BZOJ3160 万径人踪灭（FFT+manacher）

　　容易想到先统计回文串数量，这样就去掉了不连续的限制，变为统计回文序列数量。

　　显然以某个位置为对称轴的回文序列数量就是2^{其两边（包括自身）对称相等的位置数量}-1。对称有啥性质？位置和相等。这不就是卷积嘛。那么就做完了。

　　又写挂manacher，没救。

#include<iostream> 
#include<cstdio>
#include<cmath>
#include<cstdlib>
#include<cstring>
#include<algorithm>
using namespace std;
int read()
{
    int x=0,f=1;char c=getchar();
    while (c<'0'||c>'9') {if (c=='-') f=-1;c=getchar();}
    while (c>='0'&&c<='9') x=(x<<1)+(x<<3)+(c^48),c=getchar();
    return x*f;
}
#define N 270000
#define P 1000000007
int n,m,s[N],t,r[N],f[N],p[N],ans=0;
const double PI=3.14159265358979324;
struct complex
{
    double x,y;
    complex operator +(const complex&a) const
    {
        return (complex){x+a.x,y+a.y};
    }
    complex operator -(const complex&a) const
    {
        return (complex){x-a.x,y-a.y};
    }
    complex operator *(const complex&a) const
    {
        return (complex){x*a.x-y*a.y,x*a.y+y*a.x};
    }
}a[N],b[N];
void DFT(int n,complex *a,int p)
{
    for (int i=0;i<n;i++) if (i<r[i]) swap(a[i],a[r[i]]);
    for (int i=2;i<=n;i<<=1)
    {
        complex wn=(complex){cos(2*PI/i),p*sin(2*PI/i)};
        for (int j=0;j<n;j+=i)
        {
            complex w=(complex){1,0};
            for (int k=j;k<j+(i>>1);k++,w=w*wn)
            {
                complex x=a[k],y=w*a[k+(i>>1)];
                a[k]=x+y,a[k+(i>>1)]=x-y;
            }
        }
    }
}
void mul(int n,complex *a,complex *b)
{
    for (int i=0;i<n;i++) a[i].y=a[i].x-b[i].x,a[i].x=a[i].x+b[i].x;
    DFT(n,a,1);
    for (int i=0;i<n;i++) a[i]=a[i]*a[i];
    DFT(n,a,-1);
    for (int i=0;i<n;i++) a[i].x=a[i].x/n/4;
}
int main()
{
#ifndef ONLINE_JUDGE
    freopen("bzoj3160.in","r",stdin);
    freopen("bzoj3160.out","w",stdout);
    const char LL[]="%I64d";
#else
    const char LL[]="%lld";
#endif
    char c=getchar();
    while (c=='a'||c=='b') s[n++]=c-96,c=getchar();
    m=n*2-1;
    t=1;while (t<m) t<<=1;
    for (int i=0;i<t;i++) r[i]=(r[i>>1]>>1)|(i&1)*(t>>1);
    for (int i=0;i<n;i++) a[i].x=b[i].x=s[i]-1;
    mul(t,a,b);
    for (int i=0;i<m;i++) f[i]=(int){a[i].x+0.5};
    for (int i=0;i<t;i++) a[i].x=a[i].y=b[i].x=b[i].y=0;
    for (int i=0;i<n;i++) a[i].x=b[i].x=2-s[i];
    mul(t,a,b);
    for (int i=0;i<m;i++) f[i]+=(int){a[i].x+0.5};
    for (int i=0;i<m;i++) f[i]=f[i]+1>>1;
    p[0]=1;
    for (int i=1;i<m;i++) p[i]=(p[i-1]<<1)%P;
    for (int i=0;i<m;i++) ans=(ans+p[f[i]]-1)%P;
    for (int i=m-1;~i;i--) s[i]=(i&1?0:s[i>>1]);
    for (int i=m;i;i--) s[i]=s[i-1];
    s[0]=s[++m]=0;
    memset(r,0,sizeof(r));
    r[0]=0;int x=0;
    for (int i=1;i<=m;i++)
    {
        if (x+r[x]>=i) r[i]=min(r[x-(i-x)],x+r[x]-i);
        while (i-r[i]-1>=0&&i+r[i]+1<=m&&s[i+r[i]+1]==s[i-r[i]-1]) r[i]++;
        if (i+r[i]>=x+r[x]) x=i;
    }
    for (int i=0;i<=m;i++) ans=(ans-(r[i]+1>>1)+P)%P;
    cout<<ans;
    return 0;
}