"""2T-INF — Build SOA from 2-grams (Algorithm 1, TODS 2010)."""

from .soa import SOA


def build_soa(sequences):
    """
    |———— Algorithm 1: 2T-INF ————|
    Input:  finite set of sample strings S
    Output: SOA G such that S ⊆ L(G)

    For each string a₁...aₙ in S:
      add edges (src, a₁), (a₁, a₂), ..., (aₙ, sink)
    """
    G = SOA()
    symbol_states = {}

    for seq in sequences:
        if not seq:
            if not G.has_edge(G.src, G.sink):
                G.add_edge(G.src, G.sink)
            continue
        for i, token in enumerate(seq):
            if token not in symbol_states:
                symbol_states[token] = G.add_state(token)
            if i == 0:
                G.add_edge(G.src, symbol_states[token])
            if i == len(seq) - 1:
                G.add_edge(symbol_states[token], G.sink)
            if i + 1 < len(seq):
                nxt = seq[i + 1]
                if nxt not in symbol_states:
                    symbol_states[nxt] = G.add_state(nxt)
                G.add_edge(symbol_states[token], symbol_states[nxt])
    return G