2004/2005 ACM International Collegiate Programming Contest
University of Ulm Local Contest

# Problem H: Binary Search Heap Construction

Source file: heap.(c|cc|hs|java|pas)
Input file: heap.in

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 Specification

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 Specification

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)))