POJ 2955 Brackets (区间DP)
2016-10-10 19:19
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#include<stdio.h> #include<string.h> #include<algorithm> using namespace std; char a[105]; int dp[105][105]; int main() { while(~scanf("%s",a)) { if(a[0]=='e') return 0; memset(dp,0,sizeof(dp)); int n=strlen(a); for(int i=1;i<n;i++) { for(int l=0;i+l<n;l++) { int r=i+l; if((a[l]=='('&&a[r]==')'&&r-l==1)||(a[l]=='['&&a[r]==']'&&r-l==1)) { dp[l][r]=2; } else if((a[l]=='('&&a[r]==')'&&r-l>1)||(a[l]=='['&&a[r]==']'&&r-l>1)) { dp[l][r]=max(dp[l][r],dp[l+1][r-1]+2); } for(int k=l;k<=r;k++) { dp[l][r]=max(dp[l][r],dp[l][k]+dp[k][r]); } } } printf("%d\n",dp[0][n-1]); } }
Brackets
Time Limit:1000MS Memory Limit:65536KB 64bit IO Format:%lld
& %llu
Submit Status Practice POJ
2955
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
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