[ACM] POJ 1068 Parencodings(模拟）

Parencodings

Time Limit: 1000MS		Memory Limit: 10000K
Total Submissions: 19352		Accepted: 11675

Description

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.

Sample Input

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

Sample Output

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

Source

Tehran 2001

解题思路：

题意为给一个只包含括号的字符串加密有两种方法：

方法一：用p数组表示，p[i]为第i个右括号左边一共有多少左括号

方法二：用w数组表示，w[i]表示当第i个括号左右匹配时，一共包括多少右括号

要求给定加密后的p数组，求出w数组。

可以根据给的p数组先求出字符串s， p[i]-p[i-1]为第i个右括号紧跟在它前面的有多少个左括号，求出s

遍历s，每次找到右括号，然后回溯，遇到右括号就计数（回溯前找到的那个也算），直到遇到与它匹配的左括号（vis[]=0)，因为一个右括号有唯一的左括号匹配，所以一旦找到它的左括号，就用vis[]=1标记下。

代码：

[cpp]  view plain  copy

1. #include <iostream>  
2. #include <string.h>  
3. #include <algorithm>  
4. using namespace std;  
5.   
6. int p[20],w[20];  
7. bool vis[40];//注意范围，题目中n<=20是n对括号，不是单个括号的个数.  
8.   
9. int main()  
10. {  
11.     int t;cin>>t;  
12.     int n;  
13.     while(t--)  
14.     {  
15.         string s;  
16.         cin>>n;  
17.         for(int i=1;i<=n;i++)  
18.             cin>>p[i];  
19.         p[0]=0;  
20.         for(int i=1;i<=n;i++)//构造s串  
21.         {  
22.             for(int j=1;j<=(p[i]-p[i-1]);j++)  
23.                 s+="(";  
24.             s+=")";  
25.         }  
26.         int k=1;  
27.         memset(vis,0,sizeof(vis));  
28.         for(int i=0;i<2*n;i++)  
29.         {  
30.             int cnt=1;  
31.             if(s[i]==')')//遇到右括号  
32.             {  
33.                 for(int j=i-1;j>=0;j--)//回溯  
34.                 {  
35.                     if(s[j]==')')  
36.                         cnt++;  
37.                     if(s[j]=='('&&!vis[j])//和小括号匹配  
38.                     {  
39.                         vis[j]=1;  
40.                         break;  
41.                     }  
42.                 }  
43.                 w[k++]=cnt;  
44.             }  
45.         }  
46.         for(int i=1;i<=n;i++)  
47.             cout<<w[i]<<" ";  
48.         cout<<endl;  
49.     }  
50.     return 0;  
51. }