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Description
We give the following inductive definition of 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
Source
1 #include<iostream> 2 #include<cstdio> 3 #include<cstring> 4 #include<vector> 5 #include<set> 6 #include<algorithm> 7 #include<cmath> 8 #include<stdlib.h> 9 #include<map> 10 using namespace std; 11 #define N 106 12 #define inf 1<<26 13 int n; 14 char s[N]; 15 int dp[N][N]; 16 bool check(int x,int y) 17 { 18 if(s[x]==‘(‘ && s[y]==‘)‘) 19 return true; 20 if(s[x]==‘[‘ && s[y]==‘]‘) 21 return true; 22 return false; 23 } 24 int main() 25 { 26 while(scanf("%s",s) && s[0]!=‘e‘) 27 { 28 n=strlen(s); 29 //for(int i=1;i<=n;i++) 30 // printf("---%c",s[i]); 31 32 memset(dp,0,sizeof(dp)); 33 for(int i=0;i<n;i++) 34 { 35 if(check(i,i+1)) 36 dp[i][i+1]=2; 37 } 38 for(int len=1;len<n;len++) 39 { 40 for(int i=0;i+len<n;i++) 41 { 42 int j=i+len; 43 if(check(i,j)) 44 dp[i][j]=dp[i+1][j-1]+2; 45 for(int k=i;k<=j;k++) 46 { 47 dp[i][j]=max(dp[i][j],dp[i][k]+dp[k+1][j]); 48 } 49 } 50 } 51 printf("%d\n",dp[0][n-1]); 52 53 } 54 return 0; 55 }
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原文地址：http://www.cnblogs.com/UniqueColor/p/4731375.html
