HDU 5730 Shell Necklace

分治，$FFT$。

#pragma comment(linker, "/STACK:1024000000,1024000000")
#include<cstdio>
#include<cstring>
#include<cmath>
#include<algorithm>
#include<vector>
#include<map>
#include<set>
#include<queue>
#include<stack>
#include<iostream>
using namespace std;
typedef long long LL;
const double pi=acos(-1.0),eps=1e-8;
void File()
{
    freopen("D:\in.txt","r",stdin);
    freopen("D:\out.txt","w",stdout);
}
template <class T>
inline void read(T &x)
{
    char c = getchar(); x = 0;while(!isdigit(c)) c = getchar();
    while(isdigit(c)) { x = x * 10 + c - '0'; c = getchar();  }
}

#define L(x) (1 << (x))
const double PI = acos(-1.0);
const int Maxn = 300010;
double ax[Maxn], ay[Maxn], bx[Maxn], by[Maxn];
int revv(int x, int bits)
{
    int ret = 0;
    for (int i = 0; i < bits; i++)
    {
        ret <<= 1;
        ret |= x & 1;
        x >>= 1;
    }
    return ret;
}
void fft(double * a, double * b, int n, bool rev)
{
    int bits = 0;
    while (1 << bits < n) ++bits;
    for (int i = 0; i < n; i++)
    {
        int j = revv(i, bits);
        if (i < j)
            swap(a[i], a[j]), swap(b[i], b[j]);
    }
    for (int len = 2; len <= n; len <<= 1)
    {
        int half = len >> 1;
        double wmx = cos(2 * PI / len), wmy = sin(2 * PI / len);
        if (rev) wmy = -wmy;
        for (int i = 0; i < n; i += len)
        {
            double wx = 1, wy = 0;
            for (int j = 0; j < half; j++)
            {
                double cx = a[i + j], cy = b[i + j];
                double dx = a[i + j + half], dy = b[i + j + half];
                double ex = dx * wx - dy * wy, ey = dx * wy + dy * wx;
                a[i + j] = cx + ex, b[i + j] = cy + ey;
                a[i + j + half] = cx - ex, b[i + j + half] = cy - ey;
                double wnx = wx * wmx - wy * wmy, wny = wx * wmy + wy * wmx;
                wx = wnx, wy = wny;
            }
        }
    }
    if (rev)
    {
        for (int i = 0; i < n; i++)
            a[i] /= n, b[i] /= n;
    }
}
int solve(int a[],int na,int b[],int nb,int ans[])
{
    int len = max(na, nb), ln;
    for(ln=0; L(ln)<len; ++ln);
    len=L(++ln);
    for (int i = 0; i < len ; ++i)
    {
        if (i >= na) ax[i] = 0, ay[i] =0;
        else ax[i] = a[i], ay[i] = 0;
    }
    fft(ax, ay, len, 0);
    for (int i = 0; i < len; ++i)
    {
        if (i >= nb) bx[i] = 0, by[i] = 0;
        else bx[i] = b[i], by[i] = 0;
    }
    fft(bx, by, len, 0);
    for (int i = 0; i < len; ++i)
    {
        double cx = ax[i] * bx[i] - ay[i] * by[i];
        double cy = ax[i] * by[i] + ay[i] * bx[i];
        ax[i] = cx, ay[i] = cy;
    }
    fft(ax, ay, len, 1);
    for (int i = 0; i < len; ++i)
        ans[i] = (int)(ax[i] + 0.5)%313;
    return len;
}

int p[Maxn],n,dp[Maxn];
int a[Maxn],b[Maxn],c[Maxn],lena,lenb;

void get(int L,int R)
{
    if(L==R) return;
    int m=(L+R)/2;
    get(L,m);

    lena=R-L; lenb=lena;
    for(int i=0;i<m-L+1;i++) b[i]=dp[i+L];
    for(int i=m-L+1;i<lena;i++) b[i]=0;
    for(int i=0;i<lena;i++) c[i]=0;

    solve(a,lena,b,lenb,c);

    int st=lena/2;
    for(int i=m+1;i<=R;i++) dp[i]=(dp[i]+c[st++])%313;

    get(m+1,R);
}

int main()
{
    while(~scanf("%d",&n))
    {
        if(n==0) break;
        p[0]=1; for(int i=1;i<=n;i++) { scanf("%d",&p[i]); p[i]=p[i]%313; }
        for(int i=0;i<n;i++) a[i]=p[i+1];
        memset(dp,0,sizeof dp); for(int i=1;i<=n;i++) dp[i]=p[i];
        get(1,n); printf("%d
",dp[n]);
    }
    return 0;
}