poj 1141 Brackets Sequence(区间DP，求最小，输出路径，较难)
1、http://poj.org/problem?id=1141
2、题目大意
给出一个字符串，只包含()[]四种符号，添加最少的符号使得该字符串有序，跟前面做的括号的问题类似，上次是求字符串中有规律的子串的最长长度，这次是求最少添加多少字符使得有序，并且输出最终有序的字符串来
dp[i][j]表示i到j区间内字符有序添加的最小值，
if(s[i]==s[j]) dp[i][j]=dp[i+1][j-1]
else
dp[i][j]=min(dp[i][j],dp[i][k]+dp[k+1][j])
3、AC代码：
#include<stdio.h>
#include<string.h>
#include<algorithm>
using namespace std;
#define N 105
char s[N];
int dp[N][N];
int v[N][N];
int check(char a,char b)
{
if(a=='(' && b==')')
return 1;
if(a=='[' && b==']')
return 1;
return 0;
}
void output(int l,int r)
{
if(l>r)
return ;
if(l==r)
{
if(s[l]=='(' || s[l]==')')
printf("()");
else
printf("[]");
return ;
}
if(v[l][r]==-1)
{
printf("%c",s[l]);
output(l+1,r-1);
printf("%c",s[r]);
return ;
}
output(l,v[l][r]);
output(v[l][r]+1,r);
}
int main()
{
//while(scanf("%s",s)!=EOF)
//{
//while多次输入wrong answer
scanf("%s",s);
int len=strlen(s);
memset(dp,-1,sizeof(dp));
memset(v,-1,sizeof(v));
for(int i=0; i<len; i++)
{
dp[i][i]=1;
dp[i+1][i]=0;
}
for(int i=1; i<len; i++)
{
for(int j=0; j+i<len; j++)
{
int e=j+i;
if(check(s[j],s[e]))
dp[j][e]=dp[j+1][e-1];
for(int k=j; k<e; k++)
{
if(dp[j][e]>dp[j][k]+dp[k+1][e] || dp[j][e]==-1)
{
v[j][e]=k;
dp[j][e]=dp[j][k]+dp[k+1][e];
}
}
}
}
output(0,len-1);
printf("\n");
//}
return 0;
}
4、题目：
Brackets Sequence
| Time Limit: 1000MS | Memory Limit: 65536K | |||
| Total Submissions: 23444 | Accepted: 6595 | Special Judge | ||
Description
Let us define a regular brackets sequence in the following way:
1. Empty sequence is a regular sequence.
2. If S is a regular sequence, then (S) and [S] are both regular sequences.
3. If A and B are regular sequences, then AB is a regular sequence.
For example, all of the following sequences of characters are regular brackets sequences:
(), [], (()), ([]), ()[], ()[()]
And all of the following character sequences are not:
(, [, ), )(, ([)], ([(]
Some sequence of characters '(', ')', '[', and ']' is given. You are to find the shortest possible regular brackets sequence, that contains the given character sequence as a subsequence. Here, a string a1 a2 ... an is called a subsequence of the string b1 b2 ... bm, if there exist such indices 1 = i1 < i2 < ... < in = m, that aj = bij for all 1 = j = n.
1. Empty sequence is a regular sequence.
2. If S is a regular sequence, then (S) and [S] are both regular sequences.
3. If A and B are regular sequences, then AB is a regular sequence.
For example, all of the following sequences of characters are regular brackets sequences:
(), [], (()), ([]), ()[], ()[()]
And all of the following character sequences are not:
(, [, ), )(, ([)], ([(]
Some sequence of characters '(', ')', '[', and ']' is given. You are to find the shortest possible regular brackets sequence, that contains the given character sequence as a subsequence. Here, a string a1 a2 ... an is called a subsequence of the string b1 b2 ... bm, if there exist such indices 1 = i1 < i2 < ... < in = m, that aj = bij for all 1 = j = n.
Input
The input file contains at most 100 brackets (characters '(', ')', '[' and ']') that are situated on a single line without any other characters among them.
Output
Write to the output file a single line that contains some regular brackets sequence that has the minimal possible length and contains the given sequence as a subsequence.
Sample Input
([(]
Sample Output
()[()]
Source
Northeastern Europe 2001
Brackets Sequence
| Time Limit: 1000MS | Memory Limit: 65536K | |||
| Total Submissions: 23444 | Accepted: 6595 | Special Judge | ||
Description
Let us define a regular brackets sequence in the following way:
1. Empty sequence is a regular sequence.
2. If S is a regular sequence, then (S) and [S] are both regular sequences.
3. If A and B are regular sequences, then AB is a regular sequence.
For example, all of the following sequences of characters are regular brackets sequences:
(), [], (()), ([]), ()[], ()[()]
And all of the following character sequences are not:
(, [, ), )(, ([)], ([(]
Some sequence of characters '(', ')', '[', and ']' is given. You are to find the shortest possible regular brackets sequence, that contains the given character sequence as a subsequence. Here, a string a1 a2 ... an is called a subsequence of the string b1 b2 ... bm, if there exist such indices 1 = i1 < i2 < ... < in = m, that aj = bij for all 1 = j = n.
1. Empty sequence is a regular sequence.
2. If S is a regular sequence, then (S) and [S] are both regular sequences.
3. If A and B are regular sequences, then AB is a regular sequence.
For example, all of the following sequences of characters are regular brackets sequences:
(), [], (()), ([]), ()[], ()[()]
And all of the following character sequences are not:
(, [, ), )(, ([)], ([(]
Some sequence of characters '(', ')', '[', and ']' is given. You are to find the shortest possible regular brackets sequence, that contains the given character sequence as a subsequence. Here, a string a1 a2 ... an is called a subsequence of the string b1 b2 ... bm, if there exist such indices 1 = i1 < i2 < ... < in = m, that aj = bij for all 1 = j = n.
Input
The input file contains at most 100 brackets (characters '(', ')', '[' and ']') that are situated on a single line without any other characters among them.
Output
Write to the output file a single line that contains some regular brackets sequence that has the minimal possible length and contains the given sequence as a subsequence.
Sample Input
([(]
Sample Output
()[()]
Source
Northeastern Europe 2001