[TJOI2013]最长上升子序列

题目大意：

给定一个序列，初始为空。将\(1\sim n(n\le10^5)\)的数字插入到序列中，每次将一个数字插入到一个特定的位置。每插入一个数字后输出LIS长度。

思路：

首先用线段树（或rope）求出最终状态的序列，然后就变成了普通的LIS问题。

源代码：

线段树：

#include<cstdio>
#include<cctype>
#include<algorithm>
inline int getint() {register char ch;while(!isdigit(ch=getchar()));register int x=ch^'0';while(isdigit(ch=getchar())) x=(((x<<2)+x)<<1)+(ch^'0');return x;
}
const int N=1e5+1;
int n,p[N];
class SegmentTree {#define _left <<1#define _right <<1|1#define mid ((b+e)>>1)private:int val[N<<2];void push_up(const int &p) {val[p]=val[p _left]+val[p _right];}public:int find(const int &p,const int &b,const int &e,const int &x) {if(b==e) return x==b-val[p]?b:0;if(mid-val[p _left]<=x) {const int ret=find(p _right,mid+1,e,x+val[p _left]);if(ret) return ret;}return find(p _left,b,mid,x);}void add(const int &p,const int &b,const int &e,const int &x) {val[p]++;if(b==e) return;if(x<=mid) add(p _left,b,mid,x);if(x>mid) add(p _right,mid+1,e,x);push_up(p);}#undef _left#undef _right#undef mid
};
SegmentTree sgt;
class FenwickTree {private:int val[N];int lowbit(const int &x) const {return x&-x;}public:void modify(int p,const int &x) {for(;p<=n;p+=lowbit(p)) {val[p]=std::max(val[p],x);}}int query(int p) const {int ret=0;for(;p;p-=lowbit(p)) {ret=std::max(ret,val[p]);}return ret;}
};
FenwickTree bit;
int main() {n=getint();for(register int i=1;i<=n;i++) {p[i]=getint();}for(register int i=n;i>=1;i--) {p[i]=sgt.find(1,1,n,p[i])+1;sgt.add(1,1,n,p[i]);}int ans=0;for(register int i=1;i<=n;i++) {const int tmp=bit.query(p[i])+1;bit.modify(p[i],tmp);ans=std::max(ans,tmp);printf("%d\n",ans);}return 0;
}

rope：

#include<cstdio>
#include<cctype>
#include<ext/rope>
inline int getint() {register char ch;while(!isdigit(ch=getchar()));register int x=ch^'0';while(isdigit(ch=getchar())) x=(((x<<2)+x)<<1)+(ch^'0');return x;
}
const int N=1e5+1;
int n,ans[N];
__gnu_cxx::rope<int> s;
class FenwickTree {private:int val[N];int lowbit(const int &x) const {return x&-x;}public:void modify(int p,const int &x) {for(;p<=n;p+=lowbit(p)) {val[p]=std::max(val[p],x);}}int query(int p) const {int ret=0;for(;p;p-=lowbit(p)) {ret=std::max(ret,val[p]);}return ret;}
};
FenwickTree bit;
int main() {n=getint();for(register int i=1;i<=n;i++) {s.insert(getint(),i);}for(register int i=0;i<n;i++) {ans[s[i]]=bit.query(s[i])+1;bit.modify(s[i],ans[s[i]]);}for(register int i=1;i<=n;i++) {ans[i]=std::max(ans[i-1],ans[i]);printf("%d\n",ans[i]);}return 0;
}