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.
区间dp入门题,可我还是看题解才做出来。。。
用dp[i][j]表示区间i, j之间的最大匹配数。。。如果是s[i]与s[j]匹配,则dp[i][j] = dp[i + 1][j - 1] + 2,然后再将该区间分段算最大值(必须有,否则样例二过不了)
#include <vector>
#include <stdio.h>
#include <map>
#include <stdlib.h>
#include<ctype.h>
#include <iostream>
#include <queue>
#include <string.h>
#include <algorithm>
#define LL long long
using namespace std;
char s1[150];
int dp[150][150];
int main(int argc, char const *argv[]){
while(~scanf("%s", s1)){
int len = strlen(s1);
if(strcmp(s1, "end") == 0){
break;
}
memset(dp, 0, sizeof(dp));
for(int i = 2; i <= len; i++){
for(int j = 0; j < len; j++){
int k = j + i - 1;
if((s1[j] == '(' && s1[k] == ')') || (s1[j] == '[' && s1[k] == ']')){
dp[j][k] = dp[j + 1][k - 1] + 2;
}
for(int x = j; x < k; x++){
dp[j][k] = max(dp[j][k], dp[j][x] + dp[x + 1][k]);
}
}
}
printf("%d\n", dp[0][len - 1]);
}
return 0;
}