Title: BZOJ1500, Luogu P2042, Vijos P1835, codevs1758.
The gist of the title:
Give you a sequence of numbers and implement the following operations.
Problem- solving idea:
The non-rotating Treap can maintain the sequence.
The first five are basic balanced tree sequence operations (the fifth one can maintain an interval sum).
The sixth requires the maximum sub-segment sum, then we need to maintain the sub-segment sum with the current node as the sub-tree, the maximum prefix sum and the maximum suffix sum of the current sub-tree, in order to transfer the correct maximum sub-segment sum. (See the code for details on how to maintain it.)
For the rotation operation, the prefix and suffix need to be exchanged.
Also note:
1. The memory cannot be too large, MLE will be used, and the deleted nodes must be reclaimed.
2. Do not merge one by one when inserting, first build the tree according to the Cartesian tree building method (O(n)), and then merge the roots directly.
C++ Code：
#include<bits/stdc++.h>
inline int max(int a,int b){return a>b?a:b;}
inline void swap(int& a,int& b){int c=a;a=b,b=c;}
inline int readint(){
int c=getchar(),d=0,b=0;
for(;!isdigit(c);c=getchar())b=c=='-';
for(;isdigit(c);c=getchar())d=(d<<3)+(d<<1)+(c^'0');
return b?-d:d;
}
struct node{
int ls,rs,s,lm,rm,sm,smx,rot,r,tag,sz;
inline void Cng(int val){
s=val;
sm=sz*val;
lm=rm=max(sm,0);
smx=max(sm,s);
tag=1;
}
inline void rev(){
swap(ls,rs);
swap(lm,rm);
rot^=1;
}
}a[500005];
struct Memory_pool{
int p[500005],top;
Memory_pool(){
for(int i=1;i<=500004;++i)p[i]=i;
top=500004;
}
inline int New(){return p[top--];}
inline void Del(int x){p[++top]=x;}
}P;
int n,m,rt,sta[500005],top=0;
inline void pushdown(int x){
if(a[x].rot){
a[x].rot=0;
if(a[x].ls)a[a[x].ls].rev();
if(a[x].rs)a[a[x].rs].rev();
}
if(a[x].tag){
a[x].tag=0;
if(a[x].ls)a[a[x].ls].Cng(a[x].s);
if(a[x].rs)a[a[x].rs].Cng(a[x].s);
}
}
inline void update(int x){
int ls=a[x].ls,rs=a[x].rs,s=a[x].s;
if(ls&&rs){
a [x] .sz = a [ls] .sz + a [rs] .sz + 1;
a[x].sm=a[ls].sm+a[rs].sm+s;
a[x].smx=max(a[ls].smx,a[rs].smx);
a[x].smx=max(a[x].smx,a[ls].rm+s+a[rs].lm);
a[x].lm=max(a[ls].lm,a[ls].sm+s+a[rs].lm);
a[x].rm=max(a[rs].rm,a[rs].sm+s+a[ls].rm);
}else
if(ls){
a [x] .sz = a [ls] .sz + 1;
a[x].sm=a[ls].sm+s;
a[x].smx=max(a[ls].smx,a[ls].rm+s);
a[x].lm=max(a[ls].lm,a[ls].sm+s);
a[x].rm=max(a[ls].rm+s,0);
}else
if(rs){
a[x].sz=a[rs].sz+1;
a[x].sm=a[rs].sm+s;
a[x].smx=max(a[rs].smx,a[rs].lm+s);
a[x].rm=max(a[rs].rm,a[rs].sm+s);
a[x].lm=max(a[rs].lm+s,0);
}else{
a[x].sz=1;
a[x].sm=a[x].smx=s;
a[x].lm=a[x].rm=max(s,0);
}
}
int build(int n){
int x,pre;
for(int i=1;i<=n;++i){
int f=readint();
int ff=max(f,0);
a[x=P.New()]=(node){0,0,f,ff,ff,f,f,0,rand(),0,1};
for(pre=0;top&&a[sta[top]].r>a[x].r;--top)update(pre=sta[top]);
if(top)a[sta[top]].rs=x;
a[sta[++top]=x].ls=pre;
}
while(top)update(sta[top--]);
return sta[1];
}
void split(int u,int k,int& x,int& y){
if(!k){
x=0,y=u;
return;
}
if(k==a[u].sz){
x=u,y=0;
return;
}
pushdown(u);
if(a[a[u].ls].sz>=k)split(a[u].ls,k,x,a[u].ls),y=u;else
split(a[u].rs,k-a[a[u].ls].sz-1,a[u].rs,y),x=u;
update(u);
}
int merge(int x,int y){
if(x)pushdown(x);
if(y)pushdown(y);
if(!x||!y)return x|y;
if(a[x].r<a[y].r){
a[x].rs=merge(a[x].rs,y);
update(x);
return x;
}
a[y].ls=merge(x,a[y].ls);
update(y);
return y;
}
void dispose(int now){
if(!now)return;
dispose(a[now].ls);
dispose(a[now].rs);
P.Del(now);
}
int main(){
n=readint(),m=readint();
a[0]=(node){0,0,0,0,0,0,0,0,0,0,0};
srand(20170607);
rt=build(n);
while(m--){
static char s[100];
you are everything;
scanf("%s",s);
if(s[0]=='I'){
tot=readint();int rtn=build(readint()),x,y;
split (rt, tot, x, y);
rt = merge (merge (x, rtn), y);
}else
if(s[0]=='D'){
tot=readint(),n=readint();
int x,y,z;
split (rt, tot-1, x, y);
split(y,n,y,z);
dispose(y);
rt=merge(x,z);
}else
if(s[0]=='M'&&s[2]=='K'){
tot=readint(),n=readint();
int x,y,z;
split (rt, tot-1, x, y);
split(y,n,y,z);
a[y].Cng(readint());
rt = merge (merge (x, y), z);
}else
if(s[0]=='R'){
tot=readint(),n=readint();
int x,y,z;
split (rt, tot-1, x, y);
split(y,n,y,z);
a[y].rev();
rt = merge (merge (x, y), z);
}else
if(s[0]=='G'){
tot=readint(),n=readint();
int x,y,z;
split (rt, tot-1, x, y);
split(y,n,y,z);
printf("%d\n",a[y].sm);
rt = merge (merge (x, y), z);
}else printf("%d\n",a[rt].smx);
}
return 0;
}