Uvalive_6886_golf Bot (FFT fast Fourier transform)

Transmission door: Http://acm.hust.edu.cn/vjudge/contest/view.action?cid=77958#problem/C

Types of questions: number theory

The following:

In set a, 1 or 2 numbers are taken, and they become a new set of S. Q-time query, each query input a number, Q number of how many numbers belong to the set S.

Set a element number 2e5,q<=2e5,a element size <=2e5, query number 2e5

Analysis:

Violence Enumeration O (C (n,2) +n), O (n^2) is too complex.

The number of FFT statistics appear, and then directly calculate the result is OK, complexity O (NLOGN).

Only 1 digits need O (n) to mark, S1 = {1,3,5}.

The following discussion takes 2 numbers:

For example, a = {1,3,5}

To set the polynomial

Then S2 = {2,4,6,8,10}

Comprehensive: s={1,2,3,4,5,6,8,10}

Code;

#include <iostream> #include <cstdio> #include <cstring> #include <cmath> #include <

Algorithm> #define MT (a,b) memset (A,b,sizeof (a)) using namespace Std;

const int M = 201000;
    struct Complex {double x,y;
        Complex (double _x=0,double _y=0) {x=_x;
    y=_y;
    Friend Complex operator-(const Complex &a,const Complex &b) {return Complex (A.X-B.X,A.Y-B.Y);
    Friend Complex operator + (const Complex &a,const Complex &b) {return Complex (A.X+B.X,A.Y+B.Y); Friend Complex operator * (const Complex &a,const Complex &b) {return Complex (a.x*b.x-a.y*b.y,a.x*
    b.y+a.y*b.x);
}
};
    Class FFT {Complex u,t; void Change (Complex y[],int len) {for (int i=1,j=len>>1,k; i<len-1; i++) {if (i<j) swap (y[
            I],Y[J]);
            k=len>>1;
                while (j>=k) {j-=k;
            k>>=1; } if (j<k) j+=k;
        } public:void FFT (Complex y[],int len,int on) {change (Y,len);
        Double Tmp=-on*2*acos (-1.0);
            for (int h=2; h<=len; h<<=1) {Complex wn (cos (tmp/h), sin (tmp/h));
                for (int j=0; j<len; j+=h) {Complex W (1,0);
                int h2=h>>1;
                    for (int k=j; k<j+h2; k++) {u=y[k];
                    T=W*Y[K+H2];
                    Y[k]=u+t;
                    Y[k+h2]=u-t;
                W=w*wn;
            }} if (On==-1) {for (int i=0; i<len; i++) {Y[i].x/=len;

}}} G;
int flag[m*4];
Complex X[m*4];

int a[m*2];
    int main () {int n,q;
        while (~SCANF ("%d", &n)) {MT (flag,0);
        int MAXN = 0;
            for (int i=0; i<n; i++) {scanf ("%d", &a[i]);
            Flag[a[i]] = 1;
        MAXN = max (Maxn,a[i]); }

        int len = 1;
        maxn<<=1;

        while (LEN&LT;MAXN) len<<=1;
        for (int i=0; i<len; i++) {X[i] = Complex (flag[i],0);

        } g.fft (x,len,1);
        for (int i=0;i<len;i++) {X[i] = X[i]*x[i];

        } g.fft (x,len,-1);
        MT (flag,0);
        for (int i=0;i<n;i++) {flag[a[i]]++;
        for (int i=0;i<len;i++) {Flag[i] + + (int) (x[i].x+0.5); }//for (int i=0;i<len;i++) {//printf ("%d--->%d\n", i,flag[i]);//} scanf ("%d", &
        AMP;Q);
        int b;
        int ans = 0;
            while (q--) {scanf ("%d", &b);
        if (flag[b]) ans++;

    printf ("%d\n", ans);
return 0;
 /** 3 1 3 5 6 2 4 5 7 8 9 * *