CodeForces149D Coloring Brackets

题目链接

给出一个合法的括号序列，你可以将每个括号染上红色或蓝色，一对括号中有且只有一个被染色，相邻括号不能染上同一颜色，问合法染色方案个数

状态需要保存当前区间左右括号颜色，分左右边界是否为同一对括号来更新

#include <cstdio>
#include <cstring>
#include <iostream>
using namespace std;
const int mod = 1000000007;
char s[705];
int n;
int top, sta[705], match[705];
long long f[705][705][9];
void ModAdd(long long & x, long long y) {
	x += y;
	if(x >= mod) x-= mod;
}
long long DP(int l, int r, int k) {
	int lcol = k / 3, rcol = k % 3;
	if(r - l == 1) {
//		printf("%d %d %d\n", k, lcol, rcol);
		if((lcol == 0) == (rcol == 0)) return 0;
		return 1;
	}
	long long & res = f[l][r][k];
	if(res != -1) return res;
    res = 0;
	if(match[l] == r) {
		if((lcol == 0) == (rcol == 0)) return res;
		for(int i = 0; i < 3; i++) {
			if(i != 0 && lcol != 0 && i == lcol) continue;
			for(int j = 0; j < 3; j++) {
				if(j != 0 && rcol != 0 && j == rcol) continue;
				ModAdd(res, DP(l + 1, r - 1, i * 3 + j));
			}
		}
	}
	else {
		for(int i = 0; i < 3; i++) {
			for(int j = 0; j < 3; j++) {
				if(i != 0 && j != 0 && i == j) continue;
				ModAdd(res, DP(l, match[l], lcol * 3 + i) * 
				            DP(match[l] + 1, r, j * 3 + rcol) % mod);
			}
		}
	}
//	printf("%d %d %d %d %lld\n", l, r, lcol, rcol, res);
	return res;
}
int main() {
	scanf("%s", s);
	n = strlen(s);
	for(int i = 0; i < n; i++) {
		if(s[i] == '(') sta[top++] = i;
		else match[sta[--top]] = i;
	}
	long long ans = 0;
	memset(f, -1, sizeof(f));
	for(int i = 0; i < 9; i++) ModAdd(ans, DP(0, n - 1, i));
	cout << ans << endl;
	return 0;
}