模板：离散数学

离散数学

归并排序求逆序对

ll merge_sort(ll *b,ll *e)//int存答案可能会爆
{
    if(e-b<2)return 0;
    ll i=0,j=0,*m=b+(e-b)/2,ans=merge_sort(b,m)+merge_sort(m,e);
    vector<ll> l(b,m),r(m,e);
    while(i<l.size()&&j<r.size())
    {
        if(r[j]<l[i])*(b++)=r[j++],ans+=l.size()-i;
        else *(b++)=l[i++];
    }
    while(i<l.size())*(b++)=l[i++];
    while(j<r.size())*(b++)=r[j++];
    return ans;
}

快速解约瑟夫

ll josephus(ll n,ll k)//编号0~n-1，每k个出列，时间复杂度O(min(n,k))
{
    if(n<3)return k%n;
    if(n<k)return (Josephus(n-1,k)+k)%n;
    ll ret=Josephus(n-n/k,k)-n%k;
    return ret<0?ret+n:ret+ret/(k-1);
}

曼哈顿距离的变换

$|x1 −x2|+|y1 −y2| = max(|(x1 + y1)−(x2 + y2)|,|(x1 −y1)−(x2 −y2)|)$