POJ 2955 Brackets 【区间dp】【水题】
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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
66406
Source
dp[i][j]表示区间i~j中匹配的个数
#include<iostream>#include<algorithm>#include<cmath>#include<queue>#include<cstring>#include<iomanip>#define INF 0x3f3f3f3f#define ms(a,b) memset(a,b,sizeof(a))using namespace std;const int maxn = 105;char s[maxn];int dp[maxn][maxn];bool check(int i, int j){if (s[i] == '('&&s[j] == ')') return 1;if (s[i] == '['&&s[j] == ']') return 1;return 0;}int main(){while (~scanf("%s", s + 1)){if (s[1] == 'e') break;ms(dp, 0);int n = strlen(s + 1);for (int i = n; i > 0; i--){for (int j = i + 1; j <= n; j++){if (check(i, j)) dp[i][j] = dp[i + 1][j - 1] + 2;for (int k = i; k <= j; k++)dp[i][j] = max(dp[i][j], dp[i][k] + dp[k][j]);}}printf("%d\n", dp[1][n]);}}
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