POJ-2955-Brackets【区间DP】
2017-03-24 15:26
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Description
We give the following inductive definition of a “regular brackets” sequence:
the empty sequence is a regular brackets sequence,
if s is a regular brackets sequence, then (s) and [s] are regular brackets sequences, and
if a and b are regular brackets sequences, then ab is a regular brackets sequence.
no other sequence is a regular brackets sequence
For instance, all of the following character sequences are regular brackets sequences:
(), [], (()), ()[], ()[()]
while the following character sequences are not:
(, ], )(, ([)], ([(]
Given a brackets sequence of characters a1a2 … an, your goal is to find the length of the longest regular brackets sequence that is a subsequence of s. That is, you wish to find the largest m such that for indices i1, i2, …, im where 1 ≤ i1 < i2 < … < im ≤ n, ai1ai2 … aim is a regular brackets sequence.
Given the initial sequence ([([]])], the longest regular brackets subsequence is [([])].
Input
The input test file will contain multiple test cases. Each input test case consists of a single line containing only the characters (, ), [, and ]; each input test will have length between 1 and 100, inclusive. The end-of-file is marked by a line containing the word “end” and should not be processed.
Output
For each input case, the program should print the length of the longest possible regular brackets subsequence on a single line.
Sample Input
((()))
()()()
([]])
)[)(
([][][)
end
Sample Output
6
6
4
0
6
题目链接:POJ-2955
题目大意:给出括号序列,问匹配的括号有多少
题目思路:区间dp
以下是代码:
We give the following inductive definition of a “regular brackets” sequence:
the empty sequence is a regular brackets sequence,
if s is a regular brackets sequence, then (s) and [s] are regular brackets sequences, and
if a and b are regular brackets sequences, then ab is a regular brackets sequence.
no other sequence is a regular brackets sequence
For instance, all of the following character sequences are regular brackets sequences:
(), [], (()), ()[], ()[()]
while the following character sequences are not:
(, ], )(, ([)], ([(]
Given a brackets sequence of characters a1a2 … an, your goal is to find the length of the longest regular brackets sequence that is a subsequence of s. That is, you wish to find the largest m such that for indices i1, i2, …, im where 1 ≤ i1 < i2 < … < im ≤ n, ai1ai2 … aim is a regular brackets sequence.
Given the initial sequence ([([]])], the longest regular brackets subsequence is [([])].
Input
The input test file will contain multiple test cases. Each input test case consists of a single line containing only the characters (, ), [, and ]; each input test will have length between 1 and 100, inclusive. The end-of-file is marked by a line containing the word “end” and should not be processed.
Output
For each input case, the program should print the length of the longest possible regular brackets subsequence on a single line.
Sample Input
((()))
()()()
([]])
)[)(
([][][)
end
Sample Output
6
6
4
0
6
题目链接:POJ-2955
题目大意:给出括号序列,问匹配的括号有多少
题目思路:区间dp
以下是代码:
#include <iostream> #include <iomanip> #include <fstream> #include <sstream> #include <cmath> #include <cstdio> #include <cstring> #include <cctype> #include <algorithm> #include <functional> #include <numeric> #include <string> #include <set> #include <map> #include <stack> #include <vector> #include <queue> #include <deque> #include <list> using namespace std; #define maxn 200 int dp[maxn][maxn]; bool match(char a, char b) { if (a == '(' && b == ')') return 1; if (a == '[' && b == ']') return 1; return 0; } int main() { string s; while(cin >> s) { if (s == "end") break; memset(dp, 0, sizeof dp); int len = s.size(); for (int i = len - 2; i >= 0; i--) { for (int j = i + 1; j < len; j++) { dp[i][j] = dp[i + 1][j]; for (int k = i + 1; k <= j; k++) { if (match(s[i],s[k])) dp[i][j] = max(dp[i][j], dp[i + 1][k - 1] + dp[k + 1][j] + 2); } } } cout << dp[0][len - 1] << endl; } return 0; }
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