POJ 2955 Brackets
2014-03-24 23:12
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POJ 2955 ;链接:http://poj.org/problem?id=2955
题目:
Brackets
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 ofs. That is, you wish to find the largestm such that for indicesi1,i2,
…,im where 1 ≤i1 <i2 < … <im ≤n,
ai1ai2
… aim is a regular brackets sequence.
Given the initial sequence
Input
The input test file will contain multiple test cases. Each input test case consists of a single line containing only the characters
Output
For each input case, the program should print the length of the longest possible regular brackets subsequence on a single line.
Sample Input
Sample Output
POJ 2955 ;链接:http://poj.org/problem?id=2955
题目:
Brackets
Time Limit: 1000MS | Memory Limit: 65536K | |
Total Submissions: 2463 | Accepted: 1267 |
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 ofs. That is, you wish to find the largestm such that for indicesi1,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
解题思路:
这道题目和POJ 1141有点相像。可以使用dp来做,用dp[i][j]表示,原序列的从i位置到j位置的子序列。当s[i]和s[j]匹配时,dp[i][j] = max(dp[i+1][j-1]+1,d[i][k]+d[k+1][j])(k>=i&&k<j);否则,dp[i][j] = max(dp[i][j], d[i][k] + d[k+1][j])(k>=i && k < j);
代码:
#include <iostream> #include <cstring> using namespace std; #define max(x,y) x>y?x:y const int MAXN = 110; int dp[MAXN][MAXN]; string s, t; int main() { std::ios::sync_with_stdio(false); while(!cin.eof()) { t = s = ""; cin >> t; s = ' ' + t; if("end" == t) break; memset(dp, 0, sizeof(dp)); int len = t.length(); for(int r = 1; r < len; r++) { for(int i = 1; i <= len - r; i++) { int j = i + r; if(('(' == s[i] && ')' == s[j]) || ('[' == s[i] && ']' == s[j])) { dp[i][j] = dp[i+1][j-1] + 1; } for(int k = i; k < j; k++) { if(dp[i][j] < dp[i][k] + dp[k+1][j]) dp[i][j] = dp[i][k] + dp[k+1][j]; } } } cout << 2 * dp[1][len] << endl; } return 0; }
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