[ACM] POJ 1068 Parencodings(模拟）

Parencodings Time Limit: 1000MS Memory Limit: 10000KTotal 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 #include <iostream>   #include <string.h>   #include <algorithm>   using namespace std;      int p[20],w[20];   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.      int main()   {       int t;cin>>t;       int n;       while(t--)       {           string s;           cin>>n;           for(int i=1;i<=n;i++)               cin>>p[i];           p[0]=0;           for(int i=1;i<=n;i++)//构造s串           {               for(int j=1;j<=(p[i]-p[i-1]);j++)                   s+="(";               s+=")";           }           int k=1;           memset(vis,0,sizeof(vis));           for(int i=0;i<2*n;i++)           {               int cnt=1;               if(s[i]==')')//遇到右括号               {                   for(int j=i-1;j>=0;j--)//回溯                   {                       if(s[j]==')')                           cnt++;                       if(s[j]=='('&&!vis[j])//和小括号匹配                       {                           vis[j]=1;                           break;                       }                   }                   w[k++]=cnt;               }           }           for(int i=1;i<=n;i++)               cout<<w[i]<<" ";           cout<<endl;       }       return 0;   }