05二項式係數Cnk.md

一個簡單的動態規劃，配合二項式係數和楊輝三角。
$C_N^K=C_{N-1}^{K-1}+C_{N-1}^K$

#include<iostream>
#include<vector>
using namespace std;
 
int Cnk(int n, int k)
{
    vector<vector<int>>c;
    vector<int>c2;
    c2.push_back(1);
    c.push_back(c2);
    c2.push_back(1);
    c.push_back(c2);
    for(int i=2;i<n+1;i++)
    {
        vector<int>c1;
        c1.push_back(1);
        for(int j=1;j<i;++j)
        {
            int x=c[i-1][j-1]+c[i-1][j];
            c1.push_back(x);
        }
        c1.push_back(1);
        c.push_back(c1);
    }
    return c[n][k];
}
 
int main(void)
{
    int n,k;
    cin>>n>>k;
 
    cout<<Cnk(n,k)<<endl;;
    return -1;
}