Submission #104886

#	Time	Username	Problem	Language	Result	Execution time	Memory
104886		minson123	Aliens (IOI16_aliens)	C++11	100 / 100	182 ms	8044 KiB

aliens

#include "aliens.h"
#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef pair<ll,int> pli;
const int maxn=100010;
struct Section{
	int l,r;
	Section(int _l=0,int _r=0):l(_l),r(_r){}
	inline bool operator<(const Section& rhs) const{
		return l!=rhs.l?l<rhs.l:r>rhs.r;
	}
	inline bool operator==(const Section& rhs) const{
		return l==rhs.l && r==rhs.r;
	}
};
struct Line{
	ll a,b;
	int idx=0;
	Line(ll _a=0,ll _b=0,int _idx=0):a(_a),b(_b),idx(_idx){}
} dq[maxn];
vector<Section> sec;
pli dp[maxn];
inline bool check(Line l1,Line l2,Line l3){
	ll a1=l1.a,b1=l1.b;
	ll a2=l2.a,b2=l2.b;
	ll a3=l3.a,b3=l3.b;
	return (__int128)(a2-a3)*(b3-b1)>(__int128)(b3-b2)*(a1-a3);
}
inline ll get_val(ll x,Line ln){
	return ln.a*x+ln.b;
}
inline pli calc_dp(ll ext){
	int head=0,rear=0;
	dq[rear++]=Line(-2ll*sec[0].l,(ll)sec[0].l*sec[0].l,0);
	for(int i=1;i<=(int)sec.size();i++){
		while(head+1<rear && get_val(sec[i-1].r,dq[head])>get_val(sec[i-1].r,dq[head+1])) head++;
		dp[i]=pli(get_val(sec[i-1].r,dq[head])+(ll)sec[i-1].r*sec[i-1].r+ext,dp[dq[head].idx].second+1);
		if(i<(int)sec.size()){
			Line ln=Line(-2ll*sec[i].l,(ll)sec[i].l*sec[i].l+dp[i].first-(sec[i-1].r>sec[i].l?(ll)(sec[i-1].r-sec[i].l)*(sec[i-1].r-sec[i].l):0ll),i);
			while(head<rear && check(dq[rear-2],dq[rear-1],ln)) rear--;
			dq[rear++]=ln;
		}
	}
	return dp[(int)sec.size()];
}
long long take_photos(int n, int m, int k, std::vector<int> r, std::vector<int> c) {
	for(int i=0;i<n;i++){
		if(r[i]>c[i]) swap(r[i],c[i]);
		sec.push_back(Section(r[i],c[i]+1));
	}
	sort(sec.begin(),sec.end());
	sec.erase(unique(sec.begin(),sec.end()),sec.end());
	int mx=-1,sz=0;
	for(int i=0;i<(int)sec.size();i++){
		if(sec[i].r>mx) sec[sz++]=sec[i],mx=sec[i].r;
	}
	sec.erase(sec.begin()+sz,sec.end());
	k=min(k,(int)sec.size());
	ll L=0,R=(ll)m*m+10;
	while(L!=R){
		ll mid=(L+R)>>1;
		if(calc_dp(mid).second<=k) R=mid;
		else L=mid+1;
	}
	return calc_dp(R).first-R*k;
}

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