SPOJ Triple Sums(FFT+容斥原理)

# include <cstdio>
# include <cstring>
# include <cstdlib>
# include <iostream>
# include <vector>
# include <queue>
# include <stack>
# include <map>
# include <complex>
# include <set>
# include <cmath>
# include <algorithm>
using namespace std;
# define lowbit(x) ((x)&(-x))
const double pi=acos(-1.0);
# define eps 1e-
# define MOD
# define INF
# define mem(a,b) memset(a,b,sizeof(a))
# define FOR(i,a,n) for(int i=a; i<=n; ++i)
# define FDR(i,a,n) for(int i=a; i>=n; --i)
# define bug puts("H");
# define lch p<<,l,mid
# define rch p<<|,mid+,r
# define mp make_pair
# define pb push_back
typedef pair<int,int> PII;
typedef vector<int> VI;
# pragma comment(linker, "/STACK:1024000000,1024000000")
typedef long long LL;
inline int Scan() {
    int x=,f=; char ch=getchar();
    while(ch<''||ch>''){if(ch=='-') f=-; ch=getchar();}
    while(ch>=''&&ch<=''){x=x*+ch-''; ch=getchar();}
    return x*f;
}
inline void Out(int a) {
    if(a<) {putchar('-'); a=-a;}
    if(a>=) Out(a/);
    putchar(a%+'');
}
const int N=;
//Code begin....
 
typedef complex<double> cmx;
int c[N<<], val[N<<], a[N<<], b[N<<];
cmx x[N<<], y[N<<];
 
void change(cmx x[], int len) {
    int i, j, k;
    for(i=, j=len>>; i<len-; ++i) {
        if(i<j) swap(x[i],x[j]);
        k=len>>;
        while(j>=k) j-=k, k>>=;
        if(j<k) j+=k;
    }
}
void fft(cmx x[], int len, int on) {
    change(x,len);
    for(int i=; i<=len; i<<=) {
        cmx wn(cos(-on**pi/i),sin(-on**pi/i));
        for(int j=; j<len; j+=i) {
            cmx w(,);
            FOR(k,j,j+i/-) {
                cmx u=x[k], v=x[k+i/]*w;
                x[k]=u+v; x[k+i/]=u-v; w*=wn;
            }
        }
    }
    if(on==-) FOR(i,,len-) x[i]/=len;
}
int main()
{
    int n, maxx=;
    cmx three(3.0,);
    scanf("%d",&n);
    FOR(i,,n) scanf("%d",val+i), val[i]+=, maxx=max(maxx,val[i]);
    maxx*=;
    FOR(i,,n) ++a[val[i]], ++b[val[i]*], ++c[val[i]*];
    int len=;
    while(len<maxx) len<<=; //len要为2的幂次
    FOR(i,,len-) x[i]=cmx(a[i],), y[i]=cmx(b[i],);
    fft(x,len,); fft(y,len,); //将系数表达式转化为点值表达式
    FOR(i,,len-) x[i]=x[i]*x[i]*x[i]-x[i]*y[i]*three;
    fft(x,len,-);
    FOR(i,,len-) a[i]=(int(x[i].real()+0.5)+*c[i])/;
    FOR(i,,len-) {
        if(!a[i]) continue;
        printf("%d : %d\n", i-*,a[i]);
    }
    return ;
}