POJ 2955 Brackets (区间DP)
2016-08-25 18:37
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Brackets
Time Limit: 1000MS Memory Limit: 65536K
Total Submissions: 6420 Accepted: 3436
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
Source
Stanford Local 2004
给出一个串,请取出其中的一些字符组成的新串括号必须是两两匹配的。可以不连续地取,但必须保持先后顺序。
Time Limit: 1000MS Memory Limit: 65536K
Total Submissions: 6420 Accepted: 3436
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
Source
Stanford Local 2004
给出一个串,请取出其中的一些字符组成的新串括号必须是两两匹配的。可以不连续地取,但必须保持先后顺序。
#include "cstring" #include "cstdio" #include "iostream" #include "string.h" #include "algorithm" using namespace std; char s[1005]; int dp[1005][1005]; bool check(int left,int right) { if(s[left]=='('&&s[right]==')') return true; if(s[left]=='['&&s[right]==']') return true; return false; } int main() { while(scanf("%s",s)&&strcmp(s,"end")!=0) { int len=strlen(s); memset(dp,0,sizeof(dp)); //l表示区间长度。区间的长度可以从1~len for(int l=1;l<=len;l++) { //枚举该长度下的所有区间 for(int i=0;i+l-1<len;i++) { //若区间守卫可以构成一个匹配,那么答案就+2 if(check(i,i+l-1)) dp[i][i+l-1]=dp[i+1][i+l-2]+2; //合并区间 for(int j=i;j<i+l-1;j++) dp[i][i+l-1]=max(dp[i][i+l-1],dp[i][j]+dp[j+1][i+l-1]); } } printf("%d\n",dp[0][len-1]); } }
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