AOJ2401 Equation

問題ページ

解法

変数は高々10種類なので'T'と'F'の割り当ては2^10通りしかない。=で分割しておけばequationを用意する必要はない。構文解析はO(|S|)でできるので割り当てを全通り試して等しくならないものがあれば'NO'、そうでなければ'YES'を出力する。以下のBNFにしたがって再帰型構文解析を書く。

<formula>  ::= "T" | "F" | "-" <formula> | 
"(" <formula> "*" <formula> ")" |
"(" <formula> "+" <formula> ")" |
"(" <formula> "->" <formula> ")"

#include <bits/stdc++.h>
 
using namespace std;
using ll = long long;
#define int ll
using PII = pair<int, int>;
 
#define FOR(i, a, n) for (ll i = (ll)a; i < (ll)n; ++i)
#define REP(i, n) FOR(i, 0, n)
#define ALL(x) x.begin(), x.end()
 
template<typename T> T &chmin(T &a, const T &b) { return a = min(a, b); }
template<typename T> T &chmax(T &a, const T &b) { return a = max(a, b); }
template<typename T> bool IN(T a, T b, T x) { return a<=x&&x<b; }
template<typename T> T ceil(T a, T b) { return a/b + !!(a%b); }

template<typename T> vector<T> make_v(size_t a) { return vector<T>(a); }
template<typename T,typename... Ts>
auto make_v(size_t a,Ts... ts) { 
  return vector<decltype(make_v<T>(ts...))>(a,make_v<T>(ts...));
}
template<typename T,typename V> typename enable_if<is_class<T>::value==0>::type
fill_v(T &t, const V &v) { t=v; }
template<typename T,typename V> typename enable_if<is_class<T>::value!=0>::type
fill_v(T &t, const V &v ) { for(auto &e:t) fill_v(e,v); }

template<class S,class T>
ostream &operator <<(ostream& out,const pair<S,T>& a){
  out<<'('<<a.first<<','<<a.second<<')'; return out;
}
template<typename T>
istream& operator >> (istream& is, vector<T>& vec){
  for(T& x: vec) {is >> x;} return is;
}
template<class T>
ostream &operator <<(ostream& out,const vector<T>& a){
  out<<'['; for(T i: a) {out<<i<<',';} out<<']'; return out;
}

int dx[] = {0, 1, 0, -1}, dy[] = {1, 0, -1, 0}; // DRUL
const int INF = 1<<30;
const ll LLINF = 1LL<<60;
const int MOD = 1000000007;

int pos;
string s;

char formula() {
  if(s[pos] == '-') {
    pos++;
    char tmp = formula();
    if(tmp == 'F') tmp = 'T';
    else tmp = 'F';
    return tmp;
  } 
  if(s[pos] == '(') {
    pos++;
    char vl = formula();
    char op = s[pos++];
    if(op == '-') pos++;
    char vr = formula();
    if(s[pos] != ')') assert(false);
    pos++;

    char ret;
    if(op == '*') {
      if(vl == 'T' && vr == 'T') ret = 'T';
      else ret = 'F';
    } else if(op == '+') {
      if(vl == 'F' && vr == 'F') ret = 'F';
      else ret = 'T';
    } else if(op == '-') {
      if(vl == 'T' && vr == 'F') ret = 'F';
      else ret = 'T';
    }
    return ret;
  }
  return s[pos++];
}

signed main(void)
{
  cin.tie(0);
  ios::sync_with_stdio(false);

  while(1) {
    string t;
    cin >> t;
    if(t == "#") break;

    // 座圧
    int m = 0;
    map<char,int> mp;
    REP(i, t.size()) {
      if(isalpha(t[i]) && t[i]!='T' && t[i]!='F') {
        if(mp.find(t[i]) == mp.end()) mp[t[i]] = m++;
      }
    }
    REP(i, t.size()) {
      if(isalpha(t[i]) && t[i]!='T' && t[i]!='F') {
        t[i] = (char)(mp[t[i]] + 'a');
      }
    }

    // 割り当てを全部試す
    bool flag = true;
    REP(i, 1LL<<m) {
      string str = t;
      REP(j, str.size()) {
        if(isalpha(str[j]) && t[j]!='T' && t[j]!='F') {
          if(i&(1<<(str[j]-'a'))) str[j] = 'T';
          else str[j] = 'F';
        }
      }

      int idx = str.find('=');
      pos = 0;
      s = str.substr(0, idx);
      char vl = formula();
      pos = 0;
      s = str.substr(idx+1);
      char vr = formula();

      if(vl != vr) {
        flag = false;
        break;
      }
    }

    if(flag) {
      cout << "YES" << endl;
    } else {
      cout << "NO" << endl;
    }
  }

  return 0;
}