[NYIST15]括号匹配（区间dp）

Posted 2020-07-31

题目链接：http://acm.nyist.edu.cn/JudgeOnline/problem.php?pid=15

经典区间dp，首先枚举区间的大小和该区间的左边界，这时右边界也可计算出来。首先初始化一个匹配，那就是看看这两个括号是否匹配，即：

(s[i] == ‘(‘ && s[j] == ‘)‘) || (s[i] == ‘[‘ && s[j] == ‘]‘) ? dp(i,j) = dp(i+1,j-1)+2) : dp(i,j) = 0

接下来枚举i和j中间的所有点，更新dp(i,j)=max(dp(i,j), dp(i+m)+dp(m+1,j))寻找可能更优的匹配。

 

 1 /*
 2 ━━━━━┒ギリギリ♂ eye！
 3 ┓┏┓┏┓┃キリキリ♂ mind！
 4 ┛┗┛┗┛┃＼○／
 5 ┓┏┓┏┓┃ /
 6 ┛┗┛┗┛┃ノ)
 7 ┓┏┓┏┓┃
 8 ┛┗┛┗┛┃
 9 ┓┏┓┏┓┃
10 ┛┗┛┗┛┃
11 ┓┏┓┏┓┃
12 ┛┗┛┗┛┃
13 ┓┏┓┏┓┃
14 ┃┃┃┃┃┃
15 ┻┻┻┻┻┻
16 */
17 #include <algorithm>
18 #include <iostream>
19 #include <iomanip>
20 #include <cstring>
21 #include <climits>
22 #include <complex>
23 #include <cassert>
24 #include <cstdio>
25 #include <bitset>
26 #include <vector>
27 #include <deque>
28 #include <queue>
29 #include <stack>
30 #include <ctime>
31 #include <set>
32 #include <map>
33 #include <cmath>
34 using namespace std;
35 #define fr first
36 #define sc second
37 #define cl clear
38 #define BUG puts("here!!!")
39 #define W(a) while(a--)
40 #define pb(a) push_back(a)
41 #define Rint(a) scanf("%d", &a)
42 #define Rll(a) scanf("%I64d", &a)
43 #define Rs(a) scanf("%s", a)
44 #define Cin(a) cin >> a
45 #define FRead() freopen("in", "r", stdin)
46 #define FWrite() freopen("out", "w", stdout)
47 #define Rep(i, len) for(int i = 0; i < (len); i++)
48 #define For(i, a, len) for(int i = (a); i < (len); i++)
49 #define Cls(a) memset((a), 0, sizeof(a))
50 #define Clr(a, x) memset((a), (x), sizeof(a))
51 #define Full(a) memset((a), 0x7f7f7f, sizeof(a))
52 #define lrt rt << 1
53 #define rrt rt << 1 | 1
54 #define pi 3.14159265359
55 #define RT return
56 #define lowbit(x) x & (-x)
57 #define onenum(x) __builtin_popcount(x)
58 typedef long long LL;
59 typedef long double LD;
60 typedef unsigned long long ULL;
61 typedef pair<int, int> pii;
62 typedef pair<string, int> psi;
63 typedef pair<LL, LL> pll;
64 typedef map<string, int> msi;
65 typedef vector<int> vi;
66 typedef vector<LL> vl;
67 typedef vector<vl> vvl;
68 typedef vector<bool> vb;
69 
70 const int maxn = 1100;
71 int dp[maxn][maxn];
72 char s[maxn];
73 int n;
74 
75 int main() {
76     // FRead();
77     int T;
78     Rint(T);
79     W(T) {
80         Rs(s); n = strlen(s);
81         Cls(dp);
82         For(k, 2, n+1) {
83             Rep(i, n-k+1) {
84                 dp[i][i+k-1] = 0;
85                 int j = i + k - 1;
86                 if((s[i] == ‘(‘ && s[j] == ‘)‘) || (s[i] == ‘[‘ && s[j] == ‘]‘)) {
87                     dp[i][j] = dp[i+1][j-1] + 2;
88                 }
89                 For(m, i, j) {
90                     dp[i][j] = max(dp[i][j], dp[i][m] + dp[m+1][j]);
91                 }
92             }
93         }
94         printf("%d\n", n - dp[0][n-1]);
95     }
96     RT 0;
97 }