"""Hosts obtained by attaching one generator to two adjacent legs of a pattern."""
from pmap import PMap, from_word
from rewrite import glue

def attach(L, i, gen):
    """glue generator gen ('cap','T','X') onto legs i,i+1 (cyclic) of map L.
    Implemented by building the 'outer' map and gluing L into it."""
    k = L.k
    # Build host as: a word realizing gen on positions i,i+1 of a k-box drawn as Hom(k,?):
    # we rotate L so that legs i,i+1 become positions 0,1 (bottom), apply gen at the bottom,
    # i.e. compose L (as Hom(0,k)... ) -- easier: construct directly.
    Lr = L.rotated(-i)  # old position i -> new position 0
    # view Lr as a k-box; new map = gen applied to positions 0,1.
    import itertools
    off = Lr.maxdart() + 1
    nodes = dict(Lr.nodes)
    alpha = dict(Lr.alpha)
    b0, b1 = Lr.bdry[0], Lr.bdry[1]
    rest = Lr.bdry[2:]
    a0, a1 = alpha[b0], alpha[b1]
    del alpha[b0], alpha[b1]
    if gen == "cap":
        alpha[a0] = a1; alpha[a1] = a0
        newb = rest
    elif gen == "T":
        # vertex with darts: (to a0), (to a1), (new boundary)  ccw.
        # boundary ccw order is ... rest..., then legs 0,1. The new vertex sits
        # outside the disk; its ccw order: dart to leg1, dart to leg0, outer dart.
        d0, d1, dn, bn = off, off+1, off+2, off+3
        nodes[("ext",)] = ("T", [d1, d0, dn])
        alpha[d0]=a0; alpha[a0]=d0; alpha[d1]=a1; alpha[a1]=d1
        alpha[dn]=bn; alpha[bn]=dn
        newb = [bn] + rest
    elif gen == "X":
        d0, d1, e0, e1, c0, c1 = off, off+1, off+2, off+3, off+4, off+5
        # ccw at X (outside the disk): to leg1, to leg0, outer0, outer1
        nodes[("ext",)] = ("X", [d1, d0, e0, e1])
        alpha[d0]=a0; alpha[a0]=d0; alpha[d1]=a1; alpha[a1]=d1
        alpha[e0]=c0; alpha[c0]=e0; alpha[e1]=c1; alpha[c1]=e1
        newb = [c0, c1] + rest
    M = PMap(nodes, newb, alpha, Lr.loops)
    return M