;
            deque<int> st;
            rep (i, ax) {
                // mod x ごとにスライド最大値の形になる
                memo.clear();
                for (int j = i; j <= smr - sml; j += ax) {
                    memo.push_back(dp[j]);
                }
                res.assign(memo.size(), -inf);
                st.clear();
                if (x > 0) {
                    rep (i, memo.size()) memo[i] -= i;
                    rep (i, res.size()) {
                        while (!st.empty() && st.front() < i - y) st.pop_front();
                        while (!st.empty() && memo[st.back()] < memo[i]) st.pop_back();
                        st.push_back(i);
                        res[i] = memo[st.front()] + i;
                    }
                }
                else {
                    rep (i, memo.size()) memo[i] += i;
                    rrep (i, res.size()) {
                        while (!st.empty() && st.front() > i + y) st.pop_front();
                        while (!st.empty() && memo[st.back()] < memo[i]) st.pop_back();
                        st.push_back(i);
                        res[i] = memo[st.front()] - i;
                    }
                }
                rep (j, res.size()) dp[j * ax + i] = res[j];
            }
        }
        return dp;
    };
    auto dp = calc_dp(B);
    if (C.empty()) {
        if (dp[L - sml] >= 0) {
            cout << dp[L - sml] + A[M] << endl;
        }
        else {
            puts("impossible");
        }
        return 0;
    }
    if (C.size() <= 1) {
        auto [x, y] = C[0];
        ll lo = 0, hi = x * y;
        if (lo > hi) swap(lo, hi);
        ll ans = -inf;
        rep (i, smr - sml + 1) {
            if (dp[i] < 0) continue;
            if (L < (i + sml) + lo || (i + sml) + hi < L) continue;
            if ((L - (i + sml)) % x) continue;
            chmax(ans, dp[i] + A[M] + abs((L - (i + sml)) / x));
        }
        if (ans >= 0) {
            cout << ans << endl;
        }
        else {
            puts("impossible");
        }
        return 0;
    }
    auto calc_dp2 = [](vector<pair<int, ll>> B) -> vector<vector<ll>> {
        ll sml = 0, smr = 0;
        for (auto [x, y] : B) {
            if (x < 0) sml += x * y;
            else smr += x * y;
        }
        vector<ll> dp(smr - sml + 1, -inf);
        dp[0 - sml] = 0;
        vector<vector<ll>> ans{dp};
        for (auto [x, y] : B) {
            int ax = abs(x);
            vector<ll> memo;
            vector<ll> res;
            deque<int> st;
            rep (i, ax) {
                // mod x ごとにスライド最大値の形になる
                memo.clear();
                for (int j = i; j <= smr - sml; j += ax) {
                    memo.push_back(dp[j]);
                }
                res.assign(memo.size(), -inf);
                st.clear();
                if (x > 0) {
                    rep (i, memo.size()) memo[i] -= i;
                    rep (i, res.size()) {
                        while (!st.empty() && st.front() < i - y) st.pop_front();
                        while (!st.empty() && memo[st.back()] < memo[i]) st.pop_back();
                        st.push_back(i);
                        res[i] = memo[st.front()] + i;
                    }
                }
                else {
                    rep (i, memo.size()) memo[i] += i;
                    rrep (i, res.size()) {
                        while (!st.empty() && st.front() > i + y) st.pop_front();
                        while (!st.empty() && memo[st.back()] < memo[i]) st.pop_back();
                        st.push_back(i);
                        res[i] = memo[st.front()] - i;
                    }
                }
                rep (j, res.size()) dp[j * ax + i] = res[j];
            }
            ans.push_back(dp);
        }
        reverse(all(ans));
        return ans;
    };
    ll ans = -inf;
    vector<ll> g(C.size() + 1);
    rrep (i, C.size()) g[i] = gcd(g[i + 1], C[i].first);
    vector<pair<int, ll>> D;
    rrep (i, C.size()) D.emplace_back(C[i].first, min<ll>(C[i].second, M));
    auto dp2 = calc_dp2(D);
    vector<vector<vector<int>>> js(C.size() - 1);
    rep (m, C.size() - 1) {
        js[m].resize(C[m].first);
        for (ll j = 0; j < dp2[m + 1].size(); j += g[m + 1]) {
            if (dp2[m + 1][j] >= 0) js[m][j % C[m].first].push_back(j);
        }
    }
    rep (i, smr - sml + 1) {
        if (dp[i] < 0) continue;
        ll L2 = L - (i + sml);
        if (L2 % g[0]) continue;
        ll sm = dp[i] + A[M];
        int m = -1;
        rep (j, C.size() - 1) {
            ll tmp = C[j].second;
            while ((L2 - tmp * C[j].first) % g[j + 1]) --tmp;
            assert(tmp >= 0);
            if ((L2 - tmp * C[j].first) / g[j + 1] < M * M) {
                m = j;
                break;
            }
            sm += tmp;
            L2 -= tmp * C[j].first;
        }
        if (m == -1) {
            assert(L2 % C.back().first == 0);
            ll tmp = L2 / C.back().first;
            if (tmp > C.back().second) continue;
            sm += tmp;
            chmax(ans, sm);
        }
        else {
            ll sml2 = 0, smr2 = 0;
            rep2 (j, m + 1, C.size()) {
                ll x = C[m].first;
                ll y = min<ll>(C[m].second, M);
                if (x < 0) sml2 += x * y;
                else smr2 += x * y;
            }
            assert(sml2 == 0);
            auto itr = lower_bound(all(js[m][L2 % C[m].first]), L2 - sml2 - C[m].first * C[m].second) - js[m][L2 % C[m].first].begin();
            for (int jk = itr; jk < js[m].size(); ++jk) {
                ll j = js[m][L2 % C[m].first][jk];
                if (j > smr2 - sml2) break;
                ll L3 = L2 - (j + sml2);
                if (L3 < 0) break;
                ll sm2 = sm + dp2[m + 1][j];
                assert(L3 % C[m].first == 0);
                ll tmp = L3 / C[m].first;
                sm2 += tmp;
                chmax(ans, sm2);
                break;
            }
        }
    }
    if (ans >= 0) {
        cout << ans << endl;
    }
    else {
        puts("impossible");
    }
}

/*
フロベニウスの硬貨問題 : 互いに素な a,b で作れない最大の値は ab-a-b
x 以下を全て使う払い方があれば、それを必ず採用するとして良い (x 以下を使わない代わりに x 以上を使うのは明らかに少なくなる)
の 2 つから、 L-M^2 を超えない範囲で小さい方から選べるだけ選ぶ戦略が取れる
互いに素じゃない場合が面倒くさい
*/

Compilation message

vault.cpp: In function 'int main()':
vault.cpp:190:26: warning: comparison of integer expressions of different signedness: 'll' {aka 'long long int'} and 'std::vector<long long int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
  190 |         for (ll j = 0; j < dp2[m + 1].size(); j += g[m + 1]) {
      |                        ~~^~~~~~~~~~~~~~~~~~~
vault.cpp:228:35: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<std::vector<int> >::size_type' {aka 'long unsigned int'} [-Wsign-compare]
  228 |             for (int jk = itr; jk < js[m].size(); ++jk) {
      |                                ~~~^~~~~~~~~~~~~~

Subtask #1
0 / 5.0

# 결과 실행 시간 메모리 Grader output
1 Runtime error 2 ms 604 KB Execution killed with signal 6
2 Halted 0 ms 0 KB -

Subtask #2
0 / 15.0

# 결과 실행 시간 메모리 Grader output
1 Runtime error 2 ms 604 KB Execution killed with signal 6
2 Halted 0 ms 0 KB -

Subtask #3-1
10.0 / 10.0

# 결과 실행 시간 메모리 Grader output
1 Correct 0 ms 344 KB Output is correct
2 Correct 2 ms 1116 KB Output is correct
3 Correct 1 ms 348 KB Output is correct
4 Correct 2 ms 1116 KB Output is correct
5 Correct 2 ms 1116 KB Output is correct
6 Correct 1 ms 348 KB Output is correct
7 Correct 0 ms 348 KB Output is correct
8 Correct 0 ms 348 KB Output is correct
9 Correct 1 ms 344 KB Output is correct
10 Correct 1 ms 604 KB Output is correct

Subtask #3-2
0 / 10.0

# 결과 실행 시간 메모리 Grader output
1 Correct 0 ms 344 KB Output is correct
2 Correct 2 ms 1116 KB Output is correct
3 Correct 1 ms 348 KB Output is correct
4 Correct 2 ms 1116 KB Output is correct
5 Correct 2 ms 1116 KB Output is correct
6 Correct 1 ms 348 KB Output is correct
7 Correct 0 ms 348 KB Output is correct
8 Correct 0 ms 348 KB Output is correct
9 Correct 1 ms 344 KB Output is correct
10 Correct 1 ms 604 KB Output is correct
11 Runtime error 2 ms 604 KB Execution killed with signal 6
12 Halted 0 ms 0 KB -

Subtask #4-1
0 / 10.0

# 결과 실행 시간 메모리 Grader output
1 Correct 0 ms 344 KB Output is correct
2 Correct 2 ms 1116 KB Output is correct
3 Correct 1 ms 348 KB Output is correct
4 Correct 2 ms 1116 KB Output is correct
5 Correct 2 ms 1116 KB Output is correct
6 Correct 1 ms 348 KB Output is correct
7 Correct 0 ms 348 KB Output is correct
8 Correct 0 ms 348 KB Output is correct
9 Correct 1 ms 344 KB Output is correct
10 Correct 1 ms 604 KB Output is correct
11 Correct 0 ms 348 KB Output is correct
12 Correct 2 ms 1116 KB Output is correct
13 Correct 0 ms 348 KB Output is correct
14 Correct 2 ms 1116 KB Output is correct
15 Correct 2 ms 1152 KB Output is correct
16 Correct 1 ms 348 KB Output is correct
17 Correct 0 ms 348 KB Output is correct
18 Correct 0 ms 348 KB Output is correct
19 Correct 0 ms 348 KB Output is correct
20 Correct 1 ms 604 KB Output is correct
21 Correct 1 ms 348 KB Output is correct
22 Correct 0 ms 348 KB Output is correct
23 Correct 12 ms 3656 KB Output is correct
24 Correct 3 ms 2380 KB Output is correct
25 Correct 11 ms 4340 KB Output is correct
26 Correct 16 ms 7224 KB Output is correct
27 Correct 11 ms 3820 KB Output is correct
28 Runtime error 10 ms 9768 KB Execution killed with signal 6
29 Halted 0 ms 0 KB -

Subtask #4-2
0 / 10.0

# 결과 실행 시간 메모리 Grader output
1 Runtime error 2 ms 604 KB Execution killed with signal 6
2 Halted 0 ms 0 KB -

Subtask #5-1
0 / 10.0

# 결과 실행 시간 메모리 Grader output
1 Correct 0 ms 344 KB Output is correct
2 Correct 2 ms 1116 KB Output is correct
3 Correct 1 ms 348 KB Output is correct
4 Correct 2 ms 1116 KB Output is correct
5 Correct 2 ms 1116 KB Output is correct
6 Correct 1 ms 348 KB Output is correct
7 Correct 0 ms 348 KB Output is correct
8 Correct 0 ms 348 KB Output is correct
9 Correct 1 ms 344 KB Output is correct
10 Correct 1 ms 604 KB Output is correct
11 Correct 0 ms 348 KB Output is correct
12 Correct 2 ms 1116 KB Output is correct
13 Correct 0 ms 348 KB Output is correct
14 Correct 2 ms 1116 KB Output is correct
15 Correct 2 ms 1152 KB Output is correct
16 Correct 1 ms 348 KB Output is correct
17 Correct 0 ms 348 KB Output is correct
18 Correct 0 ms 348 KB Output is correct
19 Correct 0 ms 348 KB Output is correct
20 Correct 1 ms 604 KB Output is correct
21 Correct 1 ms 348 KB Output is correct
22 Correct 0 ms 348 KB Output is correct
23 Correct 12 ms 3656 KB Output is correct
24 Correct 3 ms 2380 KB Output is correct
25 Correct 11 ms 4340 KB Output is correct
26 Correct 16 ms 7224 KB Output is correct
27 Correct 11 ms 3820 KB Output is correct
28 Runtime error 10 ms 9768 KB Execution killed with signal 6
29 Halted 0 ms 0 KB -

Subtask #5-2
0 / 10.0

# 결과 실행 시간 메모리 Grader output
1 Runtime error 2 ms 604 KB Execution killed with signal 6
2 Halted 0 ms 0 KB -

Subtask #6-1
0 / 10.0

# 결과 실행 시간 메모리 Grader output
1 Correct 0 ms 344 KB Output is correct
2 Correct 2 ms 1116 KB Output is correct
3 Correct 1 ms 348 KB Output is correct
4 Correct 2 ms 1116 KB Output is correct
5 Correct 2 ms 1116 KB Output is correct
6 Correct 1 ms 348 KB Output is correct
7 Correct 0 ms 348 KB Output is correct
8 Correct 0 ms 348 KB Output is correct
9 Correct 1 ms 344 KB Output is correct
10 Correct 1 ms 604 KB Output is correct
11 Correct 0 ms 348 KB Output is correct
12 Correct 2 ms 1116 KB Output is correct
13 Correct 0 ms 348 KB Output is correct
14 Correct 2 ms 1116 KB Output is correct
15 Correct 2 ms 1152 KB Output is correct
16 Correct 1 ms 348 KB Output is correct
17 Correct 0 ms 348 KB Output is correct
18 Correct 0 ms 348 KB Output is correct
19 Correct 0 ms 348 KB Output is correct
20 Correct 1 ms 604 KB Output is correct
21 Correct 1 ms 348 KB Output is correct
22 Correct 0 ms 348 KB Output is correct
23 Correct 12 ms 3656 KB Output is correct
24 Correct 3 ms 2380 KB Output is correct
25 Correct 11 ms 4340 KB Output is correct
26 Correct 16 ms 7224 KB Output is correct
27 Correct 11 ms 3820 KB Output is correct
28 Runtime error 10 ms 9768 KB Execution killed with signal 6
29 Halted 0 ms 0 KB -

Subtask #6-2
0 / 10.0

# 결과 실행 시간 메모리 Grader output
1 Runtime error 2 ms 604 KB Execution killed with signal 6
2 Halted 0 ms 0 KB -