oj.uz

Submission #79199

# Submission time Handle Problem Language Result Execution time Memory
79199 2018-10-11T15:36:55 Z gs14004 Meetings (IOI18_meetings) C++17
60 / 100
 5500 ms 379796 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 cht{
	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 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));
					}
				}
			}
		}
		for(auto &i : rquery){
			for(int j=i.l; j<=i.r; j++){
				ret[i.idx] = min(ret[i.idx], 1ll * a[j] * i.x + b[j]);
			}
		}
		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 cht::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 cht::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:124:17: 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:156:17: 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 83 ms 87336 KB Output is correct
2 Correct 88 ms 87968 KB Output is correct
3 Correct 85 ms 87868 KB Output is correct
4 Correct 85 ms 87912 KB Output is correct
5 Correct 85 ms 87900 KB Output is correct
6 Correct 84 ms 88068 KB Output is correct
7 Correct 85 ms 88056 KB Output is correct
8 Correct 85 ms 88148 KB Output is correct
9 Correct 91 ms 88056 KB Output is correct

Subtask #2
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 83 ms 87336 KB Output is correct
2 Correct 88 ms 87968 KB Output is correct
3 Correct 85 ms 87868 KB Output is correct
4 Correct 85 ms 87912 KB Output is correct
5 Correct 85 ms 87900 KB Output is correct
6 Correct 84 ms 88068 KB Output is correct
7 Correct 85 ms 88056 KB Output is correct
8 Correct 85 ms 88148 KB Output is correct
9 Correct 91 ms 88056 KB Output is correct
10 Correct 94 ms 89296 KB Output is correct
11 Correct 92 ms 89132 KB Output is correct
12 Correct 94 ms 89216 KB Output is correct
13 Correct 92 ms 89092 KB Output is correct
14 Correct 95 ms 89204 KB Output is correct
15 Correct 92 ms 89192 KB Output is correct

Subtask #3
17.0 / 17.0

# Verdict Execution time Memory Grader output
1 Correct 83 ms 87416 KB Output is correct
2 Correct 220 ms 94444 KB Output is correct
3 Correct 2261 ms 120700 KB Output is correct
4 Correct 263 ms 118868 KB Output is correct
5 Correct 219 ms 117236 KB Output is correct
6 Correct 294 ms 120288 KB Output is correct
7 Correct 2581 ms 121864 KB Output is correct

Subtask #4
24.0 / 24.0

# Verdict Execution time Memory Grader output
1 Correct 83 ms 87416 KB Output is correct
2 Correct 220 ms 94444 KB Output is correct
3 Correct 2261 ms 120700 KB Output is correct
4 Correct 263 ms 118868 KB Output is correct
5 Correct 219 ms 117236 KB Output is correct
6 Correct 294 ms 120288 KB Output is correct
7 Correct 2581 ms 121864 KB Output is correct
8 Correct 489 ms 120140 KB Output is correct
9 Correct 851 ms 118620 KB Output is correct
10 Correct 293 ms 121856 KB Output is correct
11 Correct 307 ms 121336 KB Output is correct
12 Correct 283 ms 119020 KB Output is correct
13 Correct 283 ms 121796 KB Output is correct
14 Correct 2242 ms 120472 KB Output is correct
15 Correct 278 ms 123724 KB Output is correct
16 Correct 1379 ms 121696 KB Output is correct

Subtask #5
0 / 40.0

# Verdict Execution time Memory Grader output
1 Correct 83 ms 87336 KB Output is correct
2 Correct 88 ms 87968 KB Output is correct
3 Correct 85 ms 87868 KB Output is correct
4 Correct 85 ms 87912 KB Output is correct
5 Correct 85 ms 87900 KB Output is correct
6 Correct 84 ms 88068 KB Output is correct
7 Correct 85 ms 88056 KB Output is correct
8 Correct 85 ms 88148 KB Output is correct
9 Correct 91 ms 88056 KB Output is correct
10 Correct 94 ms 89296 KB Output is correct
11 Correct 92 ms 89132 KB Output is correct
12 Correct 94 ms 89216 KB Output is correct
13 Correct 92 ms 89092 KB Output is correct
14 Correct 95 ms 89204 KB Output is correct
15 Correct 92 ms 89192 KB Output is correct
16 Correct 83 ms 87416 KB Output is correct
17 Correct 220 ms 94444 KB Output is correct
18 Correct 2261 ms 120700 KB Output is correct
19 Correct 263 ms 118868 KB Output is correct
20 Correct 219 ms 117236 KB Output is correct
21 Correct 294 ms 120288 KB Output is correct
22 Correct 2581 ms 121864 KB Output is correct
23 Correct 489 ms 120140 KB Output is correct
24 Correct 851 ms 118620 KB Output is correct
25 Correct 293 ms 121856 KB Output is correct
26 Correct 307 ms 121336 KB Output is correct
27 Correct 283 ms 119020 KB Output is correct
28 Correct 283 ms 121796 KB Output is correct
29 Correct 2242 ms 120472 KB Output is correct
30 Correct 278 ms 123724 KB Output is correct
31 Correct 1379 ms 121696 KB Output is correct
32 Correct 2099 ms 379796 KB Output is correct
33 Correct 1611 ms 363288 KB Output is correct
34 Correct 1867 ms 354732 KB Output is correct
35 Correct 2593 ms 351748 KB Output is correct
36 Correct 2922 ms 330064 KB Output is correct
37 Correct 1902 ms 355220 KB Output is correct
38 Execution timed out 5545 ms 325284 KB Time limit exceeded
39 Halted 0 ms 0 KB -