def from_steep_pair(steep, path):
r"""
Returns an LAC-tree in bijection with the given steep pair. A check is
performed for validity.
INPUT:
- ``steep``: a steep path in the 0,1 format
- ``path``: a Dyck path in the 0,1 format
OUTPUT:
An LAC-tree in bijection with this steep pair
"""
if len(steep) != len(path):
raise ValueError('Inconsistent sizes of parameters')
n = len(path) // 2
a1 = DyckWord(steep).to_area_sequence()
a2 = DyckWord(path).to_area_sequence()
for i in range(len(a1)):
if a1[i] < a2[i]:
raise ValueError('Incompatible parameters: not nested')
Tc = DyckWord(path).to_ordered_tree().left_right_symmetry()
Tc = Tc.canonical_labelling().left_right_symmetry()
# extract marks from steep, 2 means marked north step
marks = [True]
for i in range(1, len(steep)):
if steep[i] != 0:
marks.append(0 != steep[i - 1])
marked = list(path)
curptr = 0
for i in range(len(marked)):
if marked[i] != 0:
marked[i] = 2 if marks[curptr] else 1
curptr += 1
# coloring
colorlist = [-1 for i in range(n + 2)]
colorstack = [-1]
colorptr = 0
curcolor = -1
curlabel = 0
colorlast = {}
colorcount = {}
labellist = [x.label() for x in Tc.pre_order_traversal_iter()]
for x in marked:
if 2 == x:
curcolor += 1
colorptr += 1
colorstack.insert(colorptr, curcolor)
curlabel += 1
colorlist[curlabel] = curcolor
colorlast[curcolor] = labellist[curlabel]
colorcount[curcolor] = 1
elif 1 == x:
colorptr += 1
curlabel += 1
mycolor = colorstack[colorptr]
colorlist[curlabel] = mycolor
colorlast[mycolor] = labellist[curlabel]
colorcount[mycolor] += 1
else:
colorptr -= 1
alpha = sorted(colorlast.items(), key=lambda x: x[1])
alpha = list(map(lambda x: colorcount[x[0]], alpha))
return LACTree(Tc.shape().left_right_symmetry(), alpha)
