結果

問題 No.626 Randomized 01 Knapsack
コンテスト
ユーザー Pachicobue
提出日時 2017-12-16 02:14:49
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
RE  
実行時間 -
コード長 4,826 bytes
コンパイル時間 2,868 ms
コンパイル使用メモリ 212,236 KB
最終ジャッジ日時 2025-01-05 05:43:09
ジャッジサーバーID
（参考情報） 		judge3 / judge5
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ファイルパターン 結果
other AC * 13 RE * 12
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ソースコード

diff # 

#include <bits/stdc++.h>

#define VARNAME(x) #x
#define show(x) cerr << #x << " = " << x << endl

using namespace std;
using ll = long long;
using ld = long double;

template <typename T>
ostream& operator<<(ostream& os, const vector<T>& v)
{
    os << "sz:" << v.size() << "\n[";
    for (const auto& p : v) {
        os << p << ",";
    }
    os << "]\n";
    return os;
}

template <typename S, typename T>
ostream& operator<<(ostream& os, const pair<S, T>& p)
{
    os << "(" << p.first << "," << p.second
       << ")";
    return os;
}


constexpr ll MOD = (ll)1e9 + 7LL;
constexpr ld PI = static_cast<ld>(3.1415926535898);

template <typename T>
constexpr T INF = numeric_limits<T>::max() / 10;

constexpr ll W_MAX = 30000000;
constexpr ll NW_MAX = 80000000;
constexpr ll N_MAX = 1000;
constexpr ll NVV_MAX = 30000000;

int main()
{
    cin.tie(0);
    ios::sync_with_stdio(false);

    int N;
    ll W;
    cin >> N >> W;
    using P = pair<ll, ll>;
    vector<P> p;
    ll wsum = 0;
    ll vsum = 0;
    for (int i = 0; i < N; i++) {
        ll w, v;
        cin >> v >> w;
        if (w <= W) {
            wsum += w;
            vsum += v;
            p.push_back(make_pair(v, w));
        }
    }
    if (wsum <= W) {
        cout << vsum << endl;
        return 0;
    }
    if (N == 0) {
        cout << 0 << endl;
        return 0;
    }
    auto comp = [](const P& p1, const P& p2) {
        return __int128_t(p1.first) * __int128_t(p2.second) > __int128_t(p1.second) * __int128_t(p2.first);
    };
    sort(p.begin(), p.end(), comp);
    N = p.size();
    if (W * N < NW_MAX and W < W_MAX) {
        vector<ll> dp(W + 1, 0);
        dp[0] = 0;
        for (int i = 0; i < N; i++) {
            vector<ll> tmp(W + 1, 0);
            for (int j = 0; j <= W; j++) {
                tmp[j] = max(tmp[j], dp[j]);
                if (j + p[i].second <= W) {
                    tmp[j + p[i].second] = max(tmp[j + p[i].second], dp[j] + p[i].first);
                }
            }
            dp = tmp;
        }
        cout << *max_element(dp.begin(), dp.end()) << endl;
    } else {
        ll cap = W;
        ll ans = 0;
        ll rest = N;
        ll used = 0;
        vector<P> res;
        for (used = 0; used < N and rest > N_MAX and rest * cap > NW_MAX; used++) {
            if (cap >= p[used].second) {
                rest--;
                cap -= p[used].second;
                ans += p[used].first;
            } else {
                res.push_back(p[used]);
            }
        }
        for (int i = used; i < N; i++) {
            res.push_back(p[i]);
        }

        p.clear();
        p.shrink_to_fit();
        if (rest * cap <= NW_MAX) {
            vector<ll> dp(cap + 1, 0);
            dp[0] = 0;
            for (int i = 0; i < rest; i++) {
                vector<ll> tmp(cap + 1, 0);
                for (int j = 0; j <= cap; j++) {
                    tmp[j] = max(tmp[j], dp[j]);
                    if (j + res[i].second <= W) {
                        tmp[j + res[i].second] = max(tmp[j + res[i].second], dp[j] + res[i].first);
                    }
                }
                dp = tmp;
            }
            cout << ans + *max_element(dp.begin(), dp.end()) << endl;
            return 0;
        }

        if (rest <= N_MAX) {
            ll VMAX = 0;
            for (const auto& e : res) {
                VMAX = max(VMAX, e.first);
            }
            const ll V_SMALL = (ll)sqrt(NVV_MAX / rest);
            const ll K = VMAX / V_SMALL;
            auto rescop = res;
            for (auto& e : rescop) {
                e.first = e.first / K;
            }
            ll vsum = 0;
            for (const auto& e : rescop) {
                vsum += e.first;
            }
            vector<vector<ll>> dp(rest + 1, vector<ll>(vsum + 1, INF<ll>));
            dp[0][0] = 0;
            for (int i = 0; i < rest; i++) {
                for (ll j = 0; j <= vsum; j++) {
                    if (dp[i][j] != INF<ll>) {
                        dp[i + 1][j] = min(dp[i + 1][j], dp[i][j]);
                        dp[i + 1][j + rescop[i].first] = min(dp[i + 1][j + rescop[i].first], dp[i][j] + rescop[i].second);
                    }
                }
            }
            ll maxind = vsum;
            for (ll i = vsum; i >= 0; i--) {
                if (dp[rest][i] <= cap) {
                    maxind = i;
                    break;
                }
            }

            ll pos = maxind;
            for (int i = rest; i >= 1; i--) {
                if (dp[i][pos] != dp[i - 1][pos]) {
                    ans += res[i - 1].first;
                    pos -= rescop[i - 1].first;
                }
            }
            cout << ans << endl;
            return 0;
        }
assert(false);
        cout << ans << endl;
    }
    return 0;
}
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