LuoGu: CF785D Anton and School - 2
CF: D. Anton and School - 2
钦定最后一个 “(” ，再在前面选择 $i$ 个，后面选择 $i + 1$ 。用范德蒙德卷积。
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| #include <cstdio>
#include <cstring>
using namespace std;
typedef long long L;
const int N = 2e5 + 10, mod = 1e9 + 7;
char s[N];
int n, f[N], g[N], inv[N], fact[N], ifact[N];
void init ()
{
inv[1] = 1;
for (int i = 2; i < N; ++i)
inv[i] = -(L)(mod / i) * inv[mod % i] % mod;
fact[0] = ifact[0] = 1;
for (int i = 1; i < N; ++i)
{
fact[i] = (L)fact[i - 1] * i % mod;
ifact[i] = (L)ifact[i - 1] * inv[i] % mod;
}
}
int C (int a, int b) { return a < b ? 0 : (L)fact[a] * ifact[b] % mod * ifact[a - b] % mod; }
int main ()
{
init();
scanf("%s", s + 1);
n = strlen(s + 1);
for (int i = 1; i <= n; ++i)
f[i] = f[i - 1] + (s[i] == '(');
for (int i = n; i; --i)
g[i] = g[i + 1] + (s[i] == ')');
int res = 0;
for (int i = 1; i <= n; ++i)
if (s[i] == '(' && g[i]) (res += C(f[i] + g[i] - 1, g[i] - 1)) %= mod;
printf("%d", (res + mod) % mod);
return 0;
}
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