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。
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;
}
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