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2015 HUAS Summer Trainning #5~J

时间:2015-08-12 21:36:29      阅读:102      评论:0      收藏:0      [点我收藏+]

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Description

We give the following inductive definition of a “regular brackets” sequence:

  • the empty sequence is a regular brackets sequence,
  • if s is a regular brackets sequence, then (s) and [s] are regular brackets sequences, and
  • if a and b are regular brackets sequences, then ab is a regular brackets sequence.
  • no other sequence is a regular brackets sequence

For instance, all of the following character sequences are regular brackets sequences:

(), [], (()), ()[], ()[()]

while the following character sequences are not:

(, ], )(, ([)], ([(]

Given a brackets sequence of characters a1a2 … an, your goal is to find the length of the longest regular brackets sequence that is a subsequence of s. That is, you wish to find the largest m such that for indices i1, i2, …, im where 1 ≤ i1 < i2 < … < im ≤ n, ai1ai2 … aim is a regular brackets sequence.

Given the initial sequence ([([]])], the longest regular brackets subsequence is [([])].

Input

The input test file will contain multiple test cases. Each input test case consists of a single line containing only the characters (, ), [, and ]; each input test will have length between 1 and 100, inclusive. The end-of-file is marked by a line containing the word “end” and should not be processed.

Output

For each input case, the program should print the length of the longest possible regular brackets subsequence on a single line.

Sample Input

((()))
()()()
([]])
)[)(
([][][)
end

Sample Output

6
6
4
0
6

解题思路:题目的意思是在输入的字符串中寻找有多少对括号匹配,并输出它们的个数。需要注意的是,这个问题不能用顺序解决,因为这是两种括号的匹配问题,会出现交叉情况,之前也用过的队列解决过。
程序代码:

#include <stdio.h> 
#include <string.h> 
#include <algorithm> 
using namespace std; 

int max(int x,int y)
{
 if(x>y) return x;
 else return y;
}

int check(char a,char b) 

    if(a==‘(‘ && b==‘)‘) 
        return 1; 
    if(a==‘[‘ && b==‘]‘) 
        return 1; 
    return 0; 

 
int main() 

    char str[105]; 
    int dp[105][105],i,j,k,len; 
    while(scanf("%s",str)) 
    { 
        if(!strcmp(str,"end")) 
            break; 
        len = strlen(str); 
        for(i = 0; i<len; i++) 
        { 
            dp[i][i] = 0;
            if(check(str[i],str[i+1])) 
  dp[i][i+1] = 2;
            else 
   dp[i][i+1] = 0;
        } 
        for(k = 3; k<=len; k++) 
        {
            for(i = 0; i+k-1<len; i++) 
            { 
   dp[i][i+k-1] = 0;
                if(check(str[i],str[i+k-1])) 
     dp[i][i+k-1] = dp[i+1][i+k-2]+2;
                for(j = i; j<i+k-1; j++) 
    
     dp[i][i+k-1] = max(dp[i][i+k-1],dp[i][j]+dp[j+1][i+k-1]);
            } 
        } 
        printf("%d\n",dp[0][len-1]); 
    } 
 
    return 0; 
}

2015 HUAS Summer Trainning #5~J

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原文地址:http://www.cnblogs.com/chenchunhui/p/4725434.html

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