Poj 2955 brackets(区间dp)
2017-05-13 16:45
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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 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
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
Source
Stanford Local 2004
题解:
f[i][j]表示i到j的最大括号匹配数
Time Limit: 1000MS | Memory Limit: 65536K | |
Total Submissions: 7795 | Accepted: 4136 |
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
Source
Stanford Local 2004
题解:
f[i][j]表示i到j的最大括号匹配数
#include <iostream> #include<cstdio> #include<cstring> #include<map> #include<set> #include<queue> #include<vector> #include<deque> #include<algorithm> #include<string> #include<stack> #include<cmath> using namespace std; char ch[105]; int dp[105][105]; int n; bool ok(int x,int y) { if (ch[x]=='(' && ch[y]==')') return 1; if (ch[x]=='[' && ch[y]==']') return 1; return 0; } int main() { while(~scanf("%s",&ch)) { if (ch[0]=='e') break; n=strlen(ch); memset(dp,0,sizeof(dp)); // for(int i=0;i<n;i++) // for(int j=i+1;j<n;j++) 正就是不对的 for(int i=n-1;i>=0;i--) for(int j=i+1;j<n;j++) { if (ok(i,j)) dp[i][j]=max(dp[i][j],dp[i+1][j-1]+2); for(int k=i;k<=j;k++) dp[i][j]=max(dp[i][j],dp[i][k]+dp[k][j]); } printf("%d\n",dp[0][n-1]); } return 0; }
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