#6036. 「雅礼集训 2017 Day4」编码 [前缀优化2sat]

代码里都说的很清楚了吧…

// 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;

#define 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;
#define int long long

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); }

int n;
const int maxn = 5e5 + 55;
int len[maxn], id[maxn];
string s[maxn];

struct edge {
  int v, nxt;
} e[maxn << 4];
int head[maxn << 4], cnt = 0;

void add(int u, int v) {
  e[++cnt] = { v, head[u] }, head[u] = cnt;
  u ^= 1, v ^= 1;
  e[++cnt] = { u, head[v] }, head[v] = cnt;
}

int dfn[maxn << 4], low[maxn << 4], col[maxn << 4], idx = 0, c = 0;
int st[maxn << 4], top = 0;
void tarjan(int u) {
  dfn[u] = low[u] = ++idx, st[++top] = u;
  for (int i = head[u]; i; i = e[i].nxt) {
    int v = e[i].v;
    if (!dfn[v]) {
      tarjan(v);
      cmin(low[u], low[v]);
    } else if (!col[v]) {
      cmin(low[u], dfn[v]);
    }
  }
  if (dfn[u] == low[u]) {
    ++c; int v;
    do {
    	v = st[top --];
    	col[v] = c;
		} while(v ^ u);
  }
}

int ch[maxn << 5][2], tot;
void insert(int u, int qwq) {
  int p = n + 1, las = 0;
  for (int i = 0; i < len[u]; i++) {
    int c = s[u][i] - '0';
    if (!ch[p][c]) ch[p][c] = ++tot;
    las = p, p = ch[p][c];
    add(qwq, p << 1);
    // 选 qwq 即不能选 p 
    // 前缀优化 
  }
  int pp = ++tot;
  add(qwq, pp << 1 | 1), // 选 qwq 即选 pp 
	 add(pp << 1, p << 1); // 选 pp 即不选 p 
  ch[las][s[u][len[u] - 1] - '0'] = pp; // 然后更换成 pp ，就把这个点挂到上面去。 
}

signed main() {
  // code begin.
  in >> n;
  rep(i, 1, n) { in >> s[i], id[i] = i, len[i] = s[i].length(); }
  sort(id + 1, id + n + 1, [](int x, int y) { return len[x] < len[y]; });
  tot = n + 1;
  for (int i = 1; i <= n; i++) {
    int u = id[i];
    for (int j = 0; j < len[u]; j++) {
      if (s[u][j] == '?') {
        s[u][j] = '0';
        insert(u, u << 1); // 选 0 
        s[u][j] = '1';
        insert(u, u << 1 | 1); // 选 1 
        break;
      } else {
        if (j == len[u] - 1) {
          insert(u, u << 1); // 直接插进去 
          add(u << 1 | 1, u << 1);
          // 无论咋样只能选一个，所以就连起来。 
        }
      }
    }
  }
  for (int i = 1; i <= (tot << 1 | 1); i++)
    if (!dfn[i]) tarjan(i);
  for (int i = 1; i <= tot; i++)
    if (col[i << 1] == col[i << 1 | 1]) {
      out << "NO" << '\n';
      return 0;
    }
  out << "YES" << '\n';
  return 0;
  // code end.
}