oj.uz

Submission #523880

# Submission time Handle Problem Language Result Execution time Memory
523880 2022-02-08T10:55:37 Z amunduzbaev Bodyguard (JOI21_bodyguard) C++17
100 / 100
 7966 ms 469400 KB 
#include "bits/stdc++.h"
using namespace std;

#define ar array
#define int long long

struct Line {
	mutable int k, m, p;
	bool operator<(const Line& o) const { return k < o.k; }
	bool operator<(int x) const { return p < x; }
};

struct LineContainer : multiset<Line, less<>> {
	// (for doubles, use inf = 1/.0, div(a,b) = a/b)
	static const int inf = LLONG_MAX;
	int div(int a, int b) { // floored division
		return a / b - ((a ^ b) < 0 && a % b); }
	bool isect(iterator x, iterator y) {
		if (y == end()) return x->p = inf, 0;
		if (x->k == y->k) x->p = x->m > y->m ? inf : -inf;
		else x->p = div(y->m - x->m, x->k - y->k);
		return x->p >= y->p;
	}
	void add(int k, int m) {
		auto z = insert({k, m, 0}), y = z++, x = y;
		while (isect(y, z)) z = erase(z);
		if (x != begin() && isect(--x, y)) isect(x, y = erase(y));
		while ((y = x) != begin() && (--x)->p >= y->p)
			isect(x, erase(y));
	}
	int query(int x) {
		assert(!empty());
		auto l = *lower_bound(x);
		return l.k * x + l.m;
	}
};

const int N = 5605;
const int Q = 3e6 + 5;
const int INF = 2e9 + 5;
int x[Q], y[Q], res[Q];
int a[N], t[N], t2[N], b[N], c[N];
int up[N][N], ri[N][N], dp[N][N];
LineContainer cht[N];
vector<int> tx, ty;

signed main(){
	ios::sync_with_stdio(0); cin.tie(0);
	
	auto add = [&](int x, int y){
		tx.push_back(x);
		ty.push_back(y);
	};
	
	int n, q; cin>>n>>q;
	for(int i=0;i<n;i++){
		cin>>t[i]>>a[i]>>b[i]>>c[i];
		t2[i] = t[i] + abs(a[i] - b[i]);
		add(t[i] + a[i], t[i] - a[i]);
		add(t2[i] + b[i], t2[i] - b[i]);
	}
	
	tx.push_back(INF), tx.push_back(-INF);
	ty.push_back(INF), ty.push_back(-INF);
	sort(tx.begin(), tx.end());
	sort(ty.begin(), ty.end());
	tx.erase(unique(tx.begin(), tx.end()), tx.end());
	ty.erase(unique(ty.begin(), ty.end()), ty.end());
	auto get = [&](int x, int y) -> ar<int, 2>{
		int i = lower_bound(tx.begin(), tx.end(), x) - tx.begin(), 
		j = lower_bound(ty.begin(), ty.end(), y) - ty.begin();
		return {i, j};
	};
	
	for(int i=0;i<n;i++){
		ar<int, 2> l = get(t[i] + a[i], t[i] - a[i]), 
		r = get(t2[i] + b[i], t2[i] - b[i]);
		if(l > r) swap(l, r);
		
		if(l[0] == r[0]){
			for(int j=l[1];j<r[1];j++){
				up[l[0]][j] = max(up[l[0]][j], c[i]);
			}
		} else {
			for(int j=l[0];j<r[0];j++){
				ri[j][l[1]] = max(ri[j][l[1]], c[i]);
			}
		}
	}
	
	for(int i=(int)tx.size()-2;~i;i--){
		for(int j=(int)ty.size()-2;~j;j--){
			dp[i][j] = max(dp[i+1][j] + ri[i][j] * (tx[i+1] - tx[i]),
			dp[i][j+1] + up[i][j] * (ty[j+1] - ty[j]));
		}
	}
	
	vector<int> p(q);
	for(int i=0;i<q;i++){
		int T, P; cin>>T>>P;
		x[i] = T + P, y[i] = T - P;
		p[i] = i;
		auto n = get(x[i], y[i]);
		res[i] = dp[n[0]][n[1]];
		//~ for(int j=n[0];j<(int)tx.size();j++){
			//~ res = max(res, dp[j][n[1]] + up[j][n[1]-1] * (ty[n[1]] - y));
		//~ } for(int j=n[1];j<(int)ty.size();j++){
			//~ res = max(res, dp[n[0]][j] + ri[n[0]-1][j] * (tx[n[0]] - x));
		//~ }
		//~ cout<<res / 2<<"\n";
	}
	
	sort(p.begin(), p.end(), [&](int i, int j){
		return (x[i] > x[j]);
	});
	
	int j = tx.size() - 1;
	for(auto i : p){
		while(tx[j] >= x[i]){
			for(int l=1;l<(int)ty.size();l++){
				//~ dp[j][l] + up[j][l-1] * ty[l]
				//~ -up[j][l-1]
				cht[l].add(-up[j][l-1], dp[j][l] + up[j][l-1] * ty[l]);
			} j--;
		}
		auto n = get(x[i], y[i]);
		res[i] = max(res[i], cht[n[1]].query(y[i]));
	}
	
	for(int i=0;i<N;i++) cht[i].clear();
	sort(p.begin(), p.end(), [&](int i, int j){
		return (y[i] > y[j]);
	}); 
	j = (int)ty.size() - 1;
	for(auto i : p){
		while(ty[j] >= y[i]){
			for(int l=1;l<(int)tx.size();l++){
				//~ dp[l][j] + up[l-1][j] * tx[l]
				//~ -up[l-1][j] * y
				cht[l].add(-ri[l-1][j], dp[l][j] + ri[l-1][j] * tx[l]);
			} j--;
		}
		
		auto n = get(x[i], y[i]);
		res[i] = max(res[i], cht[n[0]].query(x[i]));
	}
	
	for(int i=0;i<q;i++) cout<<res[i] / 2<<"\n";
}

Subtask #1
6.0 / 6.0

# Verdict Execution time Memory Grader output
1 Correct 5119 ms 296084 KB Output is correct
2 Correct 5209 ms 298356 KB Output is correct
3 Correct 3025 ms 180808 KB Output is correct
4 Correct 2399 ms 121600 KB Output is correct
5 Correct 5167 ms 381740 KB Output is correct

Subtask #2
7.0 / 7.0

# Verdict Execution time Memory Grader output
1 Correct 2486 ms 304936 KB Output is correct
2 Correct 959 ms 304072 KB Output is correct
3 Correct 2019 ms 307996 KB Output is correct
4 Correct 4 ms 1356 KB Output is correct
5 Correct 3202 ms 363428 KB Output is correct
6 Correct 3982 ms 240852 KB Output is correct
7 Correct 1328 ms 240708 KB Output is correct

Subtask #3
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 2486 ms 304936 KB Output is correct
2 Correct 959 ms 304072 KB Output is correct
3 Correct 2019 ms 307996 KB Output is correct
4 Correct 4 ms 1356 KB Output is correct
5 Correct 3202 ms 363428 KB Output is correct
6 Correct 3982 ms 240852 KB Output is correct
7 Correct 1328 ms 240708 KB Output is correct
8 Correct 3725 ms 304804 KB Output is correct
9 Correct 3524 ms 304556 KB Output is correct
10 Correct 3533 ms 307544 KB Output is correct
11 Correct 6 ms 1612 KB Output is correct
12 Correct 3254 ms 363488 KB Output is correct
13 Correct 3970 ms 240988 KB Output is correct
14 Correct 3210 ms 242592 KB Output is correct

Subtask #4
20.0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 2486 ms 304936 KB Output is correct
2 Correct 959 ms 304072 KB Output is correct
3 Correct 2019 ms 307996 KB Output is correct
4 Correct 4 ms 1356 KB Output is correct
5 Correct 3202 ms 363428 KB Output is correct
6 Correct 3982 ms 240852 KB Output is correct
7 Correct 1328 ms 240708 KB Output is correct
8 Correct 3725 ms 304804 KB Output is correct
9 Correct 3524 ms 304556 KB Output is correct
10 Correct 3533 ms 307544 KB Output is correct
11 Correct 6 ms 1612 KB Output is correct
12 Correct 3254 ms 363488 KB Output is correct
13 Correct 3970 ms 240988 KB Output is correct
14 Correct 3210 ms 242592 KB Output is correct
15 Correct 3697 ms 307404 KB Output is correct
16 Correct 3718 ms 307648 KB Output is correct
17 Correct 3589 ms 311472 KB Output is correct
18 Correct 24 ms 3652 KB Output is correct
19 Correct 3267 ms 365640 KB Output is correct
20 Correct 3796 ms 243240 KB Output is correct
21 Correct 2893 ms 244724 KB Output is correct

Subtask #5
52.0 / 52.0

# Verdict Execution time Memory Grader output
1 Correct 5119 ms 296084 KB Output is correct
2 Correct 5209 ms 298356 KB Output is correct
3 Correct 3025 ms 180808 KB Output is correct
4 Correct 2399 ms 121600 KB Output is correct
5 Correct 5167 ms 381740 KB Output is correct
6 Correct 2486 ms 304936 KB Output is correct
7 Correct 959 ms 304072 KB Output is correct
8 Correct 2019 ms 307996 KB Output is correct
9 Correct 4 ms 1356 KB Output is correct
10 Correct 3202 ms 363428 KB Output is correct
11 Correct 3982 ms 240852 KB Output is correct
12 Correct 1328 ms 240708 KB Output is correct
13 Correct 3725 ms 304804 KB Output is correct
14 Correct 3524 ms 304556 KB Output is correct
15 Correct 3533 ms 307544 KB Output is correct
16 Correct 6 ms 1612 KB Output is correct
17 Correct 3254 ms 363488 KB Output is correct
18 Correct 3970 ms 240988 KB Output is correct
19 Correct 3210 ms 242592 KB Output is correct
20 Correct 3697 ms 307404 KB Output is correct
21 Correct 3718 ms 307648 KB Output is correct
22 Correct 3589 ms 311472 KB Output is correct
23 Correct 24 ms 3652 KB Output is correct
24 Correct 3267 ms 365640 KB Output is correct
25 Correct 3796 ms 243240 KB Output is correct
26 Correct 2893 ms 244724 KB Output is correct
27 Correct 7966 ms 468708 KB Output is correct
28 Correct 7108 ms 469400 KB Output is correct
29 Correct 6112 ms 460732 KB Output is correct
30 Correct 2319 ms 124500 KB Output is correct
31 Correct 4545 ms 450920 KB Output is correct
32 Correct 6855 ms 387576 KB Output is correct
33 Correct 4933 ms 384432 KB Output is correct