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?…?a_n, 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, …,?i_m?where 1 ≤?i₁?<?i₂?< … <?i_m?≤?n,?a_i1a_i2?…?a_im?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 dp[i][j]表示在區間i到j匹配的最大數。

#include<stdio.h> #include<string.h> int max(int a,int b) {return a>b?a:b; } int main() {int dp[105][105];char str[105];while(scanf("%s",str)>0&&strcmp(str,"end")!=0){int len=strlen(str);memset(dp,0,sizeof(dp));for(int l=1;l<len;l++)//所求區間頭尾相差長度for(int i=0;i<len-l;i++)//區間起始位置{int j=l+i;//區間尾部位置dp[i][j]=dp[i+1][j];//當第i個在這段區間內沒有匹配的時for(int k=i+1;k<=j;k++)//當第i個與第k個位置匹配上時，狀態轉移例如以下if(str[i]=='('&&str[k]==')'||str[i]=='['&&str[k]==']')dp[i][j]=max(dp[i][j],dp[i+1][k-1]+dp[k+1][j]+2);}printf("%d\n",dp[0][len-1]);} }

總結

以上是生活随笔為你收集整理的poj2955Brackets(区间DP)的全部內容，希望文章能夠幫你解決所遇到的問題。

如果覺得生活随笔網站內容還不錯，歡迎將生活随笔推薦給好友。