题目请点我
题解:
这是一道错排问题,题意是说猜出>N/2才算是成功,那我们就需主要找到1~N/2的错排相加。
错排公式:D[i] = (i-1)*(D[i-1]+D[i-2]); 错排的数序要用组合数求出。
代码实现:
#include <iostream>
#include <cstdio>
#include <cstring>
#include <cstdlib>
#define MAX 30
#define LL long long
using namespace std;
int N;
LL D[MAX];
LL result;
void pre();
LL C(int n,int m);
int main()
{
pre();
while( scanf("%d",&N) && N ){
result = 1;
int len = N/2;
for( int i = 0; i <= len; i++ ){
result += C(N,i)*D[i];
}
printf("%I64d\n",result);
}
return 0;
}
void pre(){
memset(D,0,sizeof(D));
D[1] = 0;
D[2] = 1;
for( int i = 3; i < 15; i++ ){
D[i] = (i-1)*(D[i-1]+D[i-2]);
}
}
LL C(int n,int m){
if( m == 0 ){
return 1;
}
LL A = 1;
LL B = 1;
int len = m;
for( int i = 0; i < len; i++ ){
A *= n;
B *= m;
n--;m--;
}
return A/B;
}