题意:给定一个序列,问你最多有多少个合法的括号。
析:区间DP,dp[i][j] 表示在 第 i 到 第 j 区间内最多有多少个合法的括号。
代码如下:
#pragma comment(linker, "/STACK:1024000000,1024000000") #include <cstdio> #include <string> #include <cstdlib> #include <cmath> #include <iostream> #include <cstring> #include <set> #include <queue> #include <algorithm> #include <vector> #include <map> #include <cctype> #include <cmath> #include <stack> //#include <tr1/unordered_map> #define freopenr freopen("in.txt", "r", stdin) #define freopenw freopen("out.txt", "w", stdout) using namespace std; //using namespace std :: tr1; typedef long long LL; typedef pair<int, int> P; const int INF = 0x3f3f3f3f; const double inf = 0x3f3f3f3f3f3f; const LL LNF = 0x3f3f3f3f3f3f; const double PI = acos(-1.0); const double eps = 1e-8; const int maxn = 1e2 + 5; const int mod = 1e9 + 7; const int N = 1e6 + 5; const int dr[] = {-1, 0, 1, 0, 1, 1, -1, -1}; const int dc[] = {0, 1, 0, -1, 1, -1, 1, -1}; const char *Hex[] = {"0000", "0001", "0010", "0011", "0100", "0101", "0110", "0111", "1000", "1001", "1010", "1011", "1100", "1101", "1110", "1111"}; inline LL gcd(LL a, LL b){ return b == 0 ? a : gcd(b, a%b); } int n, m; const int mon[] = {0, 31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31}; const int monn[] = {0, 31, 29, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31}; inline int Min(int a, int b){ return a < b ? a : b; } inline int Max(int a, int b){ return a > b ? a : b; } inline LL Min(LL a, LL b){ return a < b ? a : b; } inline LL Max(LL a, LL b){ return a > b ? a : b; } inline bool is_in(int r, int c){ return r >= 0 && r < n && c >= 0 && c < m; } char s[maxn]; int dp[maxn][maxn]; bool match(char ch, char sh){ if(ch == ‘(‘ && sh == ‘)‘) return true; if(ch == ‘[‘ && sh == ‘]‘) return true; return false; } int main(){ while(scanf("%s", s) == 1 && s[0] != ‘e‘){ n = strlen(s); memset(dp, 0, sizeof dp); for(int i = n-2; i >= 0; --i) for(int j = i+1; j < n; ++j){ if(match(s[i], s[j])) dp[i][j] = dp[i+1][j-1] + 2; for(int k = i; k < j; ++k) dp[i][j] = Max(dp[i][k]+dp[k+1][j], dp[i][j]); } printf("%d\n", dp[0][n-1]); } return 0; }
原文:http://www.cnblogs.com/dwtfukgv/p/5904240.html