AOJ2613 Unordered Operators
解法
まず演算子の優先順序が*>+>-となっている場合のBNFを書いてみる。左再帰と演算子の優先順序に気をつけつつ書くと以下のようになる。
<expr1> = <expr2> ['-' <expr2>]* <expr2> = <expr3> ['+' <expr3>]* <expr3> = <factor> ['*' <factor>]* <factor> = '(' <expr1> ')' | <number>
他の優先順序の場合についても同様にBNFを書ける。BNFにしたがって再帰型構文解析を書けばよい。
#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; char op[3] = {'+', '-', '*'}; int pos; string s; ll exprA1(); ll exprA2(); ll exprA3(); ll factorA(); ll exprB1(); ll exprB2(); ll factorB(); ll exprC1(); ll exprC2(); ll factorC(); ll exprD1(); ll factorD(); ll number(); ll exprA1() { ll ret = exprA2(); while(pos < s.size()) { if(s[pos] == op[0]) { if(op[0] == '+') pos++, ret += exprA2(); else if(op[0] == '*') pos++, ret *= exprA2(); else if(op[0] == '-') pos++, ret -= exprA2(); } else { break; } } return ret; } ll exprA2() { ll ret = exprA3(); while(pos < s.size()) { if(s[pos] == op[1]) { if(op[1] == '+') pos++, ret += exprA3(); else if(op[1] == '*') pos++, ret *= exprA3(); else if(op[1] == '-') pos++, ret -= exprA3(); } else { break; } } return ret; } ll exprA3() { ll ret = factorA(); while(pos < s.size()) { if(s[pos] == op[2]) { if(op[2] == '+') pos++, ret += factorA(); else if(op[2] == '*') pos++, ret *= factorA(); else if(op[2] == '-') pos++, ret -= factorA(); } else { break; } } return ret; } ll factorA() { ll ret; if(s[pos] == '(') { pos++; ret = exprA1(); pos++; } else { ret = number(); } return ret; } ll exprB1() { ll ret = exprB2(); while(pos < s.size()) { if(s[pos] == op[0]) { if(op[0] == '+') pos++, ret += exprB2(); else if(op[0] == '*') pos++, ret *= exprB2(); else if(op[0] == '-') pos++, ret -= exprB2(); } else if(s[pos] == op[1]) { if(op[1] == '+') pos++, ret += exprB2(); else if(op[1] == '*') pos++, ret *= exprB2(); else if(op[1] == '-') pos++, ret -= exprB2(); } else { break; } } return ret; } ll exprB2() { ll ret = factorB(); while(pos < s.size()) { if(s[pos] == op[2]) { if(op[2] == '+') pos++, ret += factorB(); else if(op[2] == '*') pos++, ret *= factorB(); else if(op[2] == '-') pos++, ret -= factorB(); } else { break; } } return ret; } ll factorB() { ll ret; if(s[pos] == '(') { pos++; ret = exprB1(); pos++; } else { ret = number(); } return ret; } ll exprC1() { ll ret = exprC2(); while(pos < s.size()) { if(s[pos] == op[0]) { if(op[0] == '+') pos++, ret += exprC2(); else if(op[0] == '*') pos++, ret *= exprC2(); else if(op[0] == '-') pos++, ret -= exprC2(); } else if(s[pos] == op[1]) { if(op[1] == '+') pos++, ret += exprC2(); else if(op[1] == '*') pos++, ret *= exprC2(); else if(op[1] == '-') pos++, ret -= exprC2(); } else { break; } } return ret; } ll exprC2() { ll ret = factorC(); while(pos < s.size()) { if(s[pos] == op[1]) { if(op[1] == '+') pos++, ret += factorC(); else if(op[1] == '*') pos++, ret *= factorC(); else if(op[1] == '-') pos++, ret -= factorC(); } else if(s[pos] == op[2]) { if(op[2] == '+') pos++, ret += factorC(); else if(op[2] == '*') pos++, ret *= factorC(); else if(op[2] == '-') pos++, ret -= factorC(); } else { break; } } return ret; } ll factorC() { ll ret; if(s[pos] == '(') { pos++; ret = exprC1(); pos++; } else { ret = number(); } return ret; } ll exprD1() { ll ret = factorD(); while(pos < s.size()) { if(s[pos] == op[0]) { if(op[0] == '+') pos++, ret += factorD(); else if(op[0] == '*') pos++, ret *= factorD(); else if(op[0] == '-') pos++, ret -= factorD(); } else if(s[pos] == op[1]) { if(op[1] == '+') pos++, ret += factorD(); else if(op[1] == '*') pos++, ret *= factorD(); else if(op[1] == '-') pos++, ret -= factorD(); } else if(s[pos] == op[2]) { if(op[2] == '+') pos++, ret += factorD(); else if(op[2] == '*') pos++, ret *= factorD(); else if(op[2] == '-') pos++, ret -= factorD(); } else { break; } } return ret; } ll factorD() { ll ret; if(s[pos] == '(') { pos++; ret = exprD1(); pos++; } else { ret = number(); } return ret; } ll number() { ll ret = 0; while(pos < s.size() && isdigit(s[pos])) { ret *= 10; ret += s[pos]-'0'; pos++; } return ret; } signed main(void) { cin.tie(0); ios::sync_with_stdio(false); cin >> s; ll ans = LLONG_MIN; sort(op, op+3); do { pos = 0; ll ret = exprA1(); chmax(ans, ret); } while(next_permutation(op, op+3)); sort(op, op+3); do { pos = 0; ll ret = exprB1(); chmax(ans, ret); } while(next_permutation(op, op+3)); sort(op, op+3); do { pos = 0; ll ret = exprC1(); chmax(ans, ret); } while(next_permutation(op, op+3)); sort(op, op+3); do { pos = 0; ll ret = exprD1(); chmax(ans, ret); } while(next_permutation(op, op+3)); cout << ans << endl; return 0; }
久々に構文解析かいたらfactor置く位置とか意味不明なバグらせ方をした。