oj.uz

Submission #1049998

# Submission time Handle Problem Language Result Execution time Memory
1049998 2024-08-09T06:43:48 Z shiomusubi496 Uplifting Excursion (BOI22_vault) C++17
30 / 100
 5000 ms 24368 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;
    }
    ll ans = -inf;
    vector<ll> g(C.size() + 1);
    rrep (i, C.size()) g[i] = gcd(g[i + 1], C[i].first);
    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) {
            assert(L2 % g[j] == 0);
            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));
            auto dp2 = calc_dp(D);
            ll sml2 = 0, smr2 = 0;
            for (auto [x, y] : D) {
                if (x < 0) sml2 += x * y;
                else smr2 += x * y;
            }
            rep (j, smr2 - sml2 + 1) {
                if (dp2[j] < 0) continue;
                ll L3 = L2 - (j + sml2);
                ll sm2 = sm + dp2[j];
                if (L3 % C[m].first) continue;
                ll tmp = L3 / C[m].first;
                if (tmp > C[m].second) continue;
                if (tmp < 0) continue;
                sm2 += tmp;
                chmax(ans, sm2);
            }
        }
    }
    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

# Verdict Execution time Memory Grader output
1 Correct 1 ms 344 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 44 ms 2456 KB Output is correct
7 Correct 8 ms 856 KB Output is correct
8 Correct 39 ms 1940 KB Output is correct
9 Correct 83 ms 3332 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

# Verdict Execution time Memory Grader output
1 Correct 1 ms 344 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 44 ms 2456 KB Output is correct
7 Correct 8 ms 856 KB Output is correct
8 Correct 39 ms 1940 KB Output is correct
9 Correct 83 ms 3332 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 45 ms 2396 KB Output is correct
18 Correct 8 ms 856 KB Output is correct
19 Correct 40 ms 2076 KB Output is correct
20 Correct 87 ms 3340 KB Output is correct
21 Correct 1 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 674 ms 12484 KB Output is correct
25 Correct 107 ms 2332 KB Output is correct
26 Correct 1354 ms 23912 KB Output is correct
27 Correct 1401 ms 24368 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
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 344 KB Output is correct
2 Correct 1 ms 348 KB Output is correct
3 Correct 0 ms 344 KB Output is correct
4 Correct 850 ms 572 KB Output is correct
5 Correct 318 ms 600 KB Output is correct
6 Correct 121 ms 520 KB Output is correct
7 Correct 0 ms 348 KB Output is correct
8 Correct 0 ms 348 KB Output is correct
9 Correct 0 ms 348 KB Output is correct
10 Correct 0 ms 348 KB Output is correct

Subtask #3-2
0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 344 KB Output is correct
2 Correct 1 ms 348 KB Output is correct
3 Correct 0 ms 344 KB Output is correct
4 Correct 850 ms 572 KB Output is correct
5 Correct 318 ms 600 KB Output is correct
6 Correct 121 ms 520 KB Output is correct
7 Correct 0 ms 348 KB Output is correct
8 Correct 0 ms 348 KB Output is correct
9 Correct 0 ms 348 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 1 ms 348 KB Output is correct
16 Correct 0 ms 348 KB Output is correct
17 Correct 876 ms 552 KB Output is correct
18 Correct 359 ms 604 KB Output is correct
19 Correct 120 ms 600 KB Output is correct
20 Correct 0 ms 344 KB Output is correct
21 Correct 0 ms 348 KB Output is correct
22 Correct 0 ms 348 KB Output is correct
23 Correct 1 ms 348 KB Output is correct
24 Incorrect 2 ms 348 KB Output isn't correct
25 Halted 0 ms 0 KB -

Subtask #4-1
0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 344 KB Output is correct
2 Correct 1 ms 348 KB Output is correct
3 Correct 0 ms 344 KB Output is correct
4 Correct 850 ms 572 KB Output is correct
5 Correct 318 ms 600 KB Output is correct
6 Correct 121 ms 520 KB Output is correct
7 Correct 0 ms 348 KB Output is correct
8 Correct 0 ms 348 KB Output is correct
9 Correct 0 ms 348 KB Output is correct
10 Correct 0 ms 348 KB Output is correct
11 Correct 0 ms 348 KB Output is correct
12 Correct 1 ms 348 KB Output is correct
13 Correct 0 ms 348 KB Output is correct
14 Correct 838 ms 556 KB Output is correct
15 Correct 318 ms 604 KB Output is correct
16 Correct 119 ms 344 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 0 ms 348 KB Output is correct
21 Correct 0 ms 348 KB Output is correct
22 Correct 0 ms 348 KB Output is correct
23 Correct 8 ms 984 KB Output is correct
24 Correct 1 ms 348 KB Output is correct
25 Correct 6 ms 604 KB Output is correct
26 Execution timed out 5098 ms 1240 KB Time limit exceeded
27 Halted 0 ms 0 KB -

Subtask #4-2
0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 344 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 44 ms 2456 KB Output is correct
7 Correct 8 ms 856 KB Output is correct
8 Correct 39 ms 1940 KB Output is correct
9 Correct 83 ms 3332 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 344 KB Output is correct
13 Correct 1 ms 348 KB Output is correct
14 Correct 0 ms 344 KB Output is correct
15 Correct 850 ms 572 KB Output is correct
16 Correct 318 ms 600 KB Output is correct
17 Correct 121 ms 520 KB Output is correct
18 Correct 0 ms 348 KB Output is correct
19 Correct 0 ms 348 KB Output is correct
20 Correct 0 ms 348 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 0 ms 348 KB Output is correct
25 Correct 0 ms 348 KB Output is correct
26 Correct 1 ms 348 KB Output is correct
27 Correct 0 ms 348 KB Output is correct
28 Correct 876 ms 552 KB Output is correct
29 Correct 359 ms 604 KB Output is correct
30 Correct 120 ms 600 KB Output is correct
31 Correct 0 ms 344 KB Output is correct
32 Correct 0 ms 348 KB Output is correct
33 Correct 0 ms 348 KB Output is correct
34 Correct 1 ms 348 KB Output is correct
35 Incorrect 2 ms 348 KB Output isn't correct
36 Halted 0 ms 0 KB -

Subtask #5-1
0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 344 KB Output is correct
2 Correct 1 ms 348 KB Output is correct
3 Correct 0 ms 344 KB Output is correct
4 Correct 850 ms 572 KB Output is correct
5 Correct 318 ms 600 KB Output is correct
6 Correct 121 ms 520 KB Output is correct
7 Correct 0 ms 348 KB Output is correct
8 Correct 0 ms 348 KB Output is correct
9 Correct 0 ms 348 KB Output is correct
10 Correct 0 ms 348 KB Output is correct
11 Correct 0 ms 348 KB Output is correct
12 Correct 1 ms 348 KB Output is correct
13 Correct 0 ms 348 KB Output is correct
14 Correct 838 ms 556 KB Output is correct
15 Correct 318 ms 604 KB Output is correct
16 Correct 119 ms 344 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 0 ms 348 KB Output is correct
21 Correct 0 ms 348 KB Output is correct
22 Correct 0 ms 348 KB Output is correct
23 Correct 8 ms 984 KB Output is correct
24 Correct 1 ms 348 KB Output is correct
25 Correct 6 ms 604 KB Output is correct
26 Execution timed out 5098 ms 1240 KB Time limit exceeded
27 Halted 0 ms 0 KB -

Subtask #5-2
0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 344 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 44 ms 2456 KB Output is correct
7 Correct 8 ms 856 KB Output is correct
8 Correct 39 ms 1940 KB Output is correct
9 Correct 83 ms 3332 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 45 ms 2396 KB Output is correct
18 Correct 8 ms 856 KB Output is correct
19 Correct 40 ms 2076 KB Output is correct
20 Correct 87 ms 3340 KB Output is correct
21 Correct 1 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 674 ms 12484 KB Output is correct
25 Correct 107 ms 2332 KB Output is correct
26 Correct 1354 ms 23912 KB Output is correct
27 Correct 1401 ms 24368 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 344 KB Output is correct
31 Correct 1 ms 348 KB Output is correct
32 Correct 0 ms 344 KB Output is correct
33 Correct 850 ms 572 KB Output is correct
34 Correct 318 ms 600 KB Output is correct
35 Correct 121 ms 520 KB Output is correct
36 Correct 0 ms 348 KB Output is correct
37 Correct 0 ms 348 KB Output is correct
38 Correct 0 ms 348 KB Output is correct
39 Correct 0 ms 348 KB Output is correct
40 Correct 0 ms 348 KB Output is correct
41 Correct 0 ms 348 KB Output is correct
42 Correct 0 ms 348 KB Output is correct
43 Correct 0 ms 348 KB Output is correct
44 Correct 1 ms 348 KB Output is correct
45 Correct 0 ms 348 KB Output is correct
46 Correct 876 ms 552 KB Output is correct
47 Correct 359 ms 604 KB Output is correct
48 Correct 120 ms 600 KB Output is correct
49 Correct 0 ms 344 KB Output is correct
50 Correct 0 ms 348 KB Output is correct
51 Correct 0 ms 348 KB Output is correct
52 Correct 1 ms 348 KB Output is correct
53 Incorrect 2 ms 348 KB Output isn't correct
54 Halted 0 ms 0 KB -

Subtask #6-1
0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 344 KB Output is correct
2 Correct 1 ms 348 KB Output is correct
3 Correct 0 ms 344 KB Output is correct
4 Correct 850 ms 572 KB Output is correct
5 Correct 318 ms 600 KB Output is correct
6 Correct 121 ms 520 KB Output is correct
7 Correct 0 ms 348 KB Output is correct
8 Correct 0 ms 348 KB Output is correct
9 Correct 0 ms 348 KB Output is correct
10 Correct 0 ms 348 KB Output is correct
11 Correct 0 ms 348 KB Output is correct
12 Correct 1 ms 348 KB Output is correct
13 Correct 0 ms 348 KB Output is correct
14 Correct 838 ms 556 KB Output is correct
15 Correct 318 ms 604 KB Output is correct
16 Correct 119 ms 344 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 0 ms 348 KB Output is correct
21 Correct 0 ms 348 KB Output is correct
22 Correct 0 ms 348 KB Output is correct
23 Correct 8 ms 984 KB Output is correct
24 Correct 1 ms 348 KB Output is correct
25 Correct 6 ms 604 KB Output is correct
26 Execution timed out 5098 ms 1240 KB Time limit exceeded
27 Halted 0 ms 0 KB -

Subtask #6-2
0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 344 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 44 ms 2456 KB Output is correct
7 Correct 8 ms 856 KB Output is correct
8 Correct 39 ms 1940 KB Output is correct
9 Correct 83 ms 3332 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 45 ms 2396 KB Output is correct
18 Correct 8 ms 856 KB Output is correct
19 Correct 40 ms 2076 KB Output is correct
20 Correct 87 ms 3340 KB Output is correct
21 Correct 1 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 674 ms 12484 KB Output is correct
25 Correct 107 ms 2332 KB Output is correct
26 Correct 1354 ms 23912 KB Output is correct
27 Correct 1401 ms 24368 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 344 KB Output is correct
31 Correct 1 ms 348 KB Output is correct
32 Correct 0 ms 344 KB Output is correct
33 Correct 850 ms 572 KB Output is correct
34 Correct 318 ms 600 KB Output is correct
35 Correct 121 ms 520 KB Output is correct
36 Correct 0 ms 348 KB Output is correct
37 Correct 0 ms 348 KB Output is correct
38 Correct 0 ms 348 KB Output is correct
39 Correct 0 ms 348 KB Output is correct
40 Correct 0 ms 348 KB Output is correct
41 Correct 0 ms 348 KB Output is correct
42 Correct 0 ms 348 KB Output is correct
43 Correct 0 ms 348 KB Output is correct
44 Correct 1 ms 348 KB Output is correct
45 Correct 0 ms 348 KB Output is correct
46 Correct 876 ms 552 KB Output is correct
47 Correct 359 ms 604 KB Output is correct
48 Correct 120 ms 600 KB Output is correct
49 Correct 0 ms 344 KB Output is correct
50 Correct 0 ms 348 KB Output is correct
51 Correct 0 ms 348 KB Output is correct
52 Correct 1 ms 348 KB Output is correct
53 Incorrect 2 ms 348 KB Output isn't correct
54 Halted 0 ms 0 KB -