题目链接
BZOJ2729
题解
高考数学题。。。
我们先把老师看做男生，女生插空站
如果两个老师相邻，我们把他们看做一个男生，女生插空站
对于\(n\)个男生\(m\)个女生的方案数：
\[n!m!{n + 1 \choose m}\]
还要特判一下没有男生女生的情况
然后高精即可
#include<algorithm>
#include<iostream>
#include<cstring>
#include<cstdio>
#include<cmath>
#include<map>
#define Redge(u) for (int k = h[u],to; k; k = ed[k].nxt)
#define REP(i,n) for (int i = 1; i <= (n); i++)
#define mp(a,b) make_pair<int,int>(a,b)
#define cls(s) memset(s,0,sizeof(s))
#define cp pair<int,int>
#define LL long long int
using namespace std;
const int maxn = 100005,B = 10000,maxm = 100005,INF = 1000000000;
inline int read(){int out = 0,flag = 1; char c = getchar();while (c < 48 || c > 57){if (c == '-') flag = -1; c = getchar();}while (c >= 48 && c <= 57){out = (out << 3) + (out << 1) + c - 48; c = getchar();}return out * flag;
}
struct NUM{int s[4000],len;NUM(){cls(s); len = 0;}void out(){printf("%d",s[len]);for (int i = len - 1; i; i--)printf("%04d",s[i]);}
}A,C;
inline NUM operator *(const NUM& a,const int& b){NUM c;c.len = a.len;LL carry = 0,tmp;for (int i = 1; i <= a.len; i++){tmp = a.s[i] * b + carry;c.s[i] = tmp % B;carry = tmp / B;}while (carry) c.s[++c.len] = carry % B,carry /= B;return c;
}
inline NUM operator -(const NUM& a,const NUM& b){NUM c;c.len = a.len;int carry = 0,tmp;for (int i = 1; i <= a.len; i++){tmp = a.s[i] - b.s[i] + carry;if (tmp < 0) tmp += B,carry = -1;else carry = 0;c.s[i] = tmp;}while (c.len && !c.s[c.len]) c.len--;return c;
}
int main(){int n = read(),m = read();if (n + 3 < m || (!n && !m)){puts("0"); return 0;}n += 2;A.s[A.len = 1] = 1;for (int i = n; i > n - m + 1; i--)A = A * i;for (int i = n + 1; i; i--)A = A * i;n--;if (n + 1 >= m){C.s[C.len = 1] = 1;for (int i = n; i > n - m + 1; i--)C = C * i;for (int i = n + 1; i; i--)C = C * i;C = C * 2;}A = A - C;A.out();return 0;
}
