題目鏈接

給出一個合法的括號序列，你可以將每個括號染上紅色或藍色，一對括號中有且只有一個被染色，相鄰括號不能染上同一顏色，問合法染色方案個數

狀態需要保存當前區間左右括號顏色，分左右邊界是否為同一對括號來更新

#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;
}

CodeForces149D Coloring Brackets