记忆化搜索(DP+DFS) URAL 1183 Brackets Sequence

题目传送门

 /*
     记忆化搜索(DP+DFS)：dp[i][j] 表示第i到第j个字符，最少要加多少个括号
         dp[x][x] = 1 一定要加一个括号；dp[x][y] = 0, x > y;
         当s[x] 与 s[y] 匹配，则搜索 (x+1, y-1); 否则在x~y-1枚举找到相匹配的括号，更新最小值
 */
 #include <cstdio>
 #include <algorithm>
 #include <cmath>
 #include <iostream>
 #include <cstring>
 using namespace std;

 const int MAXN = 1e2 + ;
 const int INF = 0x3f3f3f3f;
 int dp[MAXN][MAXN];
 int pos[MAXN][MAXN];
 char s[MAXN];

 void DFS(int x, int y)
 {
     if (dp[x][y] != -)    return ;
     if (x > y)        {dp[x][y] = ;    return ;}
     if (x == y)    {dp[x][y] = ;    return ;}

     dp[x][y] = INF;
     if ((s[x]=='(' && s[y]==')') || (s[x]=='[' && s[y]==']'))
     {
         pos[x][y] = -;
         DFS (x+, y-);
         dp[x][y] = dp[x+][y-];
     }
     for (int i=x; i<y; ++i)
     {
         DFS (x, i);    DFS (i+, y);
         int cur = dp[x][i] + dp[i+][y];
         if (cur < dp[x][y])
         {
             dp[x][y] = cur;        pos[x][y] = i;
         }
     }
 }

 void print(int x, int y)
 {
     if (x > y)    return ;
     if (x == y)
     {
         if (s[x] == '(' || s[y] == ')')    printf ("()");
         else    printf ("[]");
         return ;
     }
     if (pos[x][y] == -)
     {
         printf ("%c", s[x]);
         print (x+, y-);
         printf ("%c", s[y]);
     }
     else
     {
         print (x, pos[x][y]);    print (pos[x][y]+, y);
     }
 }

 int main(void)        //URAL 1183 Brackets Sequence
 {
     //freopen ("O.in", "r", stdin);

     while (scanf ("%s", s+) == )
     {
         int len = strlen (s+);
         memset (dp, -, sizeof (dp));
         memset (pos, , sizeof (pos));

         DFS (, len);
         print (, len);    puts ("");
     }

     return ;
 }