oj.uz

Submission #1050080

# Submission time Handle Problem Language Result Execution time Memory
1050080 2024-08-09T07:15:45 Z shiomusubi496 Uplifting Excursion (BOI22_vault) C++17
30 / 100
 5000 ms 105652 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][L2 % C[m].first].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<int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
  228 |             for (int jk = itr; jk < js[m][L2 % C[m].first].size(); ++jk) {
      |                                ~~~^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Subtask #1
0 / 5.0

# Verdict Execution time Memory 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

# Verdict Execution time Memory 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

# Verdict Execution time Memory Grader output
1 Correct 1 ms 348 KB Output is correct
2 Correct 2 ms 1248 KB Output is correct
3 Correct 1 ms 344 KB Output is correct
4 Correct 2 ms 1116 KB Output is correct
5 Correct 4 ms 1184 KB Output is correct
6 Correct 1 ms 348 KB Output is correct
7 Correct 0 ms 344 KB Output is correct
8 Correct 0 ms 348 KB Output is correct
9 Correct 1 ms 348 KB Output is correct
10 Correct 1 ms 604 KB Output is correct

Subtask #3-2
0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 348 KB Output is correct
2 Correct 2 ms 1248 KB Output is correct
3 Correct 1 ms 344 KB Output is correct
4 Correct 2 ms 1116 KB Output is correct
5 Correct 4 ms 1184 KB Output is correct
6 Correct 1 ms 348 KB Output is correct
7 Correct 0 ms 344 KB Output is correct
8 Correct 0 ms 348 KB Output is correct
9 Correct 1 ms 348 KB Output is correct
10 Correct 1 ms 604 KB Output is correct
11 Runtime error 1 ms 604 KB Execution killed with signal 6
12 Halted 0 ms 0 KB -

Subtask #4-1
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 348 KB Output is correct
2 Correct 2 ms 1248 KB Output is correct
3 Correct 1 ms 344 KB Output is correct
4 Correct 2 ms 1116 KB Output is correct
5 Correct 4 ms 1184 KB Output is correct
6 Correct 1 ms 348 KB Output is correct
7 Correct 0 ms 344 KB Output is correct
8 Correct 0 ms 348 KB Output is correct
9 Correct 1 ms 348 KB Output is correct
10 Correct 1 ms 604 KB Output is correct
11 Correct 1 ms 344 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 1116 KB Output is correct
16 Correct 2 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 1 ms 344 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 11 ms 3704 KB Output is correct
24 Correct 4 ms 2380 KB Output is correct
25 Correct 12 ms 4340 KB Output is correct
26 Correct 16 ms 7120 KB Output is correct
27 Correct 21 ms 3916 KB Output is correct
28 Correct 9 ms 4836 KB Output is correct

Subtask #4-2
0 / 10.0

# Verdict Execution time Memory Grader output
1 Runtime error 2 ms 604 KB Execution killed with signal 6
2 Halted 0 ms 0 KB -

Subtask #5-1
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 348 KB Output is correct
2 Correct 2 ms 1248 KB Output is correct
3 Correct 1 ms 344 KB Output is correct
4 Correct 2 ms 1116 KB Output is correct
5 Correct 4 ms 1184 KB Output is correct
6 Correct 1 ms 348 KB Output is correct
7 Correct 0 ms 344 KB Output is correct
8 Correct 0 ms 348 KB Output is correct
9 Correct 1 ms 348 KB Output is correct
10 Correct 1 ms 604 KB Output is correct
11 Correct 1 ms 344 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 1116 KB Output is correct
16 Correct 2 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 1 ms 344 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 11 ms 3704 KB Output is correct
24 Correct 4 ms 2380 KB Output is correct
25 Correct 12 ms 4340 KB Output is correct
26 Correct 16 ms 7120 KB Output is correct
27 Correct 21 ms 3916 KB Output is correct
28 Correct 9 ms 4836 KB Output is correct
29 Correct 0 ms 348 KB Output is correct
30 Correct 3 ms 1116 KB Output is correct
31 Correct 1 ms 348 KB Output is correct
32 Correct 2 ms 1116 KB Output is correct
33 Correct 3 ms 1116 KB Output is correct
34 Correct 3 ms 348 KB Output is correct
35 Correct 0 ms 348 KB Output is correct
36 Correct 0 ms 348 KB Output is correct
37 Correct 0 ms 348 KB Output is correct
38 Correct 1 ms 604 KB Output is correct
39 Correct 0 ms 348 KB Output is correct
40 Correct 1 ms 348 KB Output is correct
41 Correct 17 ms 3496 KB Output is correct
42 Correct 4 ms 2280 KB Output is correct
43 Correct 11 ms 4340 KB Output is correct
44 Correct 17 ms 7084 KB Output is correct
45 Correct 13 ms 3880 KB Output is correct
46 Correct 9 ms 4792 KB Output is correct
47 Correct 1 ms 604 KB Output is correct
48 Correct 1 ms 600 KB Output is correct
49 Correct 196 ms 56812 KB Output is correct
50 Correct 40 ms 12668 KB Output is correct
51 Correct 208 ms 86824 KB Output is correct
52 Correct 273 ms 78492 KB Output is correct
53 Correct 147 ms 66428 KB Output is correct
54 Correct 110 ms 33228 KB Output is correct

Subtask #5-2
0 / 10.0

# Verdict Execution time Memory 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

# Verdict Execution time Memory Grader output
1 Correct 1 ms 348 KB Output is correct
2 Correct 2 ms 1248 KB Output is correct
3 Correct 1 ms 344 KB Output is correct
4 Correct 2 ms 1116 KB Output is correct
5 Correct 4 ms 1184 KB Output is correct
6 Correct 1 ms 348 KB Output is correct
7 Correct 0 ms 344 KB Output is correct
8 Correct 0 ms 348 KB Output is correct
9 Correct 1 ms 348 KB Output is correct
10 Correct 1 ms 604 KB Output is correct
11 Correct 1 ms 344 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 1116 KB Output is correct
16 Correct 2 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 1 ms 344 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 11 ms 3704 KB Output is correct
24 Correct 4 ms 2380 KB Output is correct
25 Correct 12 ms 4340 KB Output is correct
26 Correct 16 ms 7120 KB Output is correct
27 Correct 21 ms 3916 KB Output is correct
28 Correct 9 ms 4836 KB Output is correct
29 Correct 0 ms 348 KB Output is correct
30 Correct 3 ms 1116 KB Output is correct
31 Correct 1 ms 348 KB Output is correct
32 Correct 2 ms 1116 KB Output is correct
33 Correct 3 ms 1116 KB Output is correct
34 Correct 3 ms 348 KB Output is correct
35 Correct 0 ms 348 KB Output is correct
36 Correct 0 ms 348 KB Output is correct
37 Correct 0 ms 348 KB Output is correct
38 Correct 1 ms 604 KB Output is correct
39 Correct 0 ms 348 KB Output is correct
40 Correct 1 ms 348 KB Output is correct
41 Correct 17 ms 3496 KB Output is correct
42 Correct 4 ms 2280 KB Output is correct
43 Correct 11 ms 4340 KB Output is correct
44 Correct 17 ms 7084 KB Output is correct
45 Correct 13 ms 3880 KB Output is correct
46 Correct 9 ms 4792 KB Output is correct
47 Correct 1 ms 604 KB Output is correct
48 Correct 1 ms 600 KB Output is correct
49 Correct 196 ms 56812 KB Output is correct
50 Correct 40 ms 12668 KB Output is correct
51 Correct 208 ms 86824 KB Output is correct
52 Correct 273 ms 78492 KB Output is correct
53 Correct 147 ms 66428 KB Output is correct
54 Correct 110 ms 33228 KB Output is correct
55 Correct 0 ms 348 KB Output is correct
56 Correct 2 ms 1116 KB Output is correct
57 Correct 0 ms 348 KB Output is correct
58 Correct 2 ms 1116 KB Output is correct
59 Correct 2 ms 1096 KB Output is correct
60 Correct 2 ms 348 KB Output is correct
61 Correct 0 ms 348 KB Output is correct
62 Correct 0 ms 348 KB Output is correct
63 Correct 0 ms 348 KB Output is correct
64 Correct 1 ms 604 KB Output is correct
65 Correct 0 ms 348 KB Output is correct
66 Correct 0 ms 348 KB Output is correct
67 Correct 11 ms 3704 KB Output is correct
68 Correct 4 ms 2380 KB Output is correct
69 Correct 11 ms 4340 KB Output is correct
70 Correct 16 ms 7240 KB Output is correct
71 Correct 11 ms 3824 KB Output is correct
72 Correct 7 ms 4836 KB Output is correct
73 Correct 0 ms 348 KB Output is correct
74 Correct 1 ms 348 KB Output is correct
75 Correct 182 ms 56820 KB Output is correct
76 Correct 41 ms 12712 KB Output is correct
77 Correct 191 ms 86760 KB Output is correct
78 Correct 270 ms 78380 KB Output is correct
79 Correct 152 ms 66424 KB Output is correct
80 Correct 112 ms 33224 KB Output is correct
81 Execution timed out 5071 ms 105652 KB Time limit exceeded
82 Halted 0 ms 0 KB -

Subtask #6-2
0 / 10.0

# Verdict Execution time Memory Grader output
1 Runtime error 2 ms 604 KB Execution killed with signal 6
2 Halted 0 ms 0 KB -