2015
09-17

# Shaolin

Time Limit: 3000/1000 MS (Java/Others)    Memory Limit: 65535/32768 K (Java/Others)
Total Submission(s): 1945    Accepted Submission(s): 836

Problem Description
Shaolin temple is very famous for its Kongfu monks.A lot of young men go to Shaolin temple every year, trying to be a monk there. The master of Shaolin evaluates a young man mainly by his talent on understanding the Buddism scripture,
but fighting skill is also taken into account.
When a young man passes all the tests and is declared a new monk of Shaolin, there will be a fight , as a part of the welcome party. Every monk has an unique id and a unique fighting grade, which are all integers. The new monk must fight with a old monk whose
fighting grade is closest to his fighting grade. If there are two old monks satisfying that condition, the new monk will take the one whose fighting grade is less than his.
The master is the first monk in Shaolin, his id is 1，and his fighting grade is 1,000,000,000.He just lost the fighting records. But he still remembers who joined Shaolin earlier, who joined later. Please recover the fighting records for him.

Input
There are several test cases.
In each test case:
The first line is a integer n (0 <n <=100,000),meaning the number of monks who joined Shaolin after the master did.(The master is not included).Then n lines follow. Each line has two integer k and g, meaning a monk’s id and his fighting grade.( 0<= k ,g<=5,000,000)
The monks are listed by ascending order of jointing time.In other words, monks who joined Shaolin earlier come first.
The input ends with n = 0.

Output
A fight can be described as two ids of the monks who make that fight. For each test case, output all fights by the ascending order of happening time. Each fight in a line. For each fight, print the new monk’s id first ,then the old
monk’s id.

Sample Input
3
2 1
3 3
4 2
0

Sample Output
2 1
3 2
4 2

#include<iostream>
#include<cmath>
#include<cstring>
#include<ctime>
#include<cstdlib>
#include<cstdio>
using namespace std;
struct Node
{
Node* son[2];
int rank;
int size;
int key;
bool operator<(const Node &a)const
{
return rank<a.rank;   //重载小于好，用于维护堆的性质
}
int cmp(int x)const
{
if(x==key) return -1;    //比较函数，用于确定寻找的值的位置，0表示左儿子，1表示右儿子，-1代表当前节点
return x<key?0:1;
}
void maintain()//这里仅仅需要维护size
{
size = 1 + son[0]->size + son[1]->size;
}
};
struct Treap
{
Node * root;
Node *null = new Node();//定义空结点，可以有效避免NULL带来的问题
//初始化Treap
void initial()
{
srand(time(NULL));
root = null;
}
//旋转操作，d=0时代表左旋，d=1时代表右旋
void rotate(Node* &o,int d)
{
Node*  k = o->son[d^1];
o->son[d^1] = k -> son[d];
k->son[d] = o;
o->maintain();//注意，必须先维护o再维护k，因为o是子节点，不优先维护，会导致父节点出错
k->maintain();
o = k;
}
void ins(Node*  &o,int x)
{
if(o==null)
{
o = new Node();
o->son[0] = o->son[1] = null;
o->rank = rand();
o->key = x;
o->size = 1;
}
else
{
int d = o->cmp(x);
ins(o->son[d],x);
o->maintain();
if(o < o->son[d])
rotate(o,d^1);//当位于左儿子时，需要进行的是右旋，当位于右儿子时应当进行左旋，因此通项为rotate(o,d^1)
}
}
void del(Node* &o,int x)
{
int d = o->cmp(x);
if(d==-1)//已经找到待删除节点，将会有两种情况
{
if(o->son[0] == null) o = o->son[1];//左儿子为空，直接连接父节点和右儿子
else if(o->son[1] == null) o= o->son[0];//右儿子为空，同上
else
{
d = o->son[0] < o->son[1] ? 0:1;//在子节点中找到一个rank大的节点，将其旋转到当前节点，那么当前节点应当位于相反的子节点
rotate(o,d);
del(o->son[d],x);
}
}
else
del(o->son[d],x);
if(o!=null) o->maintain();//删除节点后，需要对size进行维护。需要注意的是，如果节点为空时，就不需要维护了
}
int kth(Node* o,int k)//寻找第k大数
{
if(o == null || k<=0 || k>o->size) return -1;//k过大或者过小都不能找到，Treap中没有节点也无需找
int s = (o->son[1] == null?0:o->son[1]->size);//获得右儿子的size
if(k == s+1) return o->key;//当k为 s + 1时，说明当前节点就是答案
else
if(k<=s) return kth(o->son[1],k);//当k<s时，说明第k大数在右子树，k值无需更改
else
return kth(o->son[0],k-s-1);//当k>s+1时，第k大数在左子树，需要减去右子树的值和节点本身
}
int find(Node* o,int k)//返回该数是第几大
{
if(o == null) return -1;
int d = o->cmp(k);
if(d == -1) return 1 + o->son[1]->size;
else if(d == 1) return find(o->son[d],k);
else
{
int tmp = find(o->son[d],k);
if(tmp == -1) return -1;
else
return tmp + 1 + o->son[1]->size;
}
}
} treap;
int id[5000005];
int main()
{
int n;
while(scanf("%d",&n)&&n)
{
treap.initial();
int x,y;
scanf("%d%d",&x,&y);
treap.ins(treap.root,y);
id[y] = x;
printf("%d %d\n",x,1);
for(int i =2;i<=n;i++)
{
scanf("%d%d",&x,&y);
id[y] = x;
treap.ins(treap.root,y);
int t = treap.find(treap.root,y);
int ans1,ans2,ans;
ans1 = treap.kth(treap.root,t-1);
ans2 = treap.kth(treap.root,t+1);
if(ans1 != -1)
{
if(ans2==-1) ans = ans1;
else
if(ans1 - y >= y-ans2) ans = ans2; else ans = ans1;
}
else
ans =ans2;
printf("%d %d\n",x,id[ans]);
}
}
return 0;
}