[SOJ #48]集合对称差卷积

题目大意：给你两个多项式$A,B$，求多项式$C$使得：

$$
C_n=\sum\limits_{x\oplus y=n}A_xB_y
$$
题解：$FWT$

卡点：无



C++ Code：

#include <cstdio>
#include <cctype>
namespace __IO {
	int ch;
	inline int read() {
		while (isspace(ch = getchar())) ;
		return ch & 15;
	}
}
using __IO::read;

#define maxn 2097152

int lim;
inline void init(const int n) {
	lim = 1; while (lim < n) lim <<= 1;
}
inline void FWT(long long *A, const int op = 1) {
	for (register int mid = 1; mid < lim; mid <<= 1)
		for (register int i = 0; i < lim; i += mid << 1)
			for (register int j = 0; j < mid; ++j) {
				const long long X = A[i + j], Y = A[i + j + mid];
				A[i + j] = X + Y, A[i + j + mid] = X - Y;
			}
	if (!op) for (long long *i = A; i != A + lim; ++i) *i /= lim;
}

int n;
long long A[maxn], B[maxn];
int main() {
	scanf("%d", &n);
	for (int i = 0; i < n; ++i) A[i] = read();
	for (int i = 0; i < n; ++i) B[i] = read();
	init(n + n);
	FWT(A), FWT(B);
	for (int i = 0; i < lim; ++i) A[i] = A[i] * B[i];
	FWT(A, 0);
	for (int i = 0; i < n; ++i) printf("%lld ", A[i]); puts("");
	return 0;
}