oj.uz

Submission #79200

# Submission time Handle Problem Language Result Execution time Memory
79200 2018-10-11T15:55:00 Z gs14004 Meetings (IOI18_meetings) C++17
60 / 100
 5500 ms 601468 KB 
#include <bits/stdc++.h>
#include "meetings.h"
using namespace std;
using lint = long long;
using pi = pair<int, int>;
using line = pair<lint, lint>;
const int MAXN = 750005;
const int MAXT = 2100000;
const int inf = 1e9 + 10;

struct seg{
	int lim;
	pi tree[MAXT];
	void init(vector<int> &v){
		for(lim = 1; lim <= v.size(); lim <<= 1);
		fill(tree, tree + MAXT, pi(-inf, 0));
		for(int i=0; i<v.size(); i++) tree[i + lim] = pi(v[i], i);
		for(int i=lim-1; i; i--) tree[i] = max(tree[2*i], tree[2*i+1]);
	}
	pi query(int s, int e){
		s += lim;
		e += lim;
		pi ret(-inf, 0);
		while(s < e){
			if(s%2 == 1) ret = max(ret, tree[s++]);
			if(e%2 == 0) ret = max(ret, tree[e--]);
			s >>= 1;
			e >>= 1;
		}
		if(s == e) ret = max(ret, tree[s]);
		return ret;
	}
}seg;

struct node{
	int s, e, rep; // node range
	int lp, rp; // pointers
	int h; // height
}tr[MAXN];

int ptr, loc[MAXN], parL[MAXN], parR[MAXN];
lint dp[MAXN], lgo[MAXN], rgo[MAXN];
lint L_intercept[MAXN], R_intercept[MAXN];

void make_tree(int s, int e, int v){
	int h, m;
	tie(h, m) = seg.query(s, e);
	loc[m] = v;
	tr[v] = {s, e, m, -1, -1, h};
	if(s <= m - 1){
		ptr++;
		tr[v].lp = ptr;
		make_tree(s, m-1, tr[v].lp);
	}
	if(m + 1 <= e){
		ptr++;
		tr[v].rp = ptr;
		make_tree(m+1, e, tr[v].rp);
	}
}

struct chtt{
	vector<line> v;
	int ptr;
	void clear(){
		ptr = 0;
		v.clear();
	}
	bool bad(line a, line b, line c){
		long double insecab = (long double)(b.second - a.second) / (a.first - b.first);
		long double insecbc = (long double)(c.second - b.second) / (b.first - c.first);
		return insecab >= insecbc;
	}
	void add(int x, lint y){
		if(v.size() > ptr && v.back().first == x){
			if(v.back().second <= y) return;
			else v.pop_back();
		}
		while(v.size() >= ptr + 2 && bad(v[v.size()-2], v.back(), line(x, y))){
			v.pop_back();
		}
		v.emplace_back(x, y);
	}
	lint query(int x){
		lint ret = 1e18;
		for(auto &i : v) ret = min(ret, i.first * x + i.second);
		return ret;
		if(ptr == v.size()) return 1e18;
		while(ptr + 1 < v.size() && v[ptr].first * x + v[ptr].second > v[ptr+1].first * x + v[ptr+1].second){
			ptr++;
		}
		return v[ptr].first * x + v[ptr].second;
	}
}cht;


struct segtree{
	chtt tree[MAXT];
	int lim;
	void init(int n, int *a, lint *b){
		for(lim = 1; lim <= n; lim <<= 1);
		for(int i=0; i<2*lim; i++) tree[i].clear();
		for(int i=1; i<=n; i++){
			for(int j=i+lim; j; j>>=1) tree[j].add(a[i], b[i]);
		}
	}
	lint query(int s, int e, int x){
		s += lim;
		e += lim;
		lint ret = 1e18;
		while(s < e){
			if(s%2 == 1) ret = min(ret, tree[s++].query(x));
			if(e%2 == 0) ret = min(ret, tree[e--].query(x));
			s >>= 1;
			e >>= 1;
		}
		if(s == e) ret = min(ret, tree[s].query(x));
		return ret;
	}
}chtseg;

struct tree_cht{
	struct queries{
		int s, e, x, idx;
		bool operator<(const queries &b)const{
			return x < b.x;
		}
	};
	struct range_query{
		int l, r, x, idx;
	};
	int n, par[MAXN];
	int a[MAXN]; lint b[MAXN];
	vector<int> gph[MAXN];
	vector<queries> query;
	int sz[MAXN], dfn[MAXN], chn[MAXN], cnt[MAXN], piv;
	void dfs(int x){
		sz[x] = 1;
		for(auto &i : gph[x]){
			dfs(i);
			sz[x] += sz[i];
		}
	}
	void hld(int x){
		dfn[x] = ++piv;
		cnt[chn[x]]++;
		if(gph[x].empty()) return;
		chn[gph[x][0]] = chn[x];
		hld(gph[x][0]);
		for(int i=1; i<gph[x].size(); i++){
			chn[gph[x][i]] = gph[x][i];
			hld(gph[x][i]);
		}
	}
	void build(int _n, int *p, node *t, lint *intercept){
		a[0] = inf;
		n = _n + 1;
		for(int i=1; i<n; i++){
			par[i] = p[i-1] + 1;
			gph[par[i]].push_back(i);
		}
		dfs(0);
		for(int i=0; i<n; i++){
			sort(gph[i].begin(), gph[i].end(), [&](const int &a, const int &b){
				return sz[a] > sz[b];
			});
		}
		hld(0);
		for(int i=1; i<n; i++){
			a[dfn[i]] = t[i-1].h;
			b[dfn[i]] = intercept[i-1];
		}
	}
	void add_query(int s, int e, int x){
		query.push_back({s + 1, e + 1, x, (int)query.size()});
	}
	vector<pi> prefix_query[MAXN];
	vector<range_query> rquery;
	vector<lint> batch(){
		vector<lint> ret(query.size(), 1e18);
		sort(query.begin(), query.end());
		for(int i=0; i<query.size(); i++){
			int pos = query[i].s;
			while(chn[pos] != chn[query[i].e]){
				prefix_query[dfn[pos]].push_back(pi(query[i].x, query[i].idx));
				pos = par[chn[pos]];
			}
			if(dfn[query[i].e] < dfn[pos]){
				rquery.push_back({dfn[query[i].e] + 1, dfn[pos], query[i].x, query[i].idx});
			}
		}
		for(int i=0; i<n; i++){
			if(chn[i] == i){
				cht.clear();
				for(int j=dfn[i]; j<dfn[i]+cnt[i]; j++){
					cht.add(a[j], b[j]);
					for(auto &k : prefix_query[j]){
						ret[k.second] = min(ret[k.second], cht.query(k.first));
					}
				}
			}
		}
		chtseg.init(n, a, b);
		for(auto &i : rquery){
			ret[i.idx] = min(ret[i.idx], chtseg.query(i.l, i.r, i.x));
		}
		return ret;
	}
}t1, t2;

vector<lint> minimum_costs(vector<int> H, vector<int> L, vector<int> R){
	int n = H.size();
	int q = L.size();
	seg.init(H);
	make_tree(0, n-1, 0);
	for(int i=ptr; i>=0; i--){
		dp[i] = 1ll * H[tr[i].rep] * (tr[i].e - tr[i].s + 1);
		if(~tr[i].lp){
			dp[i] = min(dp[i], dp[tr[i].lp] + 1ll * H[tr[i].rep] * (tr[i].e - tr[i].rep + 1));
		}
		if(~tr[i].rp){
			dp[i] = min(dp[i], dp[tr[i].rp] + 1ll * H[tr[i].rep] * (tr[i].rep - tr[i].s + 1));
		}
	}
	for(int i=0; i<=ptr; i++){
		if(tr[i].s - 1 >= 0) parR[i] = loc[tr[i].s - 1];
		else parR[i] = -1;
		if(tr[i].e + 1 < n) parL[i] = loc[tr[i].e + 1];
		else parL[i] = -1;
		if(~tr[i].lp){
			lgo[tr[i].lp] = lgo[i] + 1ll * H[tr[i].rep] * (tr[i].e - tr[i].rep + 1);
			rgo[tr[i].lp] = rgo[i];
		}
		if(~tr[i].rp){
			lgo[tr[i].rp] = lgo[i];
			rgo[tr[i].rp] = rgo[i] + 1ll * H[tr[i].rep] * (tr[i].rep - tr[i].s + 1);
		}
		L_intercept[i] = lgo[i] + 1ll * tr[i].h * (tr[i].e + 1);
		if(~tr[i].rp){
			L_intercept[i] = min(L_intercept[i], lgo[i] + 1ll * tr[i].h * (tr[i].rep + 1) + dp[tr[i].rp]);
		}
		R_intercept[i] = rgo[i] + 1ll * tr[i].h * (1 - tr[i].s);
		if(~tr[i].lp){
			R_intercept[i] = min(R_intercept[i], rgo[i] + 1ll * tr[i].h * (1 - tr[i].rep) + dp[tr[i].lp]);
		}
	}
	t1.build(ptr + 1, parL, tr, L_intercept);
	t2.build(ptr + 1, parR, tr, R_intercept);
	vector<pi> lca(q);
	for(int i=0; i<q; i++){
		lca[i] = seg.query(L[i], R[i]);
		t1.add_query(loc[L[i]], loc[lca[i].second], -L[i]);
		t2.add_query(loc[R[i]], loc[lca[i].second], R[i]);
	}
	auto sol1 = t1.batch();
	auto sol2 = t2.batch();
	vector<lint> ret(q);
	for(int i=0; i<q; i++){
		pi p = lca[i];
		int root_num = loc[p.second]; 
		ret[i] = 1ll * (R[i] - L[i] + 1) * p.first;
		if(L[i] < p.second){
			ret[i] = min(ret[i], sol1[i] + 1ll * (R[i] - p.second + 1) * p.first - lgo[tr[root_num].lp]);
		}
		if(p.second < R[i]){
			ret[i] = min(ret[i], sol2[i] + 1ll * (p.second - L[i] + 1) * p.first - rgo[tr[root_num].rp]);
		}
	}
	return ret;
}

Compilation message

meetings.cpp: In member function 'void seg::init(std::vector<int>&)':
meetings.cpp:15:20: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
   for(lim = 1; lim <= v.size(); lim <<= 1);
                ~~~~^~~~~~~~~~~
meetings.cpp:17:17: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
   for(int i=0; i<v.size(); i++) tree[i + lim] = pi(v[i], i);
                ~^~~~~~~~~
meetings.cpp: In member function 'void chtt::add(int, lint)':
meetings.cpp:75:15: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
   if(v.size() > ptr && v.back().first == x){
      ~~~~~~~~~^~~~~
meetings.cpp:79:18: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
   while(v.size() >= ptr + 2 && bad(v[v.size()-2], v.back(), line(x, y))){
         ~~~~~~~~~^~~~~~~~~~
meetings.cpp: In member function 'lint chtt::query(int)':
meetings.cpp:88:10: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
   if(ptr == v.size()) return 1e18;
      ~~~~^~~~~~~~~~~
meetings.cpp:89:17: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
   while(ptr + 1 < v.size() && v[ptr].first * x + v[ptr].second > v[ptr+1].first * x + v[ptr+1].second){
         ~~~~~~~~^~~~~~~~~~
meetings.cpp: In member function 'void tree_cht::hld(int)':
meetings.cpp:150:17: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
   for(int i=1; i<gph[x].size(); i++){
                ~^~~~~~~~~~~~~~
meetings.cpp: In member function 'std::vector<long long int> tree_cht::batch()':
meetings.cpp:182:17: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
   for(int i=0; i<query.size(); i++){
                ~^~~~~~~~~~~~~

Subtask #1
4.0 / 4.0

# Verdict Execution time Memory Grader output
1 Correct 145 ms 153068 KB Output is correct
2 Correct 146 ms 154052 KB Output is correct
3 Correct 151 ms 153980 KB Output is correct
4 Correct 152 ms 154020 KB Output is correct
5 Correct 147 ms 154032 KB Output is correct
6 Correct 154 ms 154352 KB Output is correct
7 Correct 150 ms 153944 KB Output is correct
8 Correct 147 ms 154076 KB Output is correct
9 Correct 146 ms 153952 KB Output is correct

Subtask #2
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 145 ms 153068 KB Output is correct
2 Correct 146 ms 154052 KB Output is correct
3 Correct 151 ms 153980 KB Output is correct
4 Correct 152 ms 154020 KB Output is correct
5 Correct 147 ms 154032 KB Output is correct
6 Correct 154 ms 154352 KB Output is correct
7 Correct 150 ms 153944 KB Output is correct
8 Correct 147 ms 154076 KB Output is correct
9 Correct 146 ms 153952 KB Output is correct
10 Correct 159 ms 155496 KB Output is correct
11 Correct 159 ms 155448 KB Output is correct
12 Correct 158 ms 155484 KB Output is correct
13 Correct 157 ms 155376 KB Output is correct
14 Correct 169 ms 156124 KB Output is correct
15 Correct 167 ms 155404 KB Output is correct

Subtask #3
17.0 / 17.0

# Verdict Execution time Memory Grader output
1 Correct 143 ms 153120 KB Output is correct
2 Correct 212 ms 161140 KB Output is correct
3 Correct 606 ms 199932 KB Output is correct
4 Correct 357 ms 191128 KB Output is correct
5 Correct 555 ms 196576 KB Output is correct
6 Correct 337 ms 192320 KB Output is correct
7 Correct 369 ms 193872 KB Output is correct

Subtask #4
24.0 / 24.0

# Verdict Execution time Memory Grader output
1 Correct 143 ms 153120 KB Output is correct
2 Correct 212 ms 161140 KB Output is correct
3 Correct 606 ms 199932 KB Output is correct
4 Correct 357 ms 191128 KB Output is correct
5 Correct 555 ms 196576 KB Output is correct
6 Correct 337 ms 192320 KB Output is correct
7 Correct 369 ms 193872 KB Output is correct
8 Correct 663 ms 197668 KB Output is correct
9 Correct 601 ms 195164 KB Output is correct
10 Correct 637 ms 198568 KB Output is correct
11 Correct 616 ms 198184 KB Output is correct
12 Correct 566 ms 195292 KB Output is correct
13 Correct 633 ms 198632 KB Output is correct
14 Correct 816 ms 213736 KB Output is correct
15 Correct 679 ms 198644 KB Output is correct
16 Correct 369 ms 193760 KB Output is correct

Subtask #5
0 / 40.0

# Verdict Execution time Memory Grader output
1 Correct 145 ms 153068 KB Output is correct
2 Correct 146 ms 154052 KB Output is correct
3 Correct 151 ms 153980 KB Output is correct
4 Correct 152 ms 154020 KB Output is correct
5 Correct 147 ms 154032 KB Output is correct
6 Correct 154 ms 154352 KB Output is correct
7 Correct 150 ms 153944 KB Output is correct
8 Correct 147 ms 154076 KB Output is correct
9 Correct 146 ms 153952 KB Output is correct
10 Correct 159 ms 155496 KB Output is correct
11 Correct 159 ms 155448 KB Output is correct
12 Correct 158 ms 155484 KB Output is correct
13 Correct 157 ms 155376 KB Output is correct
14 Correct 169 ms 156124 KB Output is correct
15 Correct 167 ms 155404 KB Output is correct
16 Correct 143 ms 153120 KB Output is correct
17 Correct 212 ms 161140 KB Output is correct
18 Correct 606 ms 199932 KB Output is correct
19 Correct 357 ms 191128 KB Output is correct
20 Correct 555 ms 196576 KB Output is correct
21 Correct 337 ms 192320 KB Output is correct
22 Correct 369 ms 193872 KB Output is correct
23 Correct 663 ms 197668 KB Output is correct
24 Correct 601 ms 195164 KB Output is correct
25 Correct 637 ms 198568 KB Output is correct
26 Correct 616 ms 198184 KB Output is correct
27 Correct 566 ms 195292 KB Output is correct
28 Correct 633 ms 198632 KB Output is correct
29 Correct 816 ms 213736 KB Output is correct
30 Correct 679 ms 198644 KB Output is correct
31 Correct 369 ms 193760 KB Output is correct
32 Correct 3150 ms 521164 KB Output is correct
33 Correct 2649 ms 508552 KB Output is correct
34 Correct 2994 ms 502200 KB Output is correct
35 Correct 4224 ms 499472 KB Output is correct
36 Correct 3628 ms 475812 KB Output is correct
37 Correct 4025 ms 502816 KB Output is correct
38 Execution timed out 5606 ms 601468 KB Time limit exceeded
39 Halted 0 ms 0 KB -