The game ranked number combination

 

It is limited, at the problem is not the solution, a lot of understanding

 

Thank you for watching this konjac

 

 

topic:

Tournament rankings

(rank.cpp/in/out 1s 128M)

N classmates participate in the competition, asked how many kinds of rankings, allowing parallel situation

Input

Enter a number N , N <= 12 is

Output

How many kinds of output ranking

Sample Input

2

Sample Output

3

HINT

Set two students for the A, B, the following three rankings

1: A first, B second

2: A second, B first

3: A, B parallel to the first

 

f (i) represents the i th students to participate in competitions, and asked how many kinds of rankings, allowing parallel situation

 

 

Can be considered under the first few people, a person can have, as the result c (n, 1) * f (n-1) because a person has been removed

 

There may be two individual, the result is c (n, 2) * f  (n-2) since it has been removed 2

 

There may be three individuals, then the result is c (n, 3) * f  (n-3) because it has been removed 3

 

……

 

You can have n individuals, then the result is c (n, n) * f   (0) is removed n al

 

ans is equal to the sum of the above circumstances

 

code:

 

 1 #include<bits/stdc++.h>
 2 using namespace std;
 3 long long a[210];
 4 long long C(long long m,long long n)//C (m中取n) 
 5 {
 6     long long ans=1;
 7     for(long long i=1;i<=n;i++)
 8     ans=ans*(m-i+1)/i;
 9     return ans;
10 }
11 signed main()
12 {
13     long long n,t;
14     scanf("%lld",&n);
15     a[1]=a[0]=1;
16     for(long long k=2;k<=n;k++)
17     {
18         for(long long i=1;i<=k;i++)
19         {
20             a[k]+=a[k-i]*C(k,i);
21         }
22     }
23     printf("%lld\n",a[n]);
24     return 0;
25 }