【题解】CF1107E：Vasya and Binary String

原题传送门
令$d{p}_{i,j,k}$表示区间$[i,j],j$的右边还可以一起删$k$个

• $d{p}_{i,j,k}=max(d{p}_{i,j-1,0}+a_{k+1})$
• $d{p}_{i,j,t}=max(d{p}_{k+1,j-1,0}+d{p}_{i,k,t+1}(s_k=s_j))$

$O(n^3)$个状态，每个状态差不多跑$O(n)$次
Code：

#include 
#define maxn 110
#define LL long long
using namespace std;
char s[maxn];
int n;
LL a[maxn], dp[maxn][maxn][maxn], sum[maxn];

inline int read(){
	int s = 0, w = 1;
	char c = getchar();
	for (; !isdigit(c); c = getchar()) if (c == '-') w = -1;
	for (; isdigit(c); c = getchar()) s = (s << 1) + (s << 3) + (c ^ 48);
	return s * w;
}

int main(){
	n = read();
	scanf("%s", s + 1);
	for (int i = 1; i <= n; ++i){
		a[i] = read();
		for (int j = 1; j < i; ++j) a[i] = max(a[i], a[j] + a[i - j]);
	}
	for (int i = 1; i <= n; ++i)
		for (int j = i + 1; j <= n; ++j) sum[i] += (s[i] == s[j]);
	for (int i = n; i; --i)
		for (int j = i; j <= n; ++j){
			for (int k = 0; k <= sum[j]; ++k) dp[i][j][k] = max(dp[i][j][k], dp[i][j - 1][0] + a[k + 1]);
			for (int k = i; k < j; ++k) if (s[k] == s[j])
				for (int t = 0; t <= sum[j]; ++t) dp[i][j][t] = max(dp[i][j][t], dp[k + 1][j - 1][0] + dp[i][k][t + 1]);
		}
	printf("%lld\n", dp[1][n][0]);
	return 0;
}