题目链接

只和区间相对位置有关，先离散化。时间点上倒序贪心，设 \(f_i\) 表示第 \(i\) 个时间点最多能选几个区间，\(g_i\) 表示在最大 \(f_i\) 的前提下转移过来最小的字典序标号，可以顺便记录前驱。区间右端点可以转移到左端点，将右端点的决策存在左端点上即可。转移只有两种，继承上一个时间点的答案，选择一个区间从右端点转移过来。于是做到 \(\mathcal O(n)\)。

#include<bits/stdc++.h>
#define ld long double
#define ui unsigned int
#define ull unsigned long long
#define int long long
#define eb emplace_back
#define pb pop_back
#define ins insert
#define mp make_pair
#define pii pair<int,int>
#define fi first
#define se second
#define power(x) ((x)*(x))
using namespace std;

namespace FastIO
{
    template<typename T=int> inline T read()
    {
        T s=0,w=1; char c=getchar();
        while(!isdigit(c)) {if(c=='-') w=-1; c=getchar();}
        while(isdigit(c)) s=(s*10)+(c^48),c=getchar();
        return s*w;
    }
    template<typename T> inline void read(T &s)
    {
        s=0; int w=1; char c=getchar();
        while(!isdigit(c)) {if(c=='-') w=-1; c=getchar();}
        while(isdigit(c)) s=(s*10)+(c^48),c=getchar();
        s=s*w;
    }
    template<typename T,typename... Args> inline void read(T &x,Args &...args)
    {
        read(x),read(args...);
    }
    template<typename T> inline void write(T x,char ch)
    {
        if(x<0) x=-x,putchar('-');
        static char stk[25]; int top=0;
        do {stk[top++]=x%10+'0',x/=10;} while(x);
        while(top) putchar(stk[--top]);
        if(ch!='~') putchar(ch);
        return;
    }
}
using namespace FastIO;

namespace MTool
{   
    #define TA template<typename T,typename... Args>
    #define TT template<typename T>
    static const int Mod=998244353;
    TT inline void Swp(T &a,T &b) {T t=a;a=b;b=t;}
    TT inline void cmax(T &a,T b) {a=max(a,b);}
    TT inline void cmin(T &a,T b) {a=min(a,b);}
    TA inline void cmax(T &a,T b,Args... args) {a=max({a,b,args...});}
    TA inline void cmin(T &a,T b,Args... args) {a=min({a,b,args...});}
    TT inline void Madd(T &a,T b) {a=a+b>=Mod?a+b-Mod:a+b;}
    TT inline void Mdel(T &a,T b) {a=a-b<0?a-b+Mod:a-b;}
    TT inline void Mmul(T &a,T b) {a=a*b%Mod;}
    TT inline void Mmod(T &a) {a=(a%Mod+Mod)%Mod;}
    TT inline T Cadd(T a,T b) {return a+b>=Mod?a+b-Mod:a+b;}
    TT inline T Cdel(T a,T b) {return a-b<0?a-b+Mod:a-b;}
    TT inline T Cmul(T a,T b) {return a*b%Mod;}
    TT inline T Cmod(T a) {return (a%Mod+Mod)%Mod;}
    TA inline void Madd(T &a,T b,Args... args) {Madd(a,Cadd(b,args...));}
    TA inline void Mdel(T &a,T b,Args... args) {Mdel(a,Cadd(b,args...));}
    TA inline void Mmul(T &a,T b,Args... args) {Mmul(a,Cmul(b,args...));}
    TA inline T Cadd(T a,T b,Args... args) {return Cadd(Cadd(a,b),args...);}
    TA inline T Cdel(T a,T b,Args... args) {return Cdel(Cdel(a,b),args...);}
    TA inline T Cmul(T a,T b,Args... args) {return Cmul(Cmul(a,b),args...);}
    TT inline T qpow(T a,T b) {int res=1; while(b) {if(b&1) Mmul(res,a); Mmul(a,a); b>>=1;} return res;}
    TT inline T qmul(T a,T b) {int res=0; while(b) {if(b&1) Madd(res,a); Madd(a,a); b>>=1;} return res;}
    TT inline T spow(T a,T b) {int res=1; while(b) {if(b&1) res=qmul(res,a); a=qmul(a,a); b>>=1;} return res;}
    TT inline void exgcd(T A,T B,T &X,T &Y) {if(!B) return X=1,Y=0,void(); exgcd(B,A%B,Y,X),Y-=X*(A/B);}
    TT inline T Ginv(T x) {T A=0,B=0; exgcd(x,Mod,A,B); return Cmod(A);}
    #undef TT
    #undef TA
}
using namespace MTool;

inline void file()
{
    freopen(".in","r",stdin);
    freopen(".out","w",stdout);
    return;
}

bool Mbe;

namespace LgxTpre
{
    static const int MAX=200010;
    static const int inf=2147483647;
    static const int INF=4557430888798830399;
    
    int n,l[MAX],r[MAX],d[MAX],cnt,now;
    int f[MAX],g[MAX],from[MAX];
    vector<pii> dec[MAX];
    
    inline void lmy_forever()
    {
    	read(n),memset(g,-1,sizeof g);
    	for(int i=1;i<=n;++i) read(l[i],r[i]),d[++cnt]=l[i],d[++cnt]=r[i];
    	sort(d+1,d+cnt+1),cnt=unique(d+1,d+cnt+1)-d-1;
    	for(int i=1;i<=n;++i) l[i]=lower_bound(d+1,d+cnt+1,l[i])-d,r[i]=lower_bound(d+1,d+cnt+1,r[i])-d,dec[l[i]].eb(mp(r[i],i));
    	for(int i=cnt;i;--i)
    	{
			for(auto [j,id]:dec[i])
			{
				if(f[i]<f[j]+1) f[i]=f[j]+1,g[i]=INF;
	    		if(f[i]==f[j]+1&&g[i]>id) g[i]=id,from[i]=j;
			}
	    	if(i!=cnt&&f[i]<f[i+1]) f[i]=f[i+1],g[i]=INF;
			if(i!=cnt&&f[i]==f[i+1]&&g[i]>g[i+1]) g[i]=g[i+1],from[i]=from[i+1];
		}
		write(f[1],'\n'),now=1,write(g[now],'~'),now=from[now];
		while(g[now]!=-1) putchar(' '),write(g[now],'~'),now=from[now];
		return puts(""),void();
	}
}

bool Med;

signed main()
{
//  file();
    fprintf(stderr,"%.3lf MB\n",abs(&Med-&Mbe)/1048576.0);
    int Tbe=clock();
    LgxTpre::lmy_forever();
    int Ted=clock();
    cerr<<1e3*(Ted-Tbe)/CLOCKS_PER_SEC<<" ms\n";
    return (0-0);
}