//
// Earley Parser
//
// Description:
// We are given CFG, i.e.,
// A -> B
// A -> aAa|bAb
// B -> aa|bb
// B -> a|b
// It determines that a given string is matched by the CFG.
//
// Algorithm:
// Earley algorithm. It generates all states with memoisation.
// Here, state is given by (rule, pos-in-rule, pos-in-text).
//
// Complexity:
// O(|G|^2 n^3) in the worst case.
// If a grammar is simple, it usually reduced to O(|G|^2 n^2).
//
// Remark:
// Because of simplicity, This implementation does not allow the
// epsilon rule. Please expand epsilon rule by hand.
// (TODO!)
//
//
#include
#include
#include
#include
#include
using namespace std;
#define fst first
#define snd second
#define all(c) ((c).begin()), ((c).end())
struct earley_parser {
vector terminal;
vector>> grammar;
int add_symbol(char c = 0) {
terminal.push_back(c);
grammar.push_back({});
return grammar.size()-1;
}
void add_grammar(int A, vector As) {
As.push_back(0);
grammar[A].push_back(As);
}
earley_parser() { add_symbol(); add_symbol(); }
bool parse(const char s[], int init) {
int n = strlen(s);
struct state { int a, k, p, i; };
vector>> chart(n+1, vector>(grammar.size()));
auto enqueue = [&](vector &curr, const state &S) {
for (auto &T: curr)
if (T.a == S.a && T.k == S.k && T.p == S.p && T.i == S.i) return;
curr.push_back(S);
};
auto symbol = [&](const state &S) { return grammar[S.a][S.k][S.p]; };
grammar[1] = { {init, 0} };
vector curr = {{1, 0, 0, 0}}, next;
for (int k = 0; k <= n; ++k) {
for (int i = 0; i < curr.size(); ++i) {
state S = curr[i];
int B = symbol(S);
if (B) {
if (!terminal[B]) {
for (int j = 0; j < grammar[B].size(); ++j)
enqueue(curr, {B, j, 0, k});
} else if (terminal[B] == s[k]) {
enqueue(next, {S.a, S.k, S.p+1, S.i});
}
} else {
for (auto &T: chart[S.i][S.a])
enqueue(curr, {T.a, T.k, T.p+1, T.i});
}
}
for (auto &T: curr)
chart[k][symbol(T)].push_back(T);
curr.swap(next);
next.clear();
}
for (auto &T: chart[n][0])
if (T.a == 1) return true;
return false;
}
};
int main() {
earley_parser parser;
// A -> B
// A -> aAa|bAb
// B -> aa|bb
// B -> a|b
int A = parser.add_symbol();
int B = parser.add_symbol();
int a = parser.add_symbol('a');
int b = parser.add_symbol('b');
parser.add_grammar(A, {B});
parser.add_grammar(A, {a,A,a});
parser.add_grammar(A, {b,A,b});
parser.add_grammar(B, {a});
parser.add_grammar(B, {b});
parser.add_grammar(B, {a,a});
parser.add_grammar(B, {b,b});
for (char s[1024]; cin >> s; ) {
cout << parser.parse(s, A) << endl;
}
}