Submission #419664

#	Time	Username	Problem	Language	Result	Execution time	Memory
419664		amoo_safar	Bodyguard (JOI21_bodyguard)	C++17	100 / 100	16105 ms	1355424 KiB

bodyguard

// vaziat meshki-ghermeze !
#include <bits/stdc++.h>

#define pb push_back
#define F first
#define S second
#define all(x) x.begin(), x.end()
#define debug(x) cerr << #x << " : " << x << '\n'
// #define int ll

using namespace std;

typedef long long ll;
typedef long double ld;
typedef string str;
typedef pair<ll, ll> pll;
typedef pair<int, int> pii;

const ll Mod = 1000000007LL;
const int N = 2 * (2802);
const int Q = 3e6 + 10;
const int Inf = 2'000'000'100;
const ll Log = 30;

// X : X + T;
// Y : X - T;

vector<ll> cx, cy;

void Add(ll x, ll y){ cx.pb(x); cy.pb(y); }
void Uni(vector<ll>& C){
	sort(all(C));
	C.resize(unique(all(C)) - C.begin());
}
void Init(){ Uni(cx); Uni(cy); }
pii Get(ll x, ll y){
	x = lower_bound(all(cx), x) - cx.begin();
	y = lower_bound(all(cy), y) - cy.begin();
	return {x, y};
}
ll T[N], T2[N], A[N], B[N], P[Q], X[Q];
ll C[N];

ll up[N][N], rt[N][N];
ll dp[N][N];

 
typedef pair < ll , ll > Line;
struct CHT{
    set < pair < Line , ll > > S;
    set < pair < ll , Line > > I;
    ll INF = 4e18;
    inline void Add(Line X)
    {
        ll t = -INF;
        auto it = S.lower_bound({X, -INF});
        while ((int)S.size())
        {
            if (it == S.begin())
                {t = -INF; break;}
            it --; ll r = Intersection(it->first, X);
            if (r <= it->second)
                I.erase({it->second, it->first}), it = S.erase(it);
            else
                {t = r; break;}
        }
        it = S.lower_bound({X, -INF});
        while ((int)S.size())
        {
            if (it == S.end())
                break;
            ll r = Intersection(X, it->first);
            Line Y = it->first;
            I.erase({it->second, it->first});
            it = S.erase(it);
            if (r <= t)
            {
                r = -INF;
                if (it != S.begin())
                    it --, r = Intersection(it->first, Y);
                S.insert({Y, r}); I.insert({r, Y}); return ;
            }
            if (it != S.end() && it->second <= r)
                continue;
            S.insert({Y, r}); I.insert({r, Y}); break;
        }
        S.insert({X, t}); I.insert({t, X});
    }
    inline ll GetMax(ll X)
    {
        auto it = I.upper_bound({X, {INF, INF}}); it --;
        return (X * it->second.first + it->second.second);
    }
    inline ll Intersection(Line X, Line Y)
    {
        if (X.first == Y.first && X.second <= Y.second)
            return (-INF);
        if (X.first == Y.first)
            return (INF);
        return ((X.second - Y.second) / (Y.first - X.first)) + ((X.second - Y.second) % (Y.first - X.first) > 0);
    }
};
CHT row[N], col[N];

ll zx[Q], zy[Q], ans[Q];
vector<int> V[N][N];

int32_t main(){
	ios::sync_with_stdio(0); cin.tie(0); cout.tie(0);
	int n, q;
	cin >> n >> q;
	// assert(q == 1);
	// for(int i = -3000; i <= 6000; i++) Add(i, i);

	// debug(Inf);
	for(int i = 1; i <= n; i++){
		cin >> T[i] >> A[i] >> B[i] >> C[i];
		T2[i] = abs(A[i] - B[i]) + T[i];
		C[i] /= 2;
		Add(T[i] + A[i], T[i] - A[i]);
		Add(T2[i]+ B[i],T2[i] - B[i]);
	}
	// Add(Q, Q);
	Add(Inf, Inf);
	Add(-Inf, -Inf);
	
	for(int i = 1; i <= q; i++){
		cin >> P[i] >> X[i];
		// Add(P[i] + X[i], P[i] - X[i]);
	}
	Init();
	for(int i = 1; i <= n; i++){
		pii st = Get(T[i] + A[i], T[i] - A[i]);
		pii fn = Get(T2[i]+ B[i],T2[i] - B[i]);
		// cerr << 
		if(st.F == fn.F){
			for(int _i = st.S; _i < fn.S; _i++)
				up[st.F][_i] = max(up[st.F][_i], C[i]);
		} else {	
			for(int _i = st.F; _i < fn.F; _i++)
				rt[_i][st.S] = max(rt[_i][st.S], C[i]);
		}
	}

	for(int i = 1; i <= q; i++){
		// if(abs(P[i] + X[i]) > 3000 || abs(P[i] - X[i]) > 3000){
		// 	cout << "0\n";
		// 	continue;
		// }
		pii st = Get(P[i] + X[i], P[i] - X[i]);
		// ll ans = dp[st.F][st.S];
		V[st.F][st.S].pb(i);
		// for(int j = st.F; j < nx; j++)
		// 	ans = max(ans, dp[j][st.S] + (cy[st.S] - (P[i] - X[i])) * up[j][st.S - 1]);
		zy[i] = (cy[st.S] - (P[i] - X[i]));
		// for(int j = st.S; j < ny; j++)
		// 	ans = max(ans, dp[st.F][j] + (cx[st.F] - (P[i] + X[i])) * rt[st.F - 1][j]);
		zx[i] = (cx[st.F] - (P[i] + X[i]));
		// assert(cx[st.F] == P[i] + X[i]);
		// assert(cy[st.S] == P[i] - X[i]);
		// cout << ans << '\n';
	}
	
	int nx = cx.size(), ny = cy.size();
	for(int i = nx - 1; i > 0; i--){
		for(int j = ny - 1; j > 0; j--){
			if(i != nx - 1 && j != ny - 1)
				dp[i][j] = max(1ll * up[i][j] * (cy[j + 1] - cy[j]) + dp[i][j + 1], 1ll * rt[i][j] * (cx[i + 1] - cx[i]) + dp[i + 1][j]);
			col[i].Add({rt[i - 1][j], dp[i][j]});
			row[j].Add({up[i][j - 1], dp[i][j]});
		
			for(auto q_id : V[i][j])
				ans[q_id] = max(row[j].GetMax(zy[q_id]), col[i].GetMax(zx[q_id]));
		}
	}
	for(int i = 1; i <= q; i++)
		cout << ans[i] << '\n';
	return 0;
}

• Subtask 1: 5 / 5
• Subtask 2: 7 / 7
• Subtask 3: 15 / 15
• Subtask 4: 20 / 20
• Subtask 5: 53 / 53