POJ 2955 Brackets——区间dp

做过很多括号序列的题以后，感觉这类题都是老套路了

dp[i][j]表示闭区间【i，j】内最长的匹配好的括号子序列，并全部初始化为0

#include <cstdio>
#include <cstring>
#include <iostream>
#include <algorithm>

using namespace std;

const int maxn = 110;

char str[maxn];
int dp[maxn][maxn], n;

bool match(char a, char b) {
if ( (a == '(' && b == ')') || (a == '[' && b == ']') ) return true;
else return false;
}

int main()
{
while (gets(str) != NULL) {
if (str[0] == 'e') break;
memset(dp, 0, sizeof(dp));
n = strlen(str) - 1;
for (int i = n - 1; i >= 0; i--) {
for (int j = i + 1; j <= n; j++) {
if (match(str[i], str[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 + 1][j]);
}
}
}
printf("%d\n", dp[0]
);
}
return 0;
}