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답안 #1050042

# 제출 시각 아이디 문제 언어 결과 실행 시간 메모리
1050042 2024-08-09T06:59:30 Z shiomusubi496 Uplifting Excursion (BOI22_vault) C++17
20 / 100
 2181 ms 24328 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, 2 * M));
    auto dp2 = calc_dp2(D);
    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 {
            vector<pair<int, ll>> D;
            rep2 (j, m + 1, C.size()) D.emplace_back(C[j].first, min<ll>(C[j].second, 2 * M));
            ll sml2 = 0, smr2 = 0;
            for (auto [x, y] : D) {
                if (x < 0) sml2 += x * y;
                else smr2 += x * y;
            }
            for (ll j = max<ll>(C[m].second + sml2 - L2, 0); j <= smr2 - sml2; j += g[m + 1]) {
                if (dp2[m + 1][j] < 0) continue;
                ll L3 = L2 - (j + sml2);
                ll sm2 = sm + dp2[m + 1][j];
                if (L3 % C[m].first) continue;
                ll tmp = L3 / C[m].first;
                // if (tmp > C[m].second) continue;
                if (tmp < 0) break;
                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
*/

Subtask #1
5.0 / 5.0

# 결과 실행 시간 메모리 Grader output
1 Correct 0 ms 348 KB Output is correct
2 Correct 0 ms 348 KB Output is correct
3 Correct 0 ms 348 KB Output is correct
4 Correct 0 ms 348 KB Output is correct
5 Correct 0 ms 348 KB Output is correct
6 Correct 43 ms 2456 KB Output is correct
7 Correct 8 ms 860 KB Output is correct
8 Correct 39 ms 1940 KB Output is correct
9 Correct 85 ms 3340 KB Output is correct
10 Correct 0 ms 348 KB Output is correct
11 Correct 0 ms 348 KB Output is correct

Subtask #2
15.0 / 15.0

# 결과 실행 시간 메모리 Grader output
1 Correct 0 ms 348 KB Output is correct
2 Correct 0 ms 348 KB Output is correct
3 Correct 0 ms 348 KB Output is correct
4 Correct 0 ms 348 KB Output is correct
5 Correct 0 ms 348 KB Output is correct
6 Correct 43 ms 2456 KB Output is correct
7 Correct 8 ms 860 KB Output is correct
8 Correct 39 ms 1940 KB Output is correct
9 Correct 85 ms 3340 KB Output is correct
10 Correct 0 ms 348 KB Output is correct
11 Correct 0 ms 348 KB Output is correct
12 Correct 0 ms 348 KB Output is correct
13 Correct 0 ms 348 KB Output is correct
14 Correct 0 ms 348 KB Output is correct
15 Correct 0 ms 348 KB Output is correct
16 Correct 0 ms 348 KB Output is correct
17 Correct 52 ms 2440 KB Output is correct
18 Correct 8 ms 860 KB Output is correct
19 Correct 40 ms 1960 KB Output is correct
20 Correct 94 ms 3352 KB Output is correct
21 Correct 0 ms 348 KB Output is correct
22 Correct 0 ms 348 KB Output is correct
23 Correct 0 ms 348 KB Output is correct
24 Correct 680 ms 12396 KB Output is correct
25 Correct 102 ms 2592 KB Output is correct
26 Correct 2181 ms 24328 KB Output is correct
27 Correct 1382 ms 23916 KB Output is correct
28 Correct 1 ms 600 KB Output is correct
29 Correct 1 ms 348 KB Output is correct

Subtask #3-1
0 / 10.0

# 결과 실행 시간 메모리 Grader output
1 Correct 0 ms 348 KB Output is correct
2 Correct 3 ms 1628 KB Output is correct
3 Correct 0 ms 604 KB Output is correct
4 Correct 3 ms 1628 KB Output is correct
5 Correct 4 ms 1700 KB Output is correct
6 Incorrect 2 ms 348 KB Output isn't correct
7 Halted 0 ms 0 KB -

Subtask #3-2
0 / 10.0

# 결과 실행 시간 메모리 Grader output
1 Correct 0 ms 348 KB Output is correct
2 Correct 3 ms 1628 KB Output is correct
3 Correct 0 ms 604 KB Output is correct
4 Correct 3 ms 1628 KB Output is correct
5 Correct 4 ms 1700 KB Output is correct
6 Incorrect 2 ms 348 KB Output isn't correct
7 Halted 0 ms 0 KB -

Subtask #4-1
0 / 10.0

# 결과 실행 시간 메모리 Grader output
1 Correct 0 ms 348 KB Output is correct
2 Correct 3 ms 1628 KB Output is correct
3 Correct 0 ms 604 KB Output is correct
4 Correct 3 ms 1628 KB Output is correct
5 Correct 4 ms 1700 KB Output is correct
6 Incorrect 2 ms 348 KB Output isn't correct
7 Halted 0 ms 0 KB -

Subtask #4-2
0 / 10.0

# 결과 실행 시간 메모리 Grader output
1 Correct 0 ms 348 KB Output is correct
2 Correct 0 ms 348 KB Output is correct
3 Correct 0 ms 348 KB Output is correct
4 Correct 0 ms 348 KB Output is correct
5 Correct 0 ms 348 KB Output is correct
6 Correct 43 ms 2456 KB Output is correct
7 Correct 8 ms 860 KB Output is correct
8 Correct 39 ms 1940 KB Output is correct
9 Correct 85 ms 3340 KB Output is correct
10 Correct 0 ms 348 KB Output is correct
11 Correct 0 ms 348 KB Output is correct
12 Correct 0 ms 348 KB Output is correct
13 Correct 3 ms 1628 KB Output is correct
14 Correct 0 ms 604 KB Output is correct
15 Correct 3 ms 1628 KB Output is correct
16 Correct 4 ms 1700 KB Output is correct
17 Incorrect 2 ms 348 KB Output isn't correct
18 Halted 0 ms 0 KB -

Subtask #5-1
0 / 10.0

# 결과 실행 시간 메모리 Grader output
1 Correct 0 ms 348 KB Output is correct
2 Correct 3 ms 1628 KB Output is correct
3 Correct 0 ms 604 KB Output is correct
4 Correct 3 ms 1628 KB Output is correct
5 Correct 4 ms 1700 KB Output is correct
6 Incorrect 2 ms 348 KB Output isn't correct
7 Halted 0 ms 0 KB -

Subtask #5-2
0 / 10.0

# 결과 실행 시간 메모리 Grader output
1 Correct 0 ms 348 KB Output is correct
2 Correct 0 ms 348 KB Output is correct
3 Correct 0 ms 348 KB Output is correct
4 Correct 0 ms 348 KB Output is correct
5 Correct 0 ms 348 KB Output is correct
6 Correct 43 ms 2456 KB Output is correct
7 Correct 8 ms 860 KB Output is correct
8 Correct 39 ms 1940 KB Output is correct
9 Correct 85 ms 3340 KB Output is correct
10 Correct 0 ms 348 KB Output is correct
11 Correct 0 ms 348 KB Output is correct
12 Correct 0 ms 348 KB Output is correct
13 Correct 0 ms 348 KB Output is correct
14 Correct 0 ms 348 KB Output is correct
15 Correct 0 ms 348 KB Output is correct
16 Correct 0 ms 348 KB Output is correct
17 Correct 52 ms 2440 KB Output is correct
18 Correct 8 ms 860 KB Output is correct
19 Correct 40 ms 1960 KB Output is correct
20 Correct 94 ms 3352 KB Output is correct
21 Correct 0 ms 348 KB Output is correct
22 Correct 0 ms 348 KB Output is correct
23 Correct 0 ms 348 KB Output is correct
24 Correct 680 ms 12396 KB Output is correct
25 Correct 102 ms 2592 KB Output is correct
26 Correct 2181 ms 24328 KB Output is correct
27 Correct 1382 ms 23916 KB Output is correct
28 Correct 1 ms 600 KB Output is correct
29 Correct 1 ms 348 KB Output is correct
30 Correct 0 ms 348 KB Output is correct
31 Correct 3 ms 1628 KB Output is correct
32 Correct 0 ms 604 KB Output is correct
33 Correct 3 ms 1628 KB Output is correct
34 Correct 4 ms 1700 KB Output is correct
35 Incorrect 2 ms 348 KB Output isn't correct
36 Halted 0 ms 0 KB -

Subtask #6-1
0 / 10.0

# 결과 실행 시간 메모리 Grader output
1 Correct 0 ms 348 KB Output is correct
2 Correct 3 ms 1628 KB Output is correct
3 Correct 0 ms 604 KB Output is correct
4 Correct 3 ms 1628 KB Output is correct
5 Correct 4 ms 1700 KB Output is correct
6 Incorrect 2 ms 348 KB Output isn't correct
7 Halted 0 ms 0 KB -

Subtask #6-2
0 / 10.0

# 결과 실행 시간 메모리 Grader output
1 Correct 0 ms 348 KB Output is correct
2 Correct 0 ms 348 KB Output is correct
3 Correct 0 ms 348 KB Output is correct
4 Correct 0 ms 348 KB Output is correct
5 Correct 0 ms 348 KB Output is correct
6 Correct 43 ms 2456 KB Output is correct
7 Correct 8 ms 860 KB Output is correct
8 Correct 39 ms 1940 KB Output is correct
9 Correct 85 ms 3340 KB Output is correct
10 Correct 0 ms 348 KB Output is correct
11 Correct 0 ms 348 KB Output is correct
12 Correct 0 ms 348 KB Output is correct
13 Correct 0 ms 348 KB Output is correct
14 Correct 0 ms 348 KB Output is correct
15 Correct 0 ms 348 KB Output is correct
16 Correct 0 ms 348 KB Output is correct
17 Correct 52 ms 2440 KB Output is correct
18 Correct 8 ms 860 KB Output is correct
19 Correct 40 ms 1960 KB Output is correct
20 Correct 94 ms 3352 KB Output is correct
21 Correct 0 ms 348 KB Output is correct
22 Correct 0 ms 348 KB Output is correct
23 Correct 0 ms 348 KB Output is correct
24 Correct 680 ms 12396 KB Output is correct
25 Correct 102 ms 2592 KB Output is correct
26 Correct 2181 ms 24328 KB Output is correct
27 Correct 1382 ms 23916 KB Output is correct
28 Correct 1 ms 600 KB Output is correct
29 Correct 1 ms 348 KB Output is correct
30 Correct 0 ms 348 KB Output is correct
31 Correct 3 ms 1628 KB Output is correct
32 Correct 0 ms 604 KB Output is correct
33 Correct 3 ms 1628 KB Output is correct
34 Correct 4 ms 1700 KB Output is correct
35 Incorrect 2 ms 348 KB Output isn't correct
36 Halted 0 ms 0 KB -