Submission #482799

#	Time	Username	Problem	Language	Result	Execution time	Memory
482799		CSQ31	3D Histogram (COCI20_histogram)	C++17	110 / 110	1093 ms	215296 KiB

histogram

#pragma GCC optimize("Ofast") 
#include<bits/stdc++.h>
using namespace std;
#define pb push_back
#define fi first
#define se second
#define sz(a) (int)(a.size())
#define all(a) a.begin(),a.end()
#define lb lower_bound
#define ub upper_bound
#define owo ios_base::sync_with_stdio(0);cin.tie(0);
#define MOD (ll)(998244353)
#define INF (ll)(1e18)
#define debug(...) fprintf(stderr, __VA_ARGS__),fflush(stderr)
#define time__(d) for(long blockTime = 0; (blockTime == 0 ? (blockTime=clock()) != 0 : false);\
debug("%s time : %.4fs\n", d, (double)(clock() - blockTime) / CLOCKS_PER_SEC))
typedef long long int ll;
typedef long double ld;
typedef pair<ll,ll> PII;
typedef pair<int,int> pii;
typedef vector<vector<int>> vii;
typedef vector<vector<ll>> VII;
ll gcd(ll a,ll b){if(!b)return a;else return gcd(b,a%b);}
bool debug = 0;
const int MAXN = 2000005;
int a[MAXN],b[MAXN],f[MAXN],g[MAXN],n;
ll ans = 0;
ll d(ll a, ll b){
	assert(b);
	return a / b + ((a^b) < 0 && (a%b));
}
struct line{
	ll m,c;
	ll eval(ll x){return m*x+c;}
	line(ll _m,ll _c):m(_m),c(_c){}
	line(){}
};
struct hull{
	vector<line>h;
	void add(line L){
		if(!h.empty() && L.m == h.back().m){
			h.back().c = max(h.back().c,L.c);
			return;
		}
		while(sz(h) >= 2){
			line c0 = h[sz(h)-1];
			line c1 = h[sz(h)-2];
			if(d(c0.c - c1.c , c1.m - c0.m) >= d(c0.c - L.c , L.m - c0.m))h.pop_back();
			else break;
		}
		h.pb(L);
	}
	ll query(ll x){
		if(h.empty())return 0;
		while(sz(h)>=2 && h[sz(h)-2].eval(x) >= h[sz(h)-1].eval(x))h.pop_back();
		return h[sz(h)-1].eval(x);
	}
}t[4*MAXN];
void build(int v,int l,int r,int tl,int tr){//this should be linear
	if(l>r)return;
	t[v].h.clear();
	//cout<<l<<" "<<r<<" "<<tl<<" "<<tr<<'\n';
	if(l==tl && r==tr){
		//cout<<"added "<<l<<" "<<r<<'\n';
		for(int i=r;i>=l;i--)t[v].add(line(g[i],g[i] * 1LL * i));
	}
	if(tl==tr)return;
	int tm = (tl+tr)/2;
	build(2*v,l,min(r,tm),tl,tm);
	build(2*v+1,max(tm+1,l),r,tm+1,tr);
	
}
ll query(int v,int l,int r,int tl,int tr,ll x){
	if(l>r)return 0;
	if(l==tl && r==tr)return t[v].query(x);
	else{
		int tm = (tl+tr)/2;
		return max(query(2*v,l,min(r,tm),tl,tm,x),
		           query(2*v+1,max(tm+1,l),r,tm+1,tr,x));
	}	
}
void solve(int l,int r){
	if(r-l<=1){
		ans = max(ans,b[l] * 1LL * a[l]);
		ans = max(ans,b[r] * 1LL * a[r]);
		ans = max(ans,min(b[l],b[r]) * 1LL * min(a[l],a[r]) * 1LL *2);
		return;
	}
	int m = (l+r)/2;
	solve(l,m);
	solve(m,r);
	f[m] = a[m];g[m] = b[m];
	for(int i=m-1;i>=l;i--)f[i] = min(a[i],f[i+1]);
	for(int i=m+1;i<=r;i++)f[i] = min(a[i],f[i-1]);
	
	for(int i=m+1;i<=r;i++)g[i] = min(b[i],g[i-1]);
	for(int i=m-1;i>=l;i--)g[i] = min(b[i],g[i+1]);
	int p = r;
	for(int i=l;i<=m;i++){ //f and g lie on left side
		while(p>=m && (f[i] > f[p] || g[i] > g[p]))p--;
		if(p<m)break;
		ans = max(ans,f[i] * 1LL * g[i] * 1LL * (p-i+1));
	}
	/*
	for(int i=l;i<=m;i++){
		for(int j=m+1;j<=r;j++){
			ans = max(ans,min(f[i],f[j]) * 1LL * min(g[i],g[j]) * (j-i+1));	
		}
	}*/
	//f lie on left and g left on right
	//f[i]  * g[r] * (r-l+1)
	//f[i] (g[r]*(-l+1) + g[r]*r)
	
	build(1,m+1,r,1,n);
	int pf = r;
	int pg = r+1;
	if(debug){
		cout<<"at "<<l<<" "<<m<<" "<<r<<'\n';
		cout<<"////////////////"<<'\n';
		for(int i=1;i<=n;i++)cout<<a[i]<<" ";
		cout<<'\n';
		for(int i=1;i<=n;i++)cout<<f[i]<<" ";
		cout<<'\n';
		for(int i=1;i<=n;i++)cout<<g[i]<<" ";
		cout<<'\n';
		cout<<"///////////////"<<'\n';
	}
	for(int i=l;i<=m;i++){
		while(pf>=m+1 && f[i] > f[pf])pf--; //[m+1,pf] is good
		while(pg-1>=m && g[i] >= g[pg-1])pg--; //[pg,r] is good
		if(debug){
			cout<<i<<" "<<m<<" "<<r<<" "<<pg<<" "<<pf<<'\n';
		}
		if(f[i] > f[pf] || g[i] < g[pg])continue;
		//for(int j=pg;j<=pf;j++)ans = max(ans,f[i] * 1LL * g[j] * (j-i+1));
		ans = max(ans,f[i] * 1LL * query(1,pg,pf,1,n,-i+1)); 
	}
}
int main(){
	owo
	//freopen("histogram.in.2a","r",stdin);
	cin>>n;
	for(int i=1;i<=n;i++)cin>>a[i]>>b[i];
	solve(1,n);
	reverse(a+1,a+n+1);
	reverse(b+1,b+n+1);
	solve(1,n);
	cout<<ans;
}
/*
13
913858 839924
806286 294915
565428 723951
995885 309497
766133 520675
211717 925495
603960 934575
908711 819343
392468 734121
839916 579960
770434 574444
433131 861816
861091 408456
7 12
1352705326752
*/

• Subtask 1: 20 / 20
• Subtask 2: 90 / 90