Submission #482610

#	Time	Username	Problem	Language	Result	Execution time	Memory
482610		CSQ31	3D Histogram (COCI20_histogram)	C++17	0 / 110	253 ms	381488 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);}

const int MAXN = 2000001;
int a[MAXN],b[MAXN],f[MAXN],g[MAXN],n;
ll ans = 0;
ll d(ll a, ll b){
	assert(a!=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();
	if(l==tl && r==tr){
		for(int i=r;i>=l;i--){
			if(i!=r && g[i] == g[i+1])continue;
			t[v].add(line(g[i],g[i] * 1LL * i));
		}
		if(l==r)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(l==r){
		ans = max(ans,a[l]*1LL*b[l]);
		return;
	}
	int m = (l+r)/2;
	solve(l,m);
	solve(m+1,r);
	f[m] = a[m];f[m+1] = a[m+1];
	g[m] = b[m];g[m+1] = b[m+1];
	for(int i=m-1;i>=l;i--)f[i] = min(a[i],f[i+1]);
	for(int i=m+2;i<=r;i++)f[i] = min(a[i],f[i-1]);
	
	for(int i=m+2;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));
	}
	//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 = m+1;
	for(int i=l;i<=m;i++){
		while(pf>m && f[i] > f[pf])pf--; //[m+1,pf] is good
		while(pg<=r && g[i] < g[pg])pg++; //[pg,r] is good
		if(pf == m || pg > r)break;
		ans = max(ans,f[i] * 1LL * query(1,pg,pf,1,n,-i+1)); 
	}
}
int main(){
	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;
}
/*
10
101 113

192 154
186 101
189 137
184 109

153 154 
178 150 
145 198
137 103
153 186
1 9
124533
* 
* 137 and 101
*/

• Subtask 1: 0 / 20
• Subtask 2: 0 / 90