骗分专题

(mu*I=epsilon)

(sum_{d|x}mu(d)=epsilon)

([gcd(x,y)==1]=sum_{d|x,d|y}mu(d))

(f=g*1\,\,\,\,\,\,g=f*mu)

DFT只能是2的幂次
循环卷积:a(n)卷b(n),NTT开到n,那么自动%n(n是2的幂次)。
bluestein可做非2的幂次

树形dp卡空间:滚动数组,树剖先走重儿子

在模p意义下有
((x+1)^p≡(x^p+1)~mod~p)

[(x+1)^m=(x+1)^{lfloorfrac m p floor imes p} imes(x+1)^{m~mod~p} ]

[(x+1)^m=(x^p+1)^{lfloorfrac m p floor} imes(x+1)^{m~mod~p} ]

二项式展开,得:

[sum_{i=0}^m{mchoose i}x^i=sum_{i=0}^{lfloorfrac m p floor}{lfloorfrac m p floorchoose i}x^{i imes p} imessum_{i=0}^{m~mod~p}{m~mod~pchoose i}x^i ]

当左边(i)(n),右边也使(x)指数也取(n)得:

[{mchoose n}={lfloorfrac m p floorchoose lfloor frac n p floor} imes {m~mod~pchoose n~mod~p} ]

(lfloor frac n p floor imes p+(n~mod~p)=n)

原文地址:https://www.cnblogs.com/Smeow/p/10582511.html