oj.uz

Submission #1050202

# Submission time Handle Problem Language Result Execution time Memory
1050202 2024-08-09T07:57:49 Z shiomusubi496 Uplifting Excursion (BOI22_vault) C++17
30 / 100
 5000 ms 104884 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, ll mx) -> vector<vector<ll>> {
        ll sml = 0, smr = 0;
        for (auto [x, y] : B) {
            if (x < 0) sml += x * y;
            else smr += x * y;
        }
        chmin(smr, mx);
        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<pair<int, ll>> 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().first < i - y) st.pop_front();
                        while (!st.empty() && st.back().second < memo[i]) st.pop_back();
                        st.emplace_back(i, memo[i]);
                        res[i] = st.front().second + i;
                    }
                }
                else {
                    rep (i, memo.size()) memo[i] += i;
                    rrep (i, res.size()) {
                        while (!st.empty() && st.front().first > i + y) st.pop_front();
                        while (!st.empty() && st.back().second < memo[i]) st.pop_back();
                        st.emplace_back(i, memo[i]);
                        res[i] = st.front().second + 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, M * M * 2);
    vector<vector<vector<int>>> js(C.size() - 1);
    rep (m, C.size() - 1) {
        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;
        }
        sml2 = (sml2 % C[m].first + C[m].first) % C[m].first;
        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 + sml2) % 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;
            }
            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");
    }
}

Compilation message

vault.cpp: In function 'int main()':
vault.cpp:199:26: 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]
  199 |         for (ll j = 0; j < dp2[m + 1].size(); j += g[m + 1]) {
      |                        ~~^~~~~~~~~~~~~~~~~~~
vault.cpp:236:35: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
  236 |             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 0 ms 348 KB Output is correct
2 Correct 1 ms 604 KB Output is correct
3 Correct 0 ms 348 KB Output is correct
4 Correct 1 ms 604 KB Output is correct
5 Correct 2 ms 604 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

# Verdict Execution time Memory Grader output
1 Correct 0 ms 348 KB Output is correct
2 Correct 1 ms 604 KB Output is correct
3 Correct 0 ms 348 KB Output is correct
4 Correct 1 ms 604 KB Output is correct
5 Correct 2 ms 604 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 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 0 ms 348 KB Output is correct
2 Correct 1 ms 604 KB Output is correct
3 Correct 0 ms 348 KB Output is correct
4 Correct 1 ms 604 KB Output is correct
5 Correct 2 ms 604 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 1 ms 348 KB Output is correct
12 Correct 1 ms 604 KB Output is correct
13 Correct 1 ms 348 KB Output is correct
14 Correct 1 ms 780 KB Output is correct
15 Correct 2 ms 604 KB Output is correct
16 Correct 3 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 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 10 ms 1360 KB Output is correct
24 Correct 2 ms 1116 KB Output is correct
25 Correct 8 ms 1492 KB Output is correct
26 Correct 11 ms 2032 KB Output is correct
27 Correct 9 ms 1564 KB Output is correct
28 Correct 4 ms 1812 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 0 ms 348 KB Output is correct
2 Correct 1 ms 604 KB Output is correct
3 Correct 0 ms 348 KB Output is correct
4 Correct 1 ms 604 KB Output is correct
5 Correct 2 ms 604 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 1 ms 348 KB Output is correct
12 Correct 1 ms 604 KB Output is correct
13 Correct 1 ms 348 KB Output is correct
14 Correct 1 ms 780 KB Output is correct
15 Correct 2 ms 604 KB Output is correct
16 Correct 3 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 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 10 ms 1360 KB Output is correct
24 Correct 2 ms 1116 KB Output is correct
25 Correct 8 ms 1492 KB Output is correct
26 Correct 11 ms 2032 KB Output is correct
27 Correct 9 ms 1564 KB Output is correct
28 Correct 4 ms 1812 KB Output is correct
29 Correct 0 ms 344 KB Output is correct
30 Correct 1 ms 604 KB Output is correct
31 Correct 1 ms 348 KB Output is correct
32 Correct 1 ms 604 KB Output is correct
33 Correct 3 ms 708 KB Output is correct
34 Correct 2 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 1 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 344 KB Output is correct
41 Correct 9 ms 1356 KB Output is correct
42 Correct 2 ms 1116 KB Output is correct
43 Correct 8 ms 1492 KB Output is correct
44 Correct 10 ms 2036 KB Output is correct
45 Correct 9 ms 1436 KB Output is correct
46 Correct 4 ms 1812 KB Output is correct
47 Correct 1 ms 604 KB Output is correct
48 Correct 1 ms 592 KB Output is correct
49 Correct 127 ms 9804 KB Output is correct
50 Correct 32 ms 4376 KB Output is correct
51 Correct 110 ms 11412 KB Output is correct
52 Correct 211 ms 12720 KB Output is correct
53 Correct 79 ms 10092 KB Output is correct
54 Correct 82 ms 8396 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 0 ms 348 KB Output is correct
2 Correct 1 ms 604 KB Output is correct
3 Correct 0 ms 348 KB Output is correct
4 Correct 1 ms 604 KB Output is correct
5 Correct 2 ms 604 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 1 ms 348 KB Output is correct
12 Correct 1 ms 604 KB Output is correct
13 Correct 1 ms 348 KB Output is correct
14 Correct 1 ms 780 KB Output is correct
15 Correct 2 ms 604 KB Output is correct
16 Correct 3 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 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 10 ms 1360 KB Output is correct
24 Correct 2 ms 1116 KB Output is correct
25 Correct 8 ms 1492 KB Output is correct
26 Correct 11 ms 2032 KB Output is correct
27 Correct 9 ms 1564 KB Output is correct
28 Correct 4 ms 1812 KB Output is correct
29 Correct 0 ms 344 KB Output is correct
30 Correct 1 ms 604 KB Output is correct
31 Correct 1 ms 348 KB Output is correct
32 Correct 1 ms 604 KB Output is correct
33 Correct 3 ms 708 KB Output is correct
34 Correct 2 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 1 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 344 KB Output is correct
41 Correct 9 ms 1356 KB Output is correct
42 Correct 2 ms 1116 KB Output is correct
43 Correct 8 ms 1492 KB Output is correct
44 Correct 10 ms 2036 KB Output is correct
45 Correct 9 ms 1436 KB Output is correct
46 Correct 4 ms 1812 KB Output is correct
47 Correct 1 ms 604 KB Output is correct
48 Correct 1 ms 592 KB Output is correct
49 Correct 127 ms 9804 KB Output is correct
50 Correct 32 ms 4376 KB Output is correct
51 Correct 110 ms 11412 KB Output is correct
52 Correct 211 ms 12720 KB Output is correct
53 Correct 79 ms 10092 KB Output is correct
54 Correct 82 ms 8396 KB Output is correct
55 Correct 0 ms 344 KB Output is correct
56 Correct 1 ms 604 KB Output is correct
57 Correct 0 ms 348 KB Output is correct
58 Correct 1 ms 604 KB Output is correct
59 Correct 2 ms 604 KB Output is correct
60 Correct 1 ms 348 KB Output is correct
61 Correct 1 ms 348 KB Output is correct
62 Correct 0 ms 348 KB Output is correct
63 Correct 1 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 1 ms 348 KB Output is correct
67 Correct 9 ms 1352 KB Output is correct
68 Correct 2 ms 1016 KB Output is correct
69 Correct 8 ms 1488 KB Output is correct
70 Correct 11 ms 2000 KB Output is correct
71 Correct 9 ms 1436 KB Output is correct
72 Correct 5 ms 1808 KB Output is correct
73 Correct 0 ms 604 KB Output is correct
74 Correct 1 ms 348 KB Output is correct
75 Correct 124 ms 9800 KB Output is correct
76 Correct 32 ms 4380 KB Output is correct
77 Correct 102 ms 11456 KB Output is correct
78 Correct 229 ms 12624 KB Output is correct
79 Correct 80 ms 10108 KB Output is correct
80 Correct 82 ms 8416 KB Output is correct
81 Execution timed out 5073 ms 104884 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 -