• 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) << '
    ';
      for (int x : answer) out << x << ' ';
      return 0;
      // code end.
    }
    
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  • 原文地址:https://www.cnblogs.com/Isaunoya/p/12641602.html
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