6.H - Parencodings

Let S = s1 s2...s2n be a well-formed string of parentheses. S can be encoded in two different ways:
q By an integer sequence P = p1 p2...pn where pi is the number of left parentheses before the ith right parenthesis in S (P-sequence).
q By an integer sequence W = w1 w2...wn where for each right parenthesis, say a in S, we associate an integer which is the number of right parentheses counting from the matched left parenthesis of a up to a. (W-sequence).

Following is an example of the above encodings:

	S		(((()()())))

	P-sequence	    4 5 6666

	W-sequence	    1 1 1456

Write a program to convert P-sequence of a well-formed string to the W-sequence of the same string.

Input

The first line of the input contains a single integer t (1 <= t <= 10), the number of test cases, followed by the input data for each test case. The first line of each test case is an integer n (1 <= n <= 20), and the second line is the P-sequence of a well-formed string. It contains n positive integers, separated with blanks, representing the P-sequence.

Output

The output file consists of exactly t lines corresponding to test cases. For each test case, the output line should contain n integers describing the W-sequence of the string corresponding to its given P-sequence.

#include<iostream>
#include<string.h>
#define endl '\n'
using namespace std;
const int N = 107;
char s[N];
int p[N];
int right1[N];
int main()
{
	ios::sync_with_stdio(0);cin.tie(0);cout.tie(0);
	int t;
	cin >> t;
	while (t--)
	{
		int n;
		cin >> n;
		memset(s, '(', sizeof(s));
		for (int i = 1;i <= n;i++)
		{
			cin >> p[i];
			if (i == 1) right1[i] = p[i] + 1;
			else
			{
				right1[i] = right1[i - 1] + p[i] - p[i - 1] + 1;
			}
		}
		for (int i = 1;i <= n;i++)
		{
			s[right1[i]] = ')';
		}
		int lp = 0, rp = 0;
		for (int i = 1;i <= n;i++)
		{
			for (int j = right1[i];j >= 1;j--)
			{
				if (s[j] == '(') lp++;
				if (s[j] == ')') rp++;
				if (lp == rp)
				{
					cout << lp << ' ';
					lp = 0;
					rp = 0;
					break;
				}
			}
		}
		cout << endl;
	}
	return 0;
}