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

 

题目传送门

 1 /*  2  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  3  dp[x][x] = 1 一定要加一个括号；dp[x][y] = 0, x > y;  4  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  5 */  6 #include <cstdio>  7 #include <algorithm>  8 #include <cmath>  9 #include <iostream> 10 #include <cstring> 11 using namespace std; 12 13 const int MAXN = 1e2 + 10; 14 const int INF = 0x3f3f3f3f; 15 int dp[MAXN][MAXN]; 16 int pos[MAXN][MAXN]; 17 char s[MAXN]; 18 19 void DFS(int x, int y) 20 { 21 if (dp[x][y] != -1) return ; 22 if (x > y) {dp[x][y] = 0; return ;} 23 if (x == y) {dp[x][y] = 1; return ;} 24 25 dp[x][y] = INF; 26 if ((s[x]=='(' && s[y]==')') || (s[x]=='[' && s[y]==']')) 27  { 28 pos[x][y] = -1; 29 DFS (x+1, y-1); 30 dp[x][y] = dp[x+1][y-1]; 31  } 32 for (int i=x; i<y; ++i) 33  { 34 DFS (x, i); DFS (i+1, y); 35 int cur = dp[x][i] + dp[i+1][y]; 36 if (cur < dp[x][y]) 37  { 38 dp[x][y] = cur; pos[x][y] = i; 39  } 40  } 41 } 42 43 void print(int x, int y) 44 { 45 if (x > y) return ; 46 if (x == y) 47  { 48 if (s[x] == '(' || s[y] == ')') printf ("()"); 49 else printf ("[]"); 50 return ; 51  } 52 if (pos[x][y] == -1) 53  { 54 printf ("%c", s[x]); 55 print (x+1, y-1); 56 printf ("%c", s[y]); 57  } 58 else 59  { 60 print (x, pos[x][y]); print (pos[x][y]+1, y); 61  } 62 } 63 64 int main(void) //URAL 1183 Brackets Sequence 65 { 66 //freopen ("O.in", "r", stdin); 67 68 while (scanf ("%s", s+1) == 1) 69  { 70 int len = strlen (s+1); 71 memset (dp, -1, sizeof (dp)); 72 memset (pos, 0, sizeof (pos)); 73 74 DFS (1, len); 75 print (1, len); puts (""); 76  } 77 78 return 0; 79 }