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 largest m 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
66406
题意:求出互相匹配的括号的总数
思路:一道区间DP,dp[i][j]存的是i~j区间内匹配的个数
#include <stdio.h>#include <string.h>#include <algorithm>using namespace std;int check(char a,char b){ if(a=='(' && b==')') return 1; if(a=='[' && b==']') return 1; return 0;}int main(){ char str[105]; int dp[105][105],i,j,k,len; while(~scanf("%s",str)) { if(!strcmp(str,"end")) break; len = strlen(str); for(i = 0; i<len; i++) { dp[i][i] = 0; if(check(str[i],str[i+1])) dp[i][i+1] = 2; else dp[i][i+1] = 0; } for(k = 3; k<=len; k++) { for(i = 0; i+k-1<len; i++) { dp[i][i+k-1] = 0; if(check(str[i],str[i+k-1])) dp[i][i+k-1] = dp[i+1][i+k-2]+2; for(j = i; j<i+k-1; j++) dp[i][i+k-1] = max(dp[i][i+k-1],dp[i][j]+dp[j+1][i+k-1]); } } printf("%d\n",dp[0][len-1]); } return 0;}
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