LeetCode 301. Remove Invalid Parentheses ( DP )

题目

删除最少的括号，让所有括号匹配起来。

大部分都是用DFS,或者BFS。我用的DP，也可以过
dp[i][j] :means it need remove at least dp[i][j] characters to get vaild parenthese from position i to postion j in string.
vector str[i][j] store the parenthese string
for example :
"()())"
dp[0][1]=0 vector[0][1]=["()"]
dp[0][2]=1 vector[0][2]=["()"]
dp[1][2]=0 vector[1][2]=["()"]
dp[0][3]=0 vector[1][2]=["()()"]
dp[0][4]=1 vector[0][4]=["()()","(())"]

dp[0][4]=min(dp[0][1]+d[1][4],....dp[0][3]+dp[4][4],dp[1][3])

class Solution {
public:
    vector<string> str[1005][1005];
    int dp[1005][1005];
    
    vector<string> removeInvalidParentheses(string s) {
        
        if(s=="")
        {
            str[0][0].push_back("");
            return str[0][0];
        }
        
        for(int i=0;i<s.length();i++)
        {
            if(s[i]=='('||s[i]==')')
            {
                dp[i][i] = 1;
                str[i][i].push_back("");
            }
            else
            {
                dp[i][i] = 0;
                string ss;
                ss+=s[i];
                str[i][i].push_back(ss);
            }
        }
        
        for(int l=1;l<s.length();l++)
        {
            for(int i=0;i+l<s.length();i++)
            {
                int j = i+l;
                
                dp[i][j]=INT_MAX;
                
                for(int k=i;k<j;k++)
                {
                    if(dp[i][j]>=dp[i][k]+dp[k+1][j])
                    {
                        dp[i][j]=dp[i][k]+dp[k+1][j];
                        str[i][j].clear();
                        for(int p=0;p<str[i][k].size();p++)
                        {
                            for(int q=0;q<str[k+1][j].size();q++)
                            {
                                string ss = str[i][k][p]+str[k+1][j][q];
                                if(std::find(str[i][j].begin(), str[i][j].end(), ss) == str[i][j].end())
                                    str[i][j].push_back(ss);
                            }
                        }
                        
                    }
                }
                
                if(s[i]=='('&&s[j]==')')
                {
                    if(l==1)
                    {
                        dp[i][j]=0;
                        str[i][j].clear();
                        str[i][j].push_back("()");
                    }
                    else
                    {
                        if(dp[i][j]>=dp[i+1][j-1])
                        {
                            if(dp[i][j]>dp[i+1][j-1])
                                str[i][j].clear();
                            
                            dp[i][j]=dp[i+1][j-1];
                            
                            for(int p=0;p<str[i+1][j-1].size();p++)
                            {
                                string ss = s[i]+str[i+1][j-1][p]+s[j];
                                if(std::find(str[i][j].begin(), str[i][j].end(), ss) == str[i][j].end())
                                    str[i][j].push_back(ss);
                            }
                        }
                        
                    
                    }
                }
                else
                {
                    if(dp[i][j]>=dp[i+1][j-1]+2)
                    {
                        if(dp[i][j]>dp[i+1][j-1]+2)
                            str[i][j].clear();
                         dp[i][j]=dp[i+1][j-1]+2;
                        
                         for(int p=0;p<str[i+1][j-1].size();p++)
                         {
                             string ss = str[i+1][j-1][p];
                             if(std::find(str[i][j].begin(), str[i][j].end(), ss) == str[i][j].end())
                                    str[i][j].push_back(ss);
                             
                         }
                    }
                }
            }
        }
        
        return str[0][s.length()-1];
        
    }
};