codeforces 131c 組合數

題目：

C. The World is a Theatre

time limit per test

2 seconds

memory limit per test

256 megabytes

input

standard input

output

standard output

There are n boys and m girls attending a theatre club. To set a play "The Big Bang Theory", they need to choose a group containing exactly t actors containing no less than 4 boys and no less than one girl. How many ways are there to choose a group? Of course, the variants that only differ in the composition of the troupe are considered different.

Perform all calculations in the 64-bit type: long long for С/С++, int64 for Delphi and long for Java.

Input

The only line of the input data contains three integers n, m, t (4 ≤ n ≤ 30, 1 ≤ m ≤ 30, 5 ≤ t ≤ n + m).

Output

Find the required number of ways.

Please do not use the %lld specificator to read or write 64-bit integers in С++. It is preferred to use cin, cout streams or the %I64d specificator.

Examples

input

5 2 5

output

10

input

4 3 5

output

3

利用組合數遞推公式：C(n, m) = C(n - 1, m - 1) + C(n - 1, m) 對應最後一個選或者不選的情況

代碼：

#include<bits/stdc++.h>
using namespace std;
const int maxn=70;///只開到35的話 20 20 40 這組樣例會因爲越界報錯

__int64 n,m,t;
__int64 c[maxn][maxn];

int main(){
    memset(c,0,sizeof(c));
    c[0][0]=1;
    for(int i=1;i<=30;++i){
        c[i][0]=c[i][i]=1;
        for(int j=1;j<=i;++j){
            c[i][j]=c[i-1][j-1]+c[i-1][j];
        }
    }
    /*for(int i=0;i<=30;++i){
        for(int j=0;j<=30;++j){
            cout<<c[i][j]<<" ";
        }
        cout<<endl;
    }*/
    scanf("%I64d%I64d%I64d",&n,&m,&t);
    __int64 ans=0;
    for(__int64 i=4;i<t;++i){
        ans+=c[n][i]*c[m][t-i];///若判一下i和n的關係以及m和t-1的關係數組就可以開小一些
    }
    printf("%I64d\n",ans);
    return 0;
}

也可以使用遞推公式每次算一下，不過會慢一些：

#include<bits/stdc++.h>
using namespace std;

__int64 n,m,t;

__int64 C(__int64 n,__int64 m){
    __int64 ans=1;
    for(__int64 i=1;i<=m;++i){
        ans*=(n-i+1);
        ans/=i;
    }
    return ans;
}

int main(){
    scanf("%I64d%I64d%I64d",&n,&m,&t);
    __int64 ans=0;
    for(__int64 i=4;i<t;++i){
        ans+=C(n,i)*C(m,t-i);
    }
    printf("%I64d\n",ans);
    return 0;
}