POJ 2955 Brackets （区间DP）

#include<stdio.h>
#include<string.h>
#include<algorithm>
using namespace std;
char a[105];
int dp[105][105];
int main()
{
while(~scanf("%s",a))
{
if(a[0]=='e')  return 0;
memset(dp,0,sizeof(dp));
int n=strlen(a);
for(int i=1;i<n;i++)
{
for(int l=0;i+l<n;l++)
{
int r=i+l;
if((a[l]=='('&&a[r]==')'&&r-l==1)||(a[l]=='['&&a[r]==']'&&r-l==1))
{
dp[l][r]=2;
}
else if((a[l]=='('&&a[r]==')'&&r-l>1)||(a[l]=='['&&a[r]==']'&&r-l>1))
{
dp[l][r]=max(dp[l][r],dp[l+1][r-1]+2);
}
for(int k=l;k<=r;k++)
{
dp[l][r]=max(dp[l][r],dp[l][k]+dp[k][r]);
}
}
}
printf("%d\n",dp[0][n-1]);
}
}

Brackets
Time Limit:1000MS     Memory Limit:65536KB     64bit IO Format:%lld
& %llu
Submit Status Practice POJ
2955

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