HDU 1141---Brackets Sequence(区间DP)

题目链接

http://poj.org/problem?id=1141

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.

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

 
 
题意:给了一个括号序列(只有"("  ")"  "["  "]") 现在让添加括号,使括号序列变得匹配,要求添加最少的括号,输出这个匹配的括号序列;
 
思路:区间DP,dp[i][j]表示区间i~j匹配添加括号后区间最小长度,dp[i][j]=dp[i][k]+dp[k+1][j] ,注意当s[i]=='('&&s[j]==')' || s[i]=='['&&s[j]==']' 时,特判一下dp[i][j]=min(dp[i][j],dp[i+1][j-1]+2);  这样可以找出匹配后的序列最小长度,但是题目要求输出匹配的序列,那么可以在定义一个数组v[i][j] 标记i~j区间的断开位置,如果s[i]=='('&&s[j]==')' || s[i]=='['&&s[j]==']' 时 v[i][j]==-1, 然后在递归调用输出即可;
 
代码如下:
#include <iostream>
#include <algorithm>
#include <cstdio>
#include <cstring>
#include <cmath>
using namespace std;
const int inf=0x3f3f3f3f;
char s[];
int v[][];
int dp[][]; void print(int l,int r)
{
if(r<l) return;
if(l==r)
{
if(s[l]=='('||s[l]==')')
printf("()");
else
printf("[]");
return;
}
if(v[l][r]==-)
{
if(s[l]=='(')
{
printf("(");
print(l+,r-);
printf(")");
}
else
{
printf("[");
print(l+,r-);
printf("]");
}
}
else
{
print(l,v[l][r]);
print(v[l][r]+,r);
}
} int main()
{
scanf("%s",s);
int len=strlen(s);
memset(dp,,sizeof(dp));
for(int i=; i<len; i++)
dp[i][i]=; for(int l=; l<len; l++)
{
for(int i=; i+l<len; i++)
{
dp[i][i+l]=inf;
for(int k=i; k<i+l; k++)
{
if(dp[i][i+l]>dp[i][k]+dp[k+][i+l])
{
dp[i][i+l]=dp[i][k]+dp[k+][i+l];
v[i][i+l]=k;
}
}
if(s[i]=='('&&s[i+l]==')'||s[i]=='['&&s[i+l]==']')
{
if(dp[i][i+l]>dp[i+][i+l-]+)
{
dp[i][i+l]=dp[i+][i+l-]+;
v[i][i+l]=-;
}
}
}
}
print(,len-);
printf("\n");
return ;
}
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