[SBT]POJ 2761 Feed the dogs
题目链接：http://poj.org/problem?id=2761
题意：给定一个序列，有N个数，给定M个询问，询问的形式为 a b c ，询问区间[a,b]内第c小的数。
解题方法：一次性读入所有的询问，然后把询问进行排序，排序的顺序为终点小的在前，终点一样，起点大的在前，然后对排序后的每个询问进行处理，每次保证SBT中只有区间[a,b]的数（用插入和删除操作来保证），然后查询第K小。
总结：注意旋转操作调整size域的顺序。 不能搞反。
代码：
#include<iostream>
#include<cstdio>
#include<algorithm>
#include<cstring>
using namespace std;
struct KEY
{
int wgt,num;
KEY(int w=0,int n=0):wgt(w),num(n){}
bool operator < (const KEY &k) const
{
if(wgt!=k.wgt)return wgt<k.wgt;
return num<k.num;
}
bool operator == (const KEY &k) const
{
return wgt==k.wgt&&num==k.num;
}
};
const int MAXN = 100010;
struct SBT
{
int l[MAXN],r[MAXN],pool[MAXN],size[MAXN],TOP,NODE,ROOT;
KEY Key[MAXN];
void init()
{
TOP = NODE = ROOT = 0;
size[0] = l[0] = r[0] = 0;
}
int newnode(KEY k)
{
int node;
if(TOP)node = pool[TOP--];
else node = ++NODE;
Key[node] = k;
size[node] = 1;
l[node] = r[node] = 0;
return node;
}
void delnode(int x)
{
pool[++TOP] = x;
Key[x].wgt = Key[x].num = size[x] = l[x] = r[x] = 0;
}
void left_rotate(int &p)
{
int x = r[p];
r[p] = l[x];
l[x] = p;
size[x] = size[p];
size[p] = size[l[p]]+size[r[p]]+1;
p = x;
}
void right_rotate(int &p)
{
int x = l[p];
l[p] = r[x];
r[x] = p;
size[x] = size[p];
size[p] = size[l[p]]+size[r[p]]+1;
p = x;
}
void Maintain(int &p,bool flag)
{
if(flag==0)
{
if(size[l[l[p]]]>size[r[p]])right_rotate(p);
else if(size[r[l[p]]]>size[r[p]])
{
left_rotate(l[p]);
right_rotate(p);
}
else return;
}
else
{
if(size[r[r[p]]]>size[l[p]])left_rotate(p);
else if(size[l[r[p]]]>size[l[p]])
{
right_rotate(r[p]);
left_rotate(p);
}
else return;
}
Maintain(l[p],0);
Maintain(r[p],1);
Maintain(p,1);
Maintain(p,0);
}
void insert(int &p,KEY k)
{
if(!p)
{
p = newnode(k);
return;
}
if(k<Key[p])insert(l[p],k);
else insert(r[p],k);
size[p] = size[l[p]]+size[r[p]]+1;
Maintain(p,!(k<Key[p]));
}
int findmin(int p)
{
if(l[p])return findmin(l[p]);
else return p;
}
void remove(int &p,KEY k)
{
if(p)
{
if(k==Key[p])
{
if(!l[p])
{
int x = p;
p = r[p];
delnode(x);
}
else if(!r[p])
{
int x = p;
p = l[p];
delnode(x);
}
else
{
int x = findmin(r[p]);
Key[p] = Key[x];
remove(r[p],Key[x]);
}
}
else if(k<Key[p])remove(l[p],k);
else remove(r[p],k);
if(p)
{
size[p] = size[l[p]]+size[r[p]]+1;
}
}
}
int Select(int p,int k)
{
int rank = size[l[p]]+1;
if(k==rank)return p;
else if(k<rank)return Select(l[p],k);
return Select(r[p],k-rank);
}
void print(int p)
{
if(!p)return ;
print(l[p]);
cout<<size[p]<<" "<<Key[p].wgt<<" "<<l[p]<<" "<<r[p]<<" "<<p<<" "<<(size[l[p]]+size[r[p]]+1)<<endl;
print(r[p]);
}
}sbt;
int arr[MAXN],res[50010];
struct Range
{
int a,b,c,num;
bool operator < (const Range &r) const
{
if(b!=r.b)return b<r.b;
else return a>r.a;
}
}R[50010];
int main()
{
int n,m;
while(scanf("%d%d",&n,&m)!=EOF)
{
int a,b;sbt.init();
for(int i=1;i<=n;i++)
{
scanf("%d",&arr[i]);
}
for(int i=1;i<=m;i++)
{
scanf("%d%d%d",&R[i].a,&R[i].b,&R[i].c);
R[i].num = i;
}
sort(R+1,R+m+1);a = R[1].a; b = R[1].b;
for(int i=a;i<=b;i++)
{
sbt.insert(sbt.ROOT,KEY(arr[i],i));
}
res[R[1].num] = sbt.Key[sbt.Select(sbt.ROOT,R[1].c)].wgt;
for(int i=2;i<=m;i++)
{
if(R[i].a<a)
{
for(int j=R[i].a;j<a;j++)
{
sbt.insert(sbt.ROOT,KEY(arr[j],j));
}
for(int j=b+1;j<=R[i].b;j++)
{
sbt.insert(sbt.ROOT,KEY(arr[j],j));
}
}
else if(R[i].a<b)
{
for(int j=a;j<R[i].a;j++){
sbt.remove(sbt.ROOT,KEY(arr[j],j));
}
for(int j=b+1;j<=R[i].b;j++){
sbt.insert(sbt.ROOT,KEY(arr[j],j));
}
}
else
{
for(int j=a;j<=b;j++){
sbt.remove(sbt.ROOT,KEY(arr[j],j));
}
for(int j=R[i].a;j<=R[i].b;j++){
sbt.insert(sbt.ROOT,KEY(arr[j],j));
}
}
a = R[i].a, b = R[i].b;
res[R[i].num] = sbt.Key[sbt.Select(sbt.ROOT,R[i].c)].wgt;
}
for(int i=1;i<=m;i++)printf("%d\n",res[i]);
}
return 0;
}