2013
11-09

# 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.

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.

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.

2
6
4 5 6 6 6 6
9
4 6 6 6 6 8 9 9 9


1 1 1 4 5 6
1 1 2 4 5 1 1 3 9

import java.util.Scanner;

public class Main {

int t;
int len;
int[] p;
int[] w;
String[] s;
int index;
int temp;
int pos;

public Main() {
Scanner scan = new Scanner(System.in);
t = scan.nextInt();
for (int i = 0; i < t; i++) {
len = scan.nextInt();
p = new int[len];
w = new int[len];
s = new String[len * 2];
for (int j = 0; j < len; j++) {
p[j] = scan.nextInt();
}
pos = 0;
temp = 0;
index = 0;
for (int k = 0; k < len; k++) {
for (; pos < p[k]; pos++) {
s[index++] = "(";
}
s[index++] = ")";
}
search();
for (int m = 0; m < len; m++) {
System.out.print(w[m] + " ");
}
System.out.println();
}
}

public void search() {
pos = 0;
int k = 0;
for (int i = 0; i < len; i++) {
for (; k < 2 * len; k++) {
if (s[k].equals(")")) {
pos = k;
k++;
break;
}
}
temp = 0;
index = 1;
for (int j = pos - 1;; j--) {
if (s[j].equals("(")) {
temp++;
index--;
} else {
index++;
}
if (index == 0) {
w[i] = temp;
break;
}
}
}
}

public static void main(String[] args) {
new Main();
}
}