P4173 残缺的字符串 [FFT]

构造 \(f(x,y) = xy(x-y)^2\)

// powered by c++11
// by Isaunoya
#include <bits/stdc++.h>

#define rep(i, x, y) for (register int i = (x); i <= (y); ++i)
#define Rep(i, x, y) for (register int i = (x); i >= (y); --i)

using namespace std;
using db = double;
using ll = long long;
using uint = unsigned int;
using ull = unsigned long long;

using pii = pair<int, int>;

#define fir first
#define sec second

template <class T>

void cmax(T& x, const T& y) {
  if (x < y) x = y;
}

template <class T>

void cmin(T& x, const T& y) {
  if (x > y) x = y;
}

#define all(v) v.begin(), v.end()
#define sz(v) ((int)v.size())
#define pb emplace_back

template <class T>

void sort(vector<T>& v) {
  sort(all(v));
}

template <class T>

void reverse(vector<T>& v) {
  reverse(all(v));
}

template <class T>

void unique(vector<T>& v) {
  sort(all(v)), v.erase(unique(all(v)), v.end());
}

void reverse(string& s) { reverse(s.begin(), s.end()); }

const int io_size = 1 << 23 | 233;
const int io_limit = 1 << 22;
struct io_in {
  char ch;
#ifndef __WIN64
  char getchar() {
    static char buf[io_size], *p1 = buf, *p2 = buf;

    return (p1 == p2) && (p2 = (p1 = buf) + fread(buf, 1, io_size, stdin), p1 == p2) ? EOF : *p1++;
  }
#endif
  io_in& operator>>(char& c) {
    for (c = getchar(); isspace(c); c = getchar())
      ;

    return *this;
  }
  io_in& operator>>(string& s) {
    for (s.clear(); isspace(ch = getchar());)
      ;

    if (!~ch) return *this;

    for (s = ch; !isspace(ch = getchar()) && ~ch; s += ch)
      ;

    return *this;
  }

  io_in& operator>>(char* str) {
    char* cur = str;
    while (*cur) *cur++ = 0;

    for (cur = str; isspace(ch = getchar());)
      ;
    if (!~ch) return *this;

    for (*cur = ch; !isspace(ch = getchar()) && ~ch; *++cur = ch)
      ;

    return *++cur = 0, *this;
  }

  template <class T>

  void read(T& x) {
    bool f = 0;
    while ((ch = getchar()) < 48 && ~ch) f ^= (ch == 45);

    x = ~ch ? (ch ^ 48) : 0;
    while ((ch = getchar()) > 47) x = x * 10 + (ch ^ 48);
    x = f ? -x : x;
  }

  io_in& operator>>(int& x) { return read(x), *this; }

  io_in& operator>>(ll& x) { return read(x), *this; }

  io_in& operator>>(uint& x) { return read(x), *this; }

  io_in& operator>>(ull& x) { return read(x), *this; }

  io_in& operator>>(db& x) {
    read(x);
    bool f = x < 0;
    x = f ? -x : x;
    if (ch ^ '.') return *this;

    double d = 0.1;
    while ((ch = getchar()) > 47) x += d * (ch ^ 48), d *= .1;
    return x = f ? -x : x, *this;
  }
} in;

struct io_out {
  char buf[io_size], *s = buf;
  int pw[233], st[233];

  io_out() {
    set(7);
    rep(i, pw[0] = 1, 9) pw[i] = pw[i - 1] * 10;
  }

  ~io_out() { flush(); }

  void io_chk() {
    if (s - buf > io_limit) flush();
  }

  void flush() { fwrite(buf, 1, s - buf, stdout), fflush(stdout), s = buf; }

  io_out& operator<<(char c) { return *s++ = c, *this; }

  io_out& operator<<(string str) {
    for (char c : str) *s++ = c;
    return io_chk(), *this;
  }

  io_out& operator<<(char* str) {
    char* cur = str;
    while (*cur) *s++ = *cur++;
    return io_chk(), *this;
  }

  template <class T>

  void write(T x) {
    if (x < 0) *s++ = '-', x = -x;

    do {
      st[++st[0]] = x % 10, x /= 10;
    } while (x);

    while (st[0]) *s++ = st[st[0]--] ^ 48;
  }

  io_out& operator<<(int x) { return write(x), io_chk(), *this; }

  io_out& operator<<(ll x) { return write(x), io_chk(), *this; }

  io_out& operator<<(uint x) { return write(x), io_chk(), *this; }

  io_out& operator<<(ull x) { return write(x), io_chk(), *this; }

  int len, lft, rig;

  void set(int _length) { len = _length; }

  io_out& operator<<(db x) {
    bool f = x < 0;
    x = f ? -x : x, lft = x, rig = 1. * (x - lft) * pw[len];
    return write(f ? -lft : lft), *s++ = '.', write(rig), io_chk(), *this;
  }
} out;

template <int sz, int mod>

struct math_t {
  math_t() {
    fac.resize(sz + 1), ifac.resize(sz + 1);
    rep(i, fac[0] = 1, sz) fac[i] = fac[i - 1] * i % mod;

    ifac[sz] = inv(fac[sz]);
    Rep(i, sz - 1, 0) ifac[i] = ifac[i + 1] * (i + 1) % mod;
  }

  vector<int> fac, ifac;

  int qpow(int x, int y) {
    int ans = 1;
    for (; y; y >>= 1, x = x * x % mod)
      if (y & 1) ans = ans * x % mod;
    return ans;
  }

  int inv(int x) { return qpow(x, mod - 2); }

  int C(int n, int m) {
    if (n < 0 || m < 0 || n < m) return 0;
    return fac[n] * ifac[m] % mod * ifac[n - m] % mod;
  }
};

int gcd(int x, int y) { return !y ? x : gcd(y, x % y); }
int lcm(int x, int y) { return x * y / gcd(x, y); }

struct cpx {
  cpx(double _x = 0, double _y = 0) {
    x = _x;
    y = _y;
  }
  double x, y;
};

cpx operator+(cpx x, cpx y) { return cpx(x.x + y.x, x.y + y.y); }

cpx operator-(cpx x, cpx y) { return cpx(x.x - y.x, x.y - y.y); }

cpx operator*(cpx x, cpx y) { return cpx(x.x * y.x - x.y * y.y, x.x * y.y + x.y * y.x); }

cpx operator*(cpx x, double y) { return cpx(x.x * y, x.y * y); }

cpx operator/(cpx x, double y) { return cpx(x.x / y, x.y / y); }

const int maxn = 2e6 + 56;
const double pi = acos(-1);

int rev[maxn], limit = 1;
void FFT(cpx* A, int type) {
  for (int i = 0; i < limit; i++)
    if (i < rev[i]) swap(A[i], A[rev[i]]);

  for (int len = 1; len < limit; len <<= 1) {
    cpx Wn = cpx(cos(pi / len), sin(pi / len) * type);
    for (int i = 0; i < limit; i += len << 1) {
      cpx w = cpx(1, 0);
      for (int j = 0; j < len; j++, w = w * Wn) {
        cpx X = A[i + j];
        cpx Y = A[i + j + len] * w;
        A[i + j] = X + Y;
        A[i + j + len] = X - Y;
      }
    }
  }
}

int n, m;
char s[maxn], t[maxn];
int a[maxn], b[maxn];

cpx A[maxn], B[maxn];
cpx ans[maxn];

signed main() {
  // code begin.
  in >> n >> m;
  in >> s >> t;
  reverse(s, s + n);

  for (int i = 0; i < n; i++)
    if (s[i] ^ '*') a[i] = s[i] - 'a' + 1;
  for (int i = 0; i < m; i++)
    if (t[i] ^ '*') b[i] = t[i] - 'a' + 1;

  int l = 0;

  while (limit <= n + m) limit <<= 1, ++l;
  for (int i = 0; i < limit; i++) rev[i] = rev[i >> 1] >> 1 | (i & 1) << l - 1;

  for (int i = 0; i < limit; i++) A[i] = B[i] = cpx();
  for (int i = 0; i < n; i++) A[i] = cpx(a[i] * a[i] * a[i]);
  for (int i = 0; i < m; i++) B[i] = cpx(b[i]);
  FFT(A, 1); FFT(B, 1);
  for (int i = 0; i < limit; i++) ans[i] = ans[i] + A[i] * B[i];

  for (int i = 0; i < limit; i++) A[i] = B[i] = cpx();
  for (int i = 0; i < n; i++) A[i] = cpx(a[i]);
  for (int i = 0; i < m; i++) B[i] = cpx(b[i] * b[i] * b[i]);
  FFT(A, 1); FFT(B, 1);
  for (int i = 0; i < limit; i++) ans[i] = ans[i] + A[i] * B[i];

  for (int i = 0; i < limit; i++) A[i] = B[i] = cpx();
  for (int i = 0; i < n; i++) A[i] = cpx(a[i] * a[i]);
  for (int i = 0; i < m; i++) B[i] = cpx(b[i] * b[i]);
  FFT(A, 1); FFT(B, 1);
  for (int i = 0; i < limit; i++) ans[i] = ans[i] - 2.0 * A[i] * B[i];

  FFT(ans, -1);
  vector<int> answer;
  for (int i = n - 1; i < m; i++)
    if(abs(ans[i].x / limit) < 0.5) answer.pb(i - n + 2);
  out << sz(answer) << '\n';
  for (int x : answer) out << x << ' ';
  return 0;
  // code end.
}