Several common calculation methods of combination number

Addition recursion: $o(n\ast n)$

Formula: $C\left(\genfrac{}{}{0ex}{}{m}{n}\right)$ = $C\left(\genfrac{}{}{0ex}{}{m}{n-1}\right)$+$C\left(\genfrac{}{}{0ex}{}{m-1}{n-1}\right)$

Understanding: This divides him into two situations: one must be selected, one is not selected

ll C[1001][1001];
memset(C,0,sizeof(C));
for(int i=0;i<=n;i++)
{
    
    
	C[i][0] = 1;
	for(int j=0;j<=i;j++)
	C[i][j] = C[i-1][j] + C[i-1][j-1];
}

Multiplication recursion: $o\left(n\right)$

Formula: $C\left(\genfrac{}{}{0ex}{}{m}{n}\right)$ = $\frac{n-m+1}{m}$*$C\left(\genfrac{}{}{0ex}{}{m-1}{n}\right)$

ll C(int m,int n)
{
    
    
	c[0] = 1;
	if(m > n-m)m = n-m;  //小优化 
	for(int i=1;i<=m;i++)
		c[i] = (n-i+1)*c[i-1]/i;
}