Codechef CUTTREE 任意模数FFT+点分治

2019-04-13 21:40发布

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题意

n-1次删除操作，每次随机删掉一条边，一个联通块的价值是这个联通块的大小的平方，问期望价值和，n≤105" role="presentation" style="position: relative;">n≤105

分析

这道题精神AC。。。。有两个点被卡了 首先一个联通块的价值可以理解为任意两点连通所以经过的边数，也就是任意两点间的距离和 ansi=(n−1−dist(x,y))i_(n−1)i_" role="presentation">ansi=(n−1−dist(x,y))i_(n−1)i_
然后展开
ansi=1(n−1)!∑d=0n−1(n−1−d)!cnt[d]1(n−1−i−d)!(n−1−i)!" role="presentation">ansi=1(n−1)!∑d=0n−1(n−1−d)!cnt[d]1(n−1−i−d)!(n−1−i)! cnt[d]" role="presentation" style="position: relative;">cnt[d]表示距离为d的个数,算距离的时候普通FFT一下， 然后最后拆系数FFT一下 可能我的拆系数不是很优美，我是写7次DFT的。。。

代码

#include #define pb push_back #define cl clear #define MP make_pair #define bin(i) (1<<(i)) using namespace std; typedef long long ll; const ll N = 400010; const ll Mod = 1e9+7; inline ll read() { ll p=0; ll f=1; char ch=getchar(); while(ch<'0' || ch>'9'){if(ch=='-') f=-1; ch=getchar();} while(ch>='0' && ch<='9'){p=p*10+ch-'0'; ch=getchar();} return p*f; } void upd(ll &x,ll y){if(x>y) x=y;} struct E{ll x,y,next;}edge[N]; ll len,first[N]; void ins(ll x,ll y){len++; edge[len].x=x; edge[len].y=y; edge[len].next=first[x]; first[x]=len;} struct node { long double r,i; node(){} node(long double _r,long double _i){r=_r; i=_i;} friend node operator + (const node &x,const node &y){return node(x.r+y.r,x.i+y.i);} friend node operator - (const node &x,const node &y){return node(x.r-y.r,x.i-y.i);} friend node operator * (const node &x,const node &y){return node(x.r*y.r-x.i*y.i,x.r*y.i+y.r*x.i);} }wn[N]; long double pi = acos(-1); ll R[N]; void DFT(node *a,ll n,ll op) { for(int i=1;iif(R[i] > i) swap(a[R[i]],a[i]); for(int i=1;i1) { for(int j=0;j1) { node w = node(1,0); for(int k=0;k*wn[i]) { node x = a[j+k]; node y = a[j+k+i]*w; a[j+k] = x+y; a[j+k+i] = x-y; } } } if(op == -1) reverse(a+1,a+n); } node c[N],d[N]; ll cnt[N]; void FFT(ll *a,ll *b,ll n,ll m) { ll mm = n+m; ll l=0,nn; for(nn=1;nn<=mm;nn<<=1) l++; for(int i=0;i<=n;i++) c[i].r = a[i],c[i].i = 0; for(int i=0;i<=m;i++) d[i].r = b[i],d[i].i = 0; for(int i=1;i>1] >> 1) | ((i&1) << (l-1)); DFT(c,nn,1); DFT(d,nn,1); for(int i=0;i1); for(int i=0;i0.5) * 2) % Mod; for(int i=0;i0; } ll a[N],b[N]; ll siz[N],p=0,mx; bool vis[N]; ll MAX_DEP = 0; void dfs2(ll x,ll f,ll dis) { siz[x] = 1; for(int k=first[x];k!=-1;k=edge[k].next) { ll y = edge[k].y; if(y==f || vis[y]) continue; dfs2(y,x,dis+1); siz[x] += siz[y]; } MAX_DEP = max(MAX_DEP , dis); } void Find_root(ll x,ll f,ll tot) { ll maxx = tot - siz[x]; for(int k=first[x];k!=-1;k=edge[k].next) { ll y = edge[k].y; if(y==f || vis[y]) continue; Find_root(y,x,tot); maxx = max(maxx , siz[y]); } if(maxx < mx) { mx = maxx; p = x; } } void calc(ll x,ll f,ll dd) { b[dd]++; for(int k=first[x];k!=-1;k=edge[k].next) { ll y = edge[k].y; if(vis[y] || y==f) continue; calc(y,x,dd+1); } } void dfs(ll x) { dfs2(x,0,0); mx = LLONG_MAX; Find_root(x,0,siz[x]); x=p; MAX_DEP = 0; dfs2(x,0,0); vis[x] = 1; for(int i=0;i<=MAX_DEP;i++) a[i] = 0; // printf("%lld %lld ",x,siz[x]); a[0] = 1; cnt[0] ++; for(int k=first[x];k!=-1;k=edge[k].next) { ll y = edge[k].y; if(vis[y]) continue; calc(y,x,1); FFT(a,b,MAX_DEP,MAX_DEP); for(int i=0;i<=MAX_DEP;i++) a[i] += b[i],b[i] = 0; } for(int k=first[x];k!=-1;k=edge[k].next) { ll y = edge[k].y; if(vis[y]) continue ; dfs(y); } } ll fac[N],inv[N]; node ka[N],kb[N],ba[N],bb[N]; ll ans[N]; int main() { ll n = read(); len = 0; memset(first,-1,sizeof(first)); ll m=n+n; ll nn,l=0; for(nn=1;nn<=m;nn<<=1) l++; for(int i=1;i1) wn[i] = node(cos(pi/i),sin(pi/i)); for(int i=1;ix = read(); ll y = read(); ins(x,y); ins(y,x); } dfs(1); fac[0] = 1; for(int i=1;i<=n;i++) fac[i] = fac[i-1] * i % Mod; inv[0] = inv[1] = 1; for(int i=2;i<=n;i++) inv[i] = (Mod - Mod/i) * inv[Mod%i] % Mod; for(int i=1;i<=n;i++) inv[i] = inv[i-1] * inv[i] % Mod; ll qm = (ll)(ceil(sqrt(Mod))); for(int i=0;ix = fac[n-1-i] * cnt[i] % Mod; // printf("%lld ",x); ka[i].r = x/qm; ba[i].r = x%qm; // printf("%lld %lld ",x/qm,x%qm); }// printf(" "); for(int i=0;ix = inv[i]; // printf("%lld ",x); kb[i].r = x/qm; bb[i].r = x%qm; // printf("%lld %lld ",x/qm,x%qm); }// printf(" "); for(int i=1;i>1] >> 1) | ((i&1) << (l-1)); DFT(ka,nn,1); DFT(kb,nn,1); DFT(ba,nn,1); DFT(bb,nn,1); // for(ll i=0;i// printf("%f %f %f %f ",ka[i].r,kb[i].r,ba[i].r,bb[i].r); // } for(int i=0;i0; for(int i=0;i1); for(int i=0;i0.5) % Mod * qm % Mod * qm % Mod) % Mod; for(int i=0;i0; for(int i=0;i1); for(int i=0;i0.5) % Mod * qm % Mod) % Mod; for(int i=0;i0; for(int i=0;i1); for(int i=0;i0.5) % Mod) % Mod; for(int i=0;i1-i] = (ans[n-1-i] * inv[n-1] % Mod * fac[n-1-i] % Mod); for(int i=0;iprintf("%lld ",ans[n-1-i]); // cout<<(double)(clock())<return 0; }

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