Read the statement of problem G for the definitions concerning trees. In the following we define the basic terminology of heaps. A heap is a tree whose internal nodes have each assigned a priority (a number) such that the priority of each internal node is less than the priority of its parent. As a consequence, the root has the greatest priority in the tree, which is one of the reasons why heaps can be used for the implementation of priority queues and for sorting.
A binary tree in which each internal node has both a label and a priority, and which is both a binary search tree with respect to the labels and a heap with respect to the priorities, is called a treap. Your task is, given a set of label-priority-pairs, with unique labels and unique priorities, to construct a treap containing this data.
Input
The input contains several test cases. Every test case starts with an integer n. You may assume that 1<=n<=50000. Then follow n pairs of strings and numbers l1/p1,...,ln/pn denoting the label and priority of each node. The strings are non-empty and composed of lower-case letters, and the numbers are non-negative integers. The last test case is followed by a zero.
Output
For each test case output on a single line a treap that contains the specified nodes. A treap is printed as (< left sub-treap >< label >/< priority >< right sub-treap >). The sub-treaps are printed recursively, and omitted if leafs.
Sample Input
7 a/7 b/6 c/5 d/4 e/3 f/2 g/1
7 a/1 b/2 c/3 d/4 e/5 f/6 g/7
7 a/3 b/6 c/4 d/7 e/2 f/5 g/1
0
Sample Output
(a/7(b/6(c/5(d/4(e/3(f/2(g/1)))))))
(((((((a/1)b/2)c/3)d/4)e/5)f/6)g/7)
(((a/3)b/6(c/4))d/7((e/2)f/5(g/1)))
#include<iostream>
#include<algorithm>
#include<cstring>
using namespace std;
const int inf=0x3f3f3f3f;
const int N=1e5+10;
struct node{
char s[110];
int v,l,r,f;
}t[N];
int cmp(node x,node y){
return strcmp(x.s,y.s)<0;
}
void insert(int x){
int d=x-1;
while(t[d].v<t[x].v)d=t[d].f;
t[x].l=t[d].r;
t[t[x].l].f=x;
t[x].f=d;
t[d].r=x;
}
void print(int x){
if(!x)return;
putchar('(');
print(t[x].l);
printf("%s/%d",t[x].s,t[x].v);
print(t[x].r);
putchar(')');
}
int main(){
int n;
while(scanf("%d",&n),n){
for(int i=1;i<=n;i++)
scanf(" %[a-z]/%d",t[i].s,&t[i].v);
sort(t+1,t+n+1,cmp);
t[0].v=inf;
t[0].l=t[0].r=t[0].f=0;
for(int i=1;i<=n;i++){
t[i].l=t[i].r=t[i].f=0;
insert(i);
/*
printf("i:%d\n",i);
printf("i r l f v s\n");
for(int j=0;j<=n;j++){
printf("%d %d %d %d %d %s\n",j,t[j].r,t[j].l,t[j].f,t[j].v,t[j].s);
}
*/
}
print(t[0].r);
putchar('\n');
}
}
