Submission #831949

#	Time	Username	Problem	Language	Result	Execution time	Memory
831949		CSQ31	Aliens (IOI16_aliens)	C++17	100 / 100	175 ms	10132 KiB

aliens

#include "aliens.h"
#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
typedef long long int ll;
typedef long double ld;
typedef pair<ll,ll> PII;
typedef pair<int,int> pii;
const int MAXN = 1e5+5;
ll dp[MAXN],l[MAXN],r[MAXN],c[MAXN],m[MAXN];
int cnt[MAXN],n;
const ll INF = 1e18;

//increasing slope
//incresing query
struct line{
	ll m = 0,c = 0;
	int cnt = 0;
	line(){}
	line(ll _m,ll _c,int _cnt):m(_m),c(_c),cnt(_cnt){}
	ll eval(ll x){return m*x+c;}
};
deque<line>hull;
void add(line t){
	while(sz(hull)>1){
		line a = hull[sz(hull)-2];
		line b = hull[sz(hull)-1];
		//inter(t,a) >=  inter(t,b)
		if((t.c - a.c) * (b.m - t.m) >= (a.m - t.m) * (t.c - b.c))hull.pop_back();
		else break;
	}	
	hull.push_back(t);
}

int num = 0;
ll query(ll x){
	while(sz(hull)>1 && hull[1].eval(x) >= hull[0].eval(x))hull.pop_front();
	num = hull[0].cnt;
	return hull[0].eval(x);
}
int find(ll mid){
	dp[0] = cnt[0] = 0;
	hull.clear();
	add(line(m[0],c[0],0));
	for(int i=1;i<=n;i++){
		dp[i] = r[i] * r[i]  - query(r[i]) + mid;
		cnt[i] = num+1;
		if(i!=n)add(line(m[i],c[i] - dp[i],cnt[i]));
	}
	//cout<<mid<<'\n';
	//for(int i=1;i<=n;i++)cout<<dp[i]<<" ";
	//cout<<'\n';
	return cnt[n];
}
ll take_photos(int N, int M, int K, vector<int> RR, vector<int> C) {
	n = N;
	vector<pii>tmp,p;
	for(int i=0;i<n;i++)tmp.pb({min(RR[i],C[i]),max(RR[i],C[i])});
	sort(all(tmp),[&](pii x,pii y){
		if(x.fi==y.fi)return x.se > y.se;
		return y.fi > x.fi;
	});
	int mx = -1;
	for(pii x:tmp){
		if(mx >= x.se)continue;
		mx = max(mx,x.se);
		p.pb(x);
	}
	n = sz(p);
	p.pb({-1,-1});
	sort(all(p),[&](pii x,pii y){
		return y.se > x.se;
	});
	for(int i=0;i<=n;i++){
		l[i] = p[i].fi;
		r[i] = p[i].se;
	}
	for(int i=0;i<n;i++){
		m[i] = 2*l[i+1] - 2;
		c[i] = max(r[i] - l[i+1] + 1,0LL); c[i]*=-c[i];
		c[i] += (l[i+1]-1)*(l[i+1]-1);
		c[i]*=-1;
	}
	
	///
	ll L = 0,R = 1e15;
	K = min(K,n);
	while(R>L){
		ll mid = (L+R+1)/2;
		if(find(mid) >= K)L = mid;
		else R = mid-1;
	}
	find(L);
	ll ans = dp[n] - K*1LL * L;
	return ans;
}

• Subtask 1: 4 / 4
• Subtask 2: 12 / 12
• Subtask 3: 9 / 9
• Subtask 4: 16 / 16
• Subtask 5: 19 / 19
• Subtask 6: 40 / 40