1183. Brackets Sequence

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 a₁a₂...a_n is called a subsequence of the string b₁b₂...b_m, if there exist such indices 1 ≤ i₁ < i₂ < ... < i_n ≤ m, that a_j=b_ij for all 1 ≤ j ≤ n.

Input

The input contains at most 100 brackets (characters '(', ')', '[' and ']') that are situated on a single line without any other characters among them.

Output

Write 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	output
([(]	()[()]

Problem Author: Andrew Stankevich  Problem Source: 2001-2002 ACM Northeastern European Regional Programming Contest

Tags: dynamic programming  (

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Difficulty: 250    Printable version    Submit solution    Discussion (18) My submissions    All submissions (5352)    All accepted submissions (1722)   Solutions rating (1349)

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题解：本题和石子合并问题和求矩阵代价类似，但在此过程中加了一个dir[][]寻找最优路径。俩字经典。

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#include<iostream>
#include<string>
#include<cstring>
#include<cstdio>
#include<cmath>
#include<cctype>
#include<algorithm>
#include<stack>
#include<queue>
#include<vector>
using namespace std;
int dp[1000][1000],i,j;
string str;
int n,k,t;
int dir[1000][1000];
void  init()
{
    cin>>str;
    getchar();
    n=str.length();
    for(int i=n;i>=1;i--)
     str[i]=str[i-1];
    //for(i=1;i<=n;i++)
     //cout<<str[i];
    //cout<<endl;
    for(int i=1;i<=n;i++)
      dp[i][i]=1;
}
void  solve()
{
    for(t=1;t<n;t++)
     for(i=1;i<=n-t;i++)
      {
          j=i+t;
          dp[i][j]=99999999;
          if((str[i]=='('&&str[j]==')')||(str[i]=='['&&str[j]==']'))
           {
               dp[i][j]=dp[i+1][j-1];
               dir[i][j]=0;
           }
          for(int k=i;k<j;k++)
            if(dp[i][k]+dp[k+1][j]<dp[i][j])
            {
              dp[i][j]=dp[i][k]+dp[k+1][j];
               dir[i][j]=k;
            }

            if(str[i]=='('||str[i]=='[')
               if(dp[i+1][j]+1<dp[i][j])
                {
                     dp[i][j]=dp[i+1][j]+1;
                     dir[i][j]=-1;
                }
            if(str[i]==')'||str[i]==']')
              if(dp[i][j-1]+1<dp[i][j])
                {
                   dp[i][j]=dp[i][j-1]+1;
                    dir[i][j]=-2;
                }

      }
}
void  print(int i,int j)
{
    if(i>j)return;
    if(i==j)
    {
        if(str[i]=='('||str[i]==')')
          cout<<"()";
        else
           cout<<"[]";

    }
    else
      {
          if(dir[i][j]==0)
          {
             if(str[i]=='('&&str[j]==')')
             {
                 cout<<'(';
                 print(i+1,j-1);
                 cout<<')';
             }
             if(str[i]=='['&&str[j]==']')
              {
                  cout<<'[';
                  print(i+1,j-1);
                  cout<<']';
              }
          }
          if(dir[i][j]>0)
            {
              print(i,dir[i][j]);
              print(dir[i][j]+1,j);
            }
          if(dir[i][j]==-1)
           {
               if(str[i]=='[')
                 {
                     cout<<str[i];
                     print(i+1,j);
                     cout<<']';
                 }
               if(str[i]=='(')
                {
                    cout<<str[i];
                    print(i+1,j);
                    cout<<')';
                }
           }
          if(dir[i][j]==-2)
          {
              if(str[i]==']')
               {
                   cout<<'[';
                   print(i,j-1);
                   cout<<str[i];
               }
              if(str[i]==')')
                {
                    cout<<'(';
                    print(i,j-1);
                    cout<<str[i];
                }
          }
      }
}
int main()
{
    init();
    solve();
    print(1,n);
    return 0;
}