51 nod 1773 A国的贸易

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于 2018-08-14 23:34:58 发布

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分类专栏： fwt

本文链接：https://blog.youkuaiyun.com/oWuHen12/article/details/81676695

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本文介绍了解决51nod1773问题的方法，使用快速沃尔什-赫达曼变换（FWT）进行高效计算。通过预处理和优化I/O操作实现了较好的性能。

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题目链接：51nod 1773

sol:

关于fwt的学习可以看下面这篇大大的博客：https://www.cnblogs.com/cjyyb/p/9065615.html
这道题卡IO，用getchar加速就可以了，这里顺手放下自己从dls扒来的板子。

这里记录下自己的板子。

code:

#include <bits/stdc++.h>
using namespace std;

typedef long long ll;
const int maxn = 3e6 + 10;
const int mod = 1e9 + 7;
const int inv2 = (mod + 1) >> 1;
const ll inf = 1.5e18;

ll A[maxn];
bool check[maxn];

#define fi first
#define se second
#define pll pair<ll, ll>

void Add(ll& x,ll y){
    x+=y;
    if(x>=mod) x-=mod;
}

void Mul(ll& x,ll y){
    x*=y;
    if(x>=mod) x%=mod;
}

void Mod(ll &x){
    if(x>=mod) x-=mod;
}

void init()
{
    memset(check, false, sizeof(check));
    for (int i = 2; i < maxn; i++)
    {
        if (!check[i])
            for (int j = i * 2; j < maxn; j += i)
            {
                check[j] = true;
            }
    }
}

struct FWT
{
    int N;
    void init(int n)
    {
        N = 1;
        while (N <= n)
            N <<= 1;
    }

    void FWT_or(ll *a, int opt)
    {
        for (int i = 1; i < N; i <<= 1)
            for (int p = i << 1, j = 0; j < N; j += p)
                for (int k = 0; k < i; ++k)
                    if (opt == 1)
                        a[i + j + k] = (a[j + k] + a[i + j + k]) % mod;
                    else
                        a[i + j + k] = (a[i + j + k] + mod - a[j + k]) % mod;
    }
    void FWT_and(ll *a, int opt)
    {
        for (int i = 1; i < N; i <<= 1)
            for (int p = i << 1, j = 0; j < N; j += p)
                for (int k = 0; k < i; ++k)
                    if (opt == 1)
                        a[j + k] = (a[j + k] + a[i + j + k]) % mod;
                    else
                        a[j + k] = (a[j + k] + mod - a[i + j + k]) % mod;
    }

    void fwt_xor(ll *a, int op)
    {
        for (int i = 1; i < N; i <<= 1)
            for (int p = i << 1, j = 0; j < N; j += p)
                for (int k = 0; k < i; ++k)
                {
                    ll x = a[j + k], y = a[i + j + k];
                    a[j + k] = (x + y);
                    Mod(a[j+k]);
                    a[i + j + k] = (x + mod - y);
                    Mod(a[i+j+k]);
                    if (op == -1)
                    {
                        // a[j + k] = a[j + k] * inv2 % mod;
                        Mul(a[j+k],inv2);
                        // a[i + j + k] = a[i + j + k] * inv2 % mod;
                        Mul(a[i+j+k],inv2);
                    }
                }
    }
} fwt;

inline ll qpow(ll a, ll b)
{
    ll ret = 1;
    while (b)
    {
        if (b & 1)
            ret = ret * a % mod;
        a = a * a % mod;
        b >>= 1;
    }
    return ret;
}

ll dp[maxn];

namespace IO{ 
    #define BUF_SIZE 100000 
    #define OUT_SIZE 100000 
    #define ll long long 
    //fread->read 

    bool IOerror=0; 
    inline char nc(){ 
        static char buf[BUF_SIZE],*p1=buf+BUF_SIZE,*pend=buf+BUF_SIZE; 
        if (p1==pend){ 
            p1=buf; pend=buf+fread(buf,1,BUF_SIZE,stdin); 
            if (pend==p1){IOerror=1;return -1;} 
            //{printf("IO error!\n");system("pause");for (;;);exit(0);} 
        } 
        return *p1++; 
    } 
    inline bool blank(char ch){return ch==' '||ch=='\n'||ch=='\r'||ch=='\t';} 
    inline void read(int &x){ 
        bool sign=0; char ch=nc(); x=0; 
        for (;blank(ch);ch=nc()); 
        if (IOerror)return; 
        if (ch=='-')sign=1,ch=nc(); 
        for (;ch>='0'&&ch<='9';ch=nc())x=x*10+ch-'0'; 
        if (sign)x=-x; 
    } 
    inline void read(ll &x){ 
        bool sign=0; char ch=nc(); x=0; 
        for (;blank(ch);ch=nc()); 
        if (IOerror)return; 
        if (ch=='-')sign=1,ch=nc(); 
        for (;ch>='0'&&ch<='9';ch=nc())x=x*10+ch-'0'; 
        if (sign)x=-x; 
    } 
    inline void read(double &x){ 
        bool sign=0; char ch=nc(); x=0; 
        for (;blank(ch);ch=nc()); 
        if (IOerror)return; 
        if (ch=='-')sign=1,ch=nc(); 
        for (;ch>='0'&&ch<='9';ch=nc())x=x*10+ch-'0'; 
        if (ch=='.'){ 
            double tmp=1; ch=nc(); 
            for (;ch>='0'&&ch<='9';ch=nc())tmp/=10.0,x+=tmp*(ch-'0'); 
        } 
        if (sign)x=-x; 
    } 
    inline void read(char *s){ 
        char ch=nc(); 
        for (;blank(ch);ch=nc()); 
        if (IOerror)return; 
        for (;!blank(ch)&&!IOerror;ch=nc())*s++=ch; 
        *s=0; 
    } 
    inline void read(char &c){ 
        for (c=nc();blank(c);c=nc()); 
        if (IOerror){c=-1;return;} 
    } 
    //fwrite->write 
    struct Ostream_fwrite{ 
        char *buf,*p1,*pend; 
        Ostream_fwrite(){buf=new char[BUF_SIZE];p1=buf;pend=buf+BUF_SIZE;} 
        void out(char ch){ 
            if (p1==pend){ 
                fwrite(buf,1,BUF_SIZE,stdout);p1=buf; 
            } 
            *p1++=ch; 
        } 
        void print(int x){ 
            static char s[15],*s1;s1=s; 
            if (!x)*s1++='0';if (x<0)out('-'),x=-x; 
            while(x)*s1++=x%10+'0',x/=10; 
            while(s1--!=s)out(*s1); 
        } 
        void println(int x){ 
            static char s[15],*s1;s1=s; 
            if (!x)*s1++='0';if (x<0)out('-'),x=-x; 
            while(x)*s1++=x%10+'0',x/=10; 
            while(s1--!=s)out(*s1); out('\n'); 
        } 
        void print(ll x){ 
            static char s[25],*s1;s1=s; 
            if (!x)*s1++='0';if (x<0)out('-'),x=-x; 
            while(x)*s1++=x%10+'0',x/=10; 
            while(s1--!=s)out(*s1); 
        } 
        void println(ll x){ 
            static char s[25],*s1;s1=s; 
            if (!x)*s1++='0';if (x<0)out('-'),x=-x; 
            while(x)*s1++=x%10+'0',x/=10; 
            while(s1--!=s)out(*s1); out('\n'); 
        } 
        void print(double x,int y){ 
            static ll mul[]={1,10,100,1000,10000,100000,1000000,10000000,100000000, 
                1000000000,10000000000LL,100000000000LL,1000000000000LL,10000000000000LL, 
                100000000000000LL,1000000000000000LL,10000000000000000LL,100000000000000000LL}; 
            if (x<-1e-12)out('-'),x=-x;x*=mul[y]; 
            ll x1=(ll)floor(x); if (x-floor(x)>=0.5)++x1; 
            ll x2=x1/mul[y],x3=x1-x2*mul[y]; print(x2); 
            if (y>0){out('.'); for (size_t i=1;i<y&&x3*mul[i]<mul[y];out('0'),++i); print(x3);} 
        } 
        void println(double x,int y){print(x,y);out('\n');} 
        void print(char *s){while (*s)out(*s++);} 
        void println(char *s){while (*s)out(*s++);out('\n');} 
        void flush(){if (p1!=buf){fwrite(buf,1,p1-buf,stdout);p1=buf;}} 
        ~Ostream_fwrite(){flush();} 
    }Ostream; 
    inline void print(int x){Ostream.print(x);} 
    inline void println(int x){Ostream.println(x);} 
    inline void print(char x){Ostream.out(x);} 
    inline void println(char x){Ostream.out(x);Ostream.out('\n');} 
    inline void print(ll x){Ostream.print(x);} 
    inline void println(ll x){Ostream.println(x);} 
    inline void print(double x,int y){Ostream.print(x,y);} 
    inline void println(double x,int y){Ostream.println(x,y);} 
    inline void print(char *s){Ostream.print(s);} 
    inline void println(char *s){Ostream.println(s);} 
    inline void println(){Ostream.out('\n');} 
    inline void flush(){Ostream.flush();}
    #undef ll 
    #undef OUT_SIZE 
    #undef BUF_SIZE 
};

int main()
{
    init();
    int n,t;
    IO::read(n);
    IO::read(t);
    for(int i=0;i<(1<<n);i++){
        IO::read(dp[i]);
    }
    fwt.init(1<<n);
    A[0] = 1;
    for(int i=0;i<n;i++) A[1<<i] = 1;
    fwt.fwt_xor(A,1);
    fwt.fwt_xor(dp,1);
    for(int i = 0;i<fwt.N;i++) A[i] = qpow(A[i],t);
    for(int i = 0;i<fwt.N;i++) dp[i] = dp[i]*A[i]%mod;
    fwt.fwt_xor(dp,-1);
    // Print(n);
    for(int i = 0;i<(1<<n);i++){
        IO::print((int)dp[i]);
        IO::print(' ');
    }
    IO::print('\n');
    return 0;
}