【bzoj2244】[SDOI2011]拦截导弹

这题就是个三维偏序。

三维偏序就是排序一维，cdq一维，数据结构一维。

然后尴尬的是还要求概率。

也就是方案数。

cdq正反各一遍，求三维偏序时，顺便dp记录方案数就好。

#include <bits/stdc++.h>
#define gc getchar()
#define N 50009
#define mid (l+r>>1)
#define ll long long
using namespace std;
int n,dp[N],ans,bit[N],len,DP[N];
double sum=0.0,g[N],G[N],bit_g[N];
vector<int> q;
struct node
{
	int x,y,pd,pos;
	bool operator <(const node &rhs) const
	{
		return x<rhs.x||(x==rhs.x&&y<rhs.y)||(x==rhs.x&&y==rhs.y&&pd);
	}
}p[N],now[N],P[N];
int read()
{
	int x=1;
	char ch;
	while (ch=gc,ch<'0'||ch>'9') if (ch=='-') x=-1;
	int s=ch-'0';
	while (ch=gc,ch<='9'&&ch>='0') s=s*10+ch-'0';
	return s*x;
}
int lowbit(int x)
{
	return x&(-x);
}
void ins(int x,int y,double z)
{
	for (;x<=n;x+=lowbit(x))
		if (bit[x]==y) bit_g[x]+=z;
		else if (bit[x]<y) bit[x]=y,bit_g[x]=z;
}
void back(int x)
{
	for (;x<=n;x+=lowbit(x)) bit[x]=bit_g[x]=0;
}
int qry(int x,double &sum,int ret=0)
{
	for (;x;x-=lowbit(x))
		if (ret==bit[x]) sum+=bit_g[x];
		else if (ret<bit[x]) ret=bit[x],sum=bit_g[x];
	return ret;
}
void solve(int l,int r)
{
	if (l==r)
	{
		if (!dp[l]) dp[l]=g[l]=1;
		return;
	}
	solve(l,mid);
	int m=0;
	for (int i=l;i<=r;i++) now[++m]=p[i],now[m].pd=(i<=mid),now[m].pos=i;
	sort(now+1,now+m+1);
	for (int i=1;i<=m;i++)
		if (now[i].pd) ins(now[i].y,dp[now[i].pos],g[now[i].pos]);
		else
		{
			double now_sum=0;
			int now_ans=qry(now[i].y,now_sum)+1;
			if (now_ans==1) continue;
			if (now_ans>dp[now[i].pos])
				dp[now[i].pos]=now_ans,g[now[i].pos]=now_sum;
			else
				if (now_ans==dp[now[i].pos])
					g[now[i].pos]+=now_sum;
		}
	for (int i=1;i<=m;i++)
		if (now[i].pd) back(now[i].y);
	solve(mid+1,r);
}
void SOLVE(int l,int r)
{
	if (l==r)
	{
		if (!DP[l]) DP[l]=G[l]=1;
		return;
	}
	SOLVE(l,mid);
	int m=0;
	for (int i=l;i<=r;i++) now[++m]=P[i],now[m].pd=(i<=mid),now[m].pos=i;
	sort(now+1,now+m+1);
	for (int i=1;i<=m;i++)
		if (now[i].pd) ins(now[i].y,DP[now[i].pos],G[now[i].pos]);
		else
		{
			double now_sum=0;
			int now_ans=qry(now[i].y,now_sum)+1;
			if (now_ans==1) continue;
			if (now_ans>DP[now[i].pos])
				DP[now[i].pos]=now_ans,G[now[i].pos]=now_sum;
			else
				if (now_ans==DP[now[i].pos])
					G[now[i].pos]+=now_sum;
		}
	for (int i=1;i<=m;i++)
		if (now[i].pd) back(now[i].y);
	SOLVE(mid+1,r);
}
int main()
{
	n=read();
	for (int i=n;i>=1;i--) p[i].x=read(),p[i].y=read(),q.push_back(p[i].y);
	sort(q.begin(),q.end());
	len=unique(q.begin(),q.end())-q.begin();
	for (int i=1;i<=n;i++)
		p[i].y=lower_bound(q.begin(),q.end(),p[i].y)-q.begin()+1;
	solve(1,n);
	for (int i=1;i<=n;i++) ans=max(ans,dp[i]);
	for (int i=1;i<=n;i++)
		if (ans==dp[i]) sum+=g[i]*G[n-i+1];
	for (int i=1;i<=n;i++) P[i]=p[n-i+1],P[i].x=-P[i].x,P[i].y=n-P[i].y+1;
	//for (int i=1;i<=n;i++) cout<<P[i].x<<" "<<P[i].y<<endl;
	SOLVE(1,n);
	//for (int i=1;i<=n;i++) cout<<G[i]<<endl;
	printf("%d\n",ans);
	for (int i=1;i<=n;i++)
		if (dp[n-i+1]+DP[i]==ans+1)
			printf("%.5lf%s",g[n-i+1]*G[i]/sum,i==n?"\n":" ");
		else
			printf("%.5lf%s",0.0,i==n?"\n":" ");
	return 0;
}