CF914G Sum the Fibonacci FWT子集卷积

Posted 2021-10-30 itst

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一道良心的练习FWT和子集卷积的板子……

具体来说就是先把所有满足\(s_a \& s_b = 0\)的\(s_a \mid s_b\)的值用子集卷积算出来，将所有\(s_a \oplus s_b\)用xor卷积算出来，把斐波那契数代进去，然后将三个数组and卷积，最后取\(2^i (i \in Z)\)的位置的答案的和

#include<bits/stdc++.h>
//this code is written by Itst
using namespace std;

int read(){
    int a = 0; char c = getchar();
    while(!isdigit(c)) c = getchar();
    while(isdigit(c)){
        a = a * 10 + c - 48;
        c = getchar();
    }
    return a;
}

const int _ = (1 << 17) + 3 , MOD = 1e9 + 7;
#define lowbit(x) (x & (-x))
int fib[_] , arr[_] , cnt1[_] , Or[18][_] , ansOr[_] , tmp[_] , And[_] , Xor[_] , N;

void orFWT(int *arr , long long tp){
    for(int i = 0 ; i < 17 ; ++i)
        for(int j = 0 ; j < 1 << 17 ; j += 1 << (i + 1))
            for(int k = 0 ; k < 1 << i ; ++k)
                arr[(1 << i) + j + k] = (arr[(1 << i) + j + k] + tp * arr[j + k] + MOD) % MOD;
}

void andFWT(int *arr , long long tp){
    for(int i = 0 ; i < 17 ; ++i)
        for(int j = 0 ; j < 1 << 17 ; j += 1 << (i + 1))
            for(int k = 0 ; k < 1 << i ; ++k)
                arr[j + k] = (arr[j + k] + tp * arr[(1 << i) + j + k] + MOD) % MOD;
}

void xorFWT(int *arr , long long tp){
    for(int i = 0 ; i < 17 ; ++i)
        for(int j = 0 ; j < 1 << 17 ; j += 1 << (i + 1))
            for(int k = 0 ; k < 1 << i ; ++k){
                int x = arr[j + k] , y = arr[(1 << i) + j + k];
                arr[j + k] = (x + y) % MOD;
                arr[(1 << i) + j + k] = (x - y + MOD) % MOD;
                if(tp == -1){
                    if(arr[j + k] & 1) arr[j + k] += MOD;
                    arr[j + k] >>= 1;
                    if(arr[(1 << i) + j + k] & 1) arr[(1 << i) + j + k] += MOD;
                    arr[(1 << i) + j + k] >>= 1;
                }
            }
}

void init(){
    for(int i = 1 ; i < 1 << 17 ; ++i)
        cnt1[i] = cnt1[i - lowbit(i)] + 1;
    fib[1] = 1;
    for(int i = 2 ; i < 1 << 17 ; ++i)
        fib[i] = (fib[i - 1] + fib[i - 2]) % MOD;
}

int main(){
#ifndef ONLINE_JUDGE
    freopen("in","r",stdin);
    //freopen("out","w",stdout);
#endif
    init();
    N = read();
    for(int i = 1 ; i <= N ; ++i){
        int p = read();
        ++arr[p]; ++Or[cnt1[p]][p];
    }
    memcpy(And , arr , sizeof(arr)); memcpy(Xor , arr , sizeof(arr));
    for(int i = 0 ; i <= 17 ; ++i)
        orFWT(Or[i] , 1);
    for(int i = 0 ; i <= 17 ; ++i){
        memset(tmp , 0 , sizeof(tmp));
        for(int j = 0 ; j <= i ; ++j)
            for(int k = 0 ; k < 1 << 17 ; ++k)
                tmp[k] = (tmp[k] + 1ll * Or[j][k] * Or[i - j][k]) % MOD;
        orFWT(tmp , -1);
        for(int k = 0 ; k < 1 << 17 ; ++k)
            if(cnt1[k] == i)
                ansOr[k] = tmp[k];
    }
    xorFWT(Xor , 1);
    for(int i = 0 ; i < 1 << 17 ; ++i)
        Xor[i] = 1ll * Xor[i] * Xor[i] % MOD;
    xorFWT(Xor , -1);
    for(int i = 0 ; i < 1 << 17 ; ++i){
        ansOr[i] = 1ll * ansOr[i] * fib[i] % MOD;
        And[i] = 1ll * And[i] * fib[i] % MOD;
        Xor[i] = 1ll * Xor[i] * fib[i] % MOD;
    }
    andFWT(ansOr , 1); andFWT(And , 1); andFWT(Xor , 1);
    for(int i = 0 ; i < 1 << 17 ; ++i)
        And[i] = 1ll * ansOr[i] * And[i] % MOD * Xor[i] % MOD;
    andFWT(And , -1);
    int ans = 0;
    for(int i = 1 ; i < 1 << 17 ; i <<= 1)
        ans = (ans + And[i]) % MOD;
    cout << ans;
    return 0;
}