Submission #624525

#	Time	Username	Problem	Language	Result	Execution time	Memory
624525		maomao90	Bodyguard (JOI21_bodyguard)	C++17	100 / 100	11803 ms	1817364 KiB

bodyguard

// Hallelujah, praise the one who set me free
// Hallelujah, death has lost its grip on me
// You have broken every chain, There's salvation in your name
// Jesus Christ, my living hope
#include <bits/stdc++.h> 
using namespace std;

#define REP(i, s, e) for (int i = (s); i < (e); i++)
#define RREP(i, s, e) for (int i = (s); i >= (e); i--)
template <class T>
inline bool mnto(T& a, T b) {return a > b ? a = b, 1 : 0;}
template <class T>
inline bool mxto(T& a, T b) {return a < b ? a = b, 1: 0;}
typedef long long ll;
typedef long double ld;
#define FI first
#define SE second
typedef pair<int, int> ii;
typedef pair<ll, ll> pll;
typedef tuple<ll, ll, ll> iii;
#define ALL(_a) _a.begin(), _a.end()
#define SZ(_a) (int) _a.size()
#define pb push_back
typedef vector<int> vi;
typedef vector<ll> vll;
typedef vector<ii> vii;
typedef vector<iii> viii;

#ifndef DEBUG
#define cerr if (0) cerr
#endif

const int INF = 1000000005;
const ll LINF = 1000000000000000005ll;
const int MAXN = 2805;
const int MAXQ = 3000005;

struct thing {
    ll a, s, e, c;
};
struct line {
    ll m, c;
    bool operator< (const line &o) const {
        return m < o.m;
    }
    ll isect(const line &o) const {
        return (c - o.c) / (o.m - m);
    }
    ll eval(ll x) {
        return m * x + c;
    }
};

int n, q;
vector<thing> hor, ver;
vll vy, vx;
ll adj[MAXN * 3][MAXN * 3][2];
ll dist[MAXN * 3][MAXN * 3];
iii qry[MAXQ];
ll ans[MAXQ];
viii dqry[MAXN * 3];
vector<pair<line, int>> dupd[MAXN * 3];

void dnc(viii &qry, vector<pair<line, int>> &upd, int lo, int hi) {
    if (qry.empty()) {
        return;
    }
    assert(!upd.empty());
    if (lo == hi) {
        assert(SZ(upd) == 1);
        for (iii q : qry) {
            mxto(ans[get<2>(q)], upd[0].FI.eval(get<0>(q)));
        }
        return;
    }
    viii lqry, rqry;
    vector<pair<line, int>> lupd, rupd;
    int mid = lo + hi >> 1;
    for (iii q : qry) {
        if (get<1>(q) <= mid) {
            lqry.pb(q);
            auto [a, b, c] = q;
        } else {
            rqry.pb(q);
        }
    }
    for (pair<line, int> u : upd) {
        if (u.SE <= mid) {
            lupd.pb(u);
        } else {
            rupd.pb(u);
        }
    }
    deque<line> hull;
    auto insert = [&] (line l) {
        if (!hull.empty() && l.m == hull.back().m) {
            if (l.c >= hull.back().c) {
                hull.pop_back();
            } else {
                return;
            }
        }
        int n = SZ(hull);
        while (n >= 2 && l.isect(hull[n - 1]) <= hull[n - 1].isect(hull[n - 2])) {
            hull.pop_back();
            n--;
        }
        hull.pb(l);
    };
    auto ask = [&] (ll x) {
        while (SZ(hull) >= 2 && hull[1].eval(x) >= hull[0].eval(x)) {
            hull.pop_front();
        }
        return hull[0].eval(x);
    };
    for (pair<line, int> u : rupd) {
        insert(u.FI);
    }
    for (auto [x, _, id] : lqry) {
        mxto(ans[id], ask(x));
    }
    dnc(lqry, lupd, lo, mid); dnc(rqry, rupd, mid + 1, hi);
}

int main() {
#ifndef DEBUG
    ios::sync_with_stdio(0), cin.tie(0);
#endif
    cin >> n >> q;
    REP (i, 0, n) {
        ll t, a, b, c; cin >> t >> a >> b >> c;
        if (a < b) {
            hor.pb({t - a, a + t, b + t + (b - a), c / 2});
        } else {
            ver.pb({a + t, t - a, t + (a - b) - b, c / 2});
        }
    }
    for (auto [a, s, e, c] : ver) {
        vy.pb(s);
        vy.pb(e);
    }
    for (auto [a, s, e, c] : hor) {
        vy.pb(a);
    }
    sort(ALL(vy));
    vy.resize(unique(ALL(vy)) - vy.begin());
    for (auto [a, s, e, c] : hor) {
        vx.pb(s);
        vx.pb(e);
    }
    for (auto [a, s, e, c] : ver) {
        vx.pb(a);
    }
    sort(ALL(vx));
    vx.resize(unique(ALL(vx)) - vx.begin());
    for (auto [a, s, e, c] : hor) {
        int na = lower_bound(ALL(vy), a) - vy.begin(), 
            ns = lower_bound(ALL(vx), s) - vx.begin(),
            ne = lower_bound(ALL(vx), e) - vx.begin();
        REP (i, ns, ne) {
            mxto(adj[na][i][0], c);
        }
    }
    for (auto [a, s, e, c] : ver) {
        int na = lower_bound(ALL(vx), a) - vx.begin(), 
            ns = lower_bound(ALL(vy), s) - vy.begin(),
            ne = lower_bound(ALL(vy), e) - vy.begin();
        REP (i, ns, ne) {
            mxto(adj[i][na][1], c);
        }
    }
    RREP (i, SZ(vy) - 1, 0) {
        RREP (j, SZ(vx) - 1, 0) {
            if (j + 1 < SZ(vx)) {
                mxto(dist[i][j], dist[i][j + 1] +
                        (ll) adj[i][j][0] * (vx[j + 1] - vx[j]));
            }
            if (i + 1 < SZ(vy)) {
                mxto(dist[i][j], dist[i + 1][j] +
                        (ll) adj[i][j][1] * (vy[i + 1] - vy[i]));
            }
            //cerr << vy[i] << ' ' << vx[j] << ": " << dist[i][j] << '\n';
        }
    }
    REP (i, 0, q) {
        int t, x; cin >> t >> x;
        qry[i] = {t + x, t - x, i};
    }
    REP (i, 0, q) {
        auto [x, y, id] = qry[i];
        int lby = lower_bound(ALL(vy), y) - vy.begin(),
            lbx = lower_bound(ALL(vx), x) - vx.begin();
        if (lby >= SZ(vy) || lbx >= SZ(vx)) {
            continue;
        }
        dqry[lby].pb({vy[lby] - y, lbx, id});
        /*
        while (ptr[lby] >= lbx) {
            hulls[lby].insert({adj[lby][ptr[lby]][1], dist[lby][ptr[lby]]});
            ptr[lby]--;
        }
        mxto(ans[id], hulls[lby].qry(vy[lby] - y));
        */
    }
    REP (i, 0, SZ(vy)) {
        REP (j, 0, SZ(vx)) {
            dupd[i].pb({line{i == 0 ? 0 : adj[i - 1][j][1], dist[i][j]}, j});
        }
    }
    REP (i, 0, SZ(vy)) {
        sort(ALL(dqry[i])); sort(ALL(dupd[i]));
        dnc(dqry[i], dupd[i], 0, SZ(vx) - 1);
    }
    REP (i, 0, SZ(vx)) {
        dqry[i].clear(); dupd[i].clear();
    }
    REP (i, 0, q) {
        auto [x, y, id] = qry[i];
        int lby = lower_bound(ALL(vy), y) - vy.begin(),
            lbx = lower_bound(ALL(vx), x) - vx.begin();
        if (lbx >= SZ(vx) || lby >= SZ(vy)) {
            continue;
        }
        dqry[lbx].pb({vx[lbx] - x, lby, id});
        /*
        while (ptr[lbx] >= lby) {
            hulls[lbx].insert({adj[lbx][ptr[lbx]][0], dist[lbx][ptr[lbx]]});
            ptr[lbx]--;
        }
        mxto(ans[id], hulls[lbx].qry(vx[lbx] - x));
        */
    }
    REP (i, 0, SZ(vy)) {
        REP (j, 0, SZ(vx)) {
            dupd[j].pb({line{j == 0 ? 0 : adj[i][j - 1][0], dist[i][j]}, i});
        }
    }
    REP (i, 0, SZ(vx)) {
        sort(ALL(dqry[i])); sort(ALL(dupd[i]));
        dnc(dqry[i], dupd[i], 0, SZ(vy) - 1);
    }
    REP (i, 0, q) {
        cout << ans[i] << '\n';
    }
    return 0;
}

/*
2 2
1 2 1 4
3 1 3 2
1 2
3 3
*/

Compilation message (stderr)

bodyguard.cpp: In function 'void dnc(viii&, std::vector<std::pair<line, int> >&, int, int)':
bodyguard.cpp:79:18: warning: suggest parentheses around '+' inside '>>' [-Wparentheses]
   79 |     int mid = lo + hi >> 1;
      |               ~~~^~~~
bodyguard.cpp:83:18: warning: structured binding declaration set but not used [-Wunused-but-set-variable]
   83 |             auto [a, b, c] = q;
      |                  ^~~~~~~~~

• Subtask 1: 6 / 6
• Subtask 2: 7 / 7
• Subtask 3: 15 / 15
• Subtask 4: 20 / 20
• Subtask 5: 52 / 52