oj.uz

Submission #523878

# Submission time Handle Problem Language Result Execution time Memory
523878 2022-02-08T10:49:04 Z amunduzbaev Bodyguard (JOI21_bodyguard) C++17
100 / 100
 6988 ms 515892 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;
	vector<int> a(n), b(n), c(n), t(n), t2(n);
	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 4842 ms 318416 KB Output is correct
2 Correct 4913 ms 322608 KB Output is correct
3 Correct 3077 ms 205072 KB Output is correct
4 Correct 2427 ms 146116 KB Output is correct
5 Correct 5097 ms 404176 KB Output is correct

Subtask #2
7.0 / 7.0

# Verdict Execution time Memory Grader output
1 Correct 2436 ms 304912 KB Output is correct
2 Correct 976 ms 304116 KB Output is correct
3 Correct 2032 ms 307844 KB Output is correct
4 Correct 6 ms 1368 KB Output is correct
5 Correct 3164 ms 363424 KB Output is correct
6 Correct 3249 ms 240840 KB Output is correct
7 Correct 1442 ms 240764 KB Output is correct

Subtask #3
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 2436 ms 304912 KB Output is correct
2 Correct 976 ms 304116 KB Output is correct
3 Correct 2032 ms 307844 KB Output is correct
4 Correct 6 ms 1368 KB Output is correct
5 Correct 3164 ms 363424 KB Output is correct
6 Correct 3249 ms 240840 KB Output is correct
7 Correct 1442 ms 240764 KB Output is correct
8 Correct 3424 ms 304860 KB Output is correct
9 Correct 3460 ms 304552 KB Output is correct
10 Correct 3153 ms 307536 KB Output is correct
11 Correct 5 ms 1612 KB Output is correct
12 Correct 3333 ms 363456 KB Output is correct
13 Correct 3232 ms 240980 KB Output is correct
14 Correct 2878 ms 242516 KB Output is correct

Subtask #4
20.0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 2436 ms 304912 KB Output is correct
2 Correct 976 ms 304116 KB Output is correct
3 Correct 2032 ms 307844 KB Output is correct
4 Correct 6 ms 1368 KB Output is correct
5 Correct 3164 ms 363424 KB Output is correct
6 Correct 3249 ms 240840 KB Output is correct
7 Correct 1442 ms 240764 KB Output is correct
8 Correct 3424 ms 304860 KB Output is correct
9 Correct 3460 ms 304552 KB Output is correct
10 Correct 3153 ms 307536 KB Output is correct
11 Correct 5 ms 1612 KB Output is correct
12 Correct 3333 ms 363456 KB Output is correct
13 Correct 3232 ms 240980 KB Output is correct
14 Correct 2878 ms 242516 KB Output is correct
15 Correct 3263 ms 307492 KB Output is correct
16 Correct 3235 ms 307636 KB Output is correct
17 Correct 3264 ms 311460 KB Output is correct
18 Correct 26 ms 3688 KB Output is correct
19 Correct 3008 ms 365728 KB Output is correct
20 Correct 3236 ms 243156 KB Output is correct
21 Correct 2934 ms 244736 KB Output is correct

Subtask #5
52.0 / 52.0

# Verdict Execution time Memory Grader output
1 Correct 4842 ms 318416 KB Output is correct
2 Correct 4913 ms 322608 KB Output is correct
3 Correct 3077 ms 205072 KB Output is correct
4 Correct 2427 ms 146116 KB Output is correct
5 Correct 5097 ms 404176 KB Output is correct
6 Correct 2436 ms 304912 KB Output is correct
7 Correct 976 ms 304116 KB Output is correct
8 Correct 2032 ms 307844 KB Output is correct
9 Correct 6 ms 1368 KB Output is correct
10 Correct 3164 ms 363424 KB Output is correct
11 Correct 3249 ms 240840 KB Output is correct
12 Correct 1442 ms 240764 KB Output is correct
13 Correct 3424 ms 304860 KB Output is correct
14 Correct 3460 ms 304552 KB Output is correct
15 Correct 3153 ms 307536 KB Output is correct
16 Correct 5 ms 1612 KB Output is correct
17 Correct 3333 ms 363456 KB Output is correct
18 Correct 3232 ms 240980 KB Output is correct
19 Correct 2878 ms 242516 KB Output is correct
20 Correct 3263 ms 307492 KB Output is correct
21 Correct 3235 ms 307636 KB Output is correct
22 Correct 3264 ms 311460 KB Output is correct
23 Correct 26 ms 3688 KB Output is correct
24 Correct 3008 ms 365728 KB Output is correct
25 Correct 3236 ms 243156 KB Output is correct
26 Correct 2934 ms 244736 KB Output is correct
27 Correct 6892 ms 515784 KB Output is correct
28 Correct 6988 ms 515892 KB Output is correct
29 Correct 6182 ms 504932 KB Output is correct
30 Correct 2391 ms 170544 KB Output is correct
31 Correct 4720 ms 474144 KB Output is correct
32 Correct 6254 ms 422524 KB Output is correct
33 Correct 5450 ms 414304 KB Output is correct