def create_full_tree(depth):
if depth == 0:
terminal = Terminal.random_terminal()
node = Node("terminal", terminal)
return Tree(node)
else:
function = Function.random_function()
root_node = Node("function", function)
result = Tree(root_node)
for i in range(2): #function.arity()
result.add_child(Initializer.create_full_tree(depth - 1))
return result
def create_full_tree(depth):
if depth == 0:
terminal = Terminal.random_terminal()
node = Node("terminal", terminal)
return Tree(node)
else:
function = Function.random_function()
root_node = Node("function", function)
result = Tree(root_node)
for i in range(2): #function.arity()
result.add_child(Initializer.create_full_tree(depth - 1))
return result
def read_tree(self, line):
parents = list(map(int, line.split()))
#print("parents:", parents, "# parents:", len(parents))
trees = dict()
root = None
for i in range(1, len(parents) + 1):
#print("i:", i, "; trees' keys:", trees.keys(), "; parents[i-1]:", parents[i-1])
# if we haven't processed it, and its listed parent is actually sensical (has a parent)
if i - 1 not in trees.keys() and parents[i - 1] != -1:
idx = i
prev = None
#print("\tin if; idx = i = ", i)
# follows parent links, starting with index i
while True:
#print("\t\tin while loops")
parent = parents[idx - 1]
#print("\t\t\tparent:", parent)
if parent == -1:
#print("*** parent is -1!")
break
tree = Tree()
#print("\t\t\tprev:", prev)
if prev is not None:
#print("\t\t\tprev isn't None, so adding it as a children to Tree")
tree.add_child(prev)
trees[idx - 1] = tree
tree.idx = idx - 1
#print("\t\t\ttrees:", trees)
#print("\t\t\ttree = ", tree, "idx:", tree.idx)
if parent - 1 in trees.keys(): # simply checks if we should point its parent to the current node
#print("\t\t\t\tparent -1 is in trees!")
trees[parent - 1].add_child(tree)
break
elif parent == 0: # make it the root
#print("\t\t\t\tparent = 0")
root = tree
break
else:
#print("\t\t\t\tset prev to be = tree; idx = parent", idx, "=", parent)
prev = tree
idx = parent
#print("# trees:", len(trees.keys()))
#all_nodes = []
#self.dfs(root, all_nodes)
#print("all_nodes:", len(all_nodes))
#exit()
return root
def tree_sort(l: List(int)) -> List(int):
"""
A python implementation of tree sort
Tree sort constructs a binary search tree where each left branch is less
than the parent, and each right branch is greater than the parent. When
the tree is traversed in inorder the nodes are in ascending order
"""
tree = Tree()
[tree.add_child(n) for n in l]
return tree.collate()
def rec(x,y,attrNameList,attrs,parent_examples,class_values):
node = Tree()
is_pure,first_item = is_pure_set(y)
if(x.__len__()==0):
class_amount = list()
for y_value in class_values:
class_amount.append((y_value,get_sum_y_value(parent_examples, y_value)))
return Tree(max(class_amount,key=itemgetter(1)),class_amount)
elif(is_pure):
return Tree(first_item + " " + str(y.__len__()),[(first_item,y.__len__())])
elif(attrNameList.__len__()==0):
class_amount = list()
for y_value in class_values:
class_amount.append((y_value, get_sum_y_value(y, y_value)))
return Tree(max(class_amount, key=itemgetter(1)),class_amount)
else:
best_gain,best_gain_index = find_best_gain_index(x,y,attrs,attrNameList,class_values)
node.name = attrNameList[best_gain_index]
adsf = list()
for class_value in class_values:
adsf.append((class_value,y.count(class_value)))
node.values = adsf
tmp_attrs = attrs.copy()
x_values = tmp_attrs.pop(attrNameList[best_gain_index])
for value in x_values:
'''
höger eller vänster
'''
dx = x.copy()
dy = y.copy()
ddx, ddy = update_data_set(dx, dy, best_gain_index, value)
tmp_attrNameList = attrNameList[:]
tmp_attrNameList[best_gain_index] = None
node.add_child(rec(ddx,ddy,tmp_attrNameList,tmp_attrs,dy,class_values))
# best_gain, best_gain_index = find_best_gain_index(ddx, ddy, tmp_attrs, tmp_attrNameList, class_values)
# if best_gain == 1 or best_gain == 0:
# return Tree('leaf')
# if best_gain_index > -1:
# node.add_child(rec(ddx, ddy,tmp_attrNameList,tmp_attrs,dx,class_values))
return node
def test_tree():
# initialize tree
tree = Tree("Apple")
assert tree.preorder_traversal(tree.root) == 'Apple, '
# test add_child, pre-order and post-order traversal
tree.add_child('Apple', 'Pear', tree.root)
assert tree.preorder_traversal(tree.root) == 'Apple, Pear, '
assert tree.postorder_traversal(tree.root) == 'Pear, Apple, '
tree.add_child('Apple', 'Orange', tree.root)
tree.add_child('Apple', 'Grape', tree.root)
tree.add_child('Orange', 'Mango', tree.root)
tree.add_child('Orange', 'Peach', tree.root)
tree.add_child('Grape', 'Watermelon', tree.root)
assert tree.preorder_traversal(
tree.root) == 'Apple, Pear, Orange, Mango, Peach, Grape, Watermelon, '
assert tree.postorder_traversal(
tree.root) == 'Pear, Mango, Peach, Orange, Watermelon, Grape, Apple, '
# test has
assert tree.has('Apple', tree.root)
assert tree.has('Pear', tree.root)
assert tree.has('Orange', tree.root)
assert tree.has('Grape', tree.root)
assert tree.has('Mango', tree.root)
assert tree.has('Watermelon', tree.root)
assert not tree.has('Pineapple', tree.root)
assert not tree.has('Plum', tree.root)
assert not tree.has('Kiwi', tree.root)
# test is_empty
assert not tree.is_empty(tree.root)
assert tree.is_empty(None)
# test nuke
tree.nuke()
assert tree.is_empty(tree.root)
def read_tree(self, line):
# print("line:",line)
# 3 3 5 5 11 5 6 9 6 11 0 11
# parents = list(map(int, line.split()))
parents = line
trees = dict()
root = None
# 1 - 13
for i in range(1, len(parents) + 1):
if i - 1 not in trees.keys() and parents[i - 1] != -1:
idx = i # 1 2 7 8
prev = None
while True:
parent = parents[
idx - 1] # parent = 3 5 11 0 --- 3 5 11 -- 6 9
if parent == -1:
break
tree = Tree() # 实例化
if prev is not None:
tree.add_child(
prev
) # null 5这棵树的孩子结点的3 11这棵树的孩子结点为5 0这棵树的孩子结点为11 5这棵树的孩子结点为3 11这棵树的孩子结点为5
trees[
idx -
1] = tree # trees[0]为空Tree() trees[5]为 5这棵树 trees[4]为 11这棵树 trees[10]为 0这棵树 trees[1]为 3这棵树 trees[2]为 5这棵树 trees[6]为 6这棵树 trees[7]为 9这棵树
# tree.idx为树的编号
tree.idx = idx - 1 # 0 2 4 10 1 2 -- 6 7
if parent - 1 in trees.keys():
trees[parent - 1].add_child(tree)
break
elif parent == 0:
root = tree # 0这棵树是root
break
else:
prev = tree # prev为 Tree() tree.idx = 0 prev= 5这棵树 prev= 11这棵树 prev= 0这棵树 prev= 3这棵树 5这棵树 9
idx = parent # idx = 3 5 11 0 3 5
return root
def init_tree() -> Tree:
"""
Generates a tree that looks like
6
/ \
5 8
/\ /\
2 7 9
/\ /\
1 3 10
/\
4
"""
tree = Tree()
children = [6, 8, 9, 5, 2, 1, 3, 7, 10, 4]
[tree.add_child(child) for child in children]
return tree
class PN:
def __init__(self,
name,
root,
evaluate,
result,
get_pn_dpn,
max_nodes,
delete_subtrees=False,
immediateEvaluation=True):
self.pn_tree = Tree()
self.name = name
self.evaluate = evaluate
self.result = result
self.get_pn_dpn = get_pn_dpn
self.max_nodes = max_nodes
self.delete_subtrees = delete_subtrees
self.immediateEvaluation = immediateEvaluation
self.root = root
self.pn_tree.set_root(self.root)
self.eval_count = 0
self.terminated = False
def terminate(self):
self.terminated = True
def evaluate_node(self, node):
self.evaluate(node)
self.eval_count += 1
def reset(self, node):
self.eval_count = 0
self.root = node
self.pn_tree.clear()
self.pn_tree.set_root(self.root)
def set_second_level(self, evaluate):
pass
def set_evaluate(self, evaluate):
self.evaluate = evaluate
def set_limit(self, max_nodes):
self.max_nodes = max_nodes
def get_size(self):
return self.pn_tree.node_count
def get_node_count(self):
return self.pn_tree.node_count + self.pn_tree.deleted_count
def perform_search(self):
if self.immediateEvaluation:
self.evaluate_node(self.root)
self.set_pn_dpn(self.root)
current_node = self.root
while self.root.pn != 0 and self.root.dpn != 0 and self.pn_tree.node_count <= self.max_nodes and not self.terminated:
most_proving = self.select_most_proving_node(current_node)
if not self.immediateEvaluation:
self.evaluate_node(most_proving)
self.set_pn_dpn(most_proving)
self.expand_node(most_proving)
current_node = self.update_ancestors(most_proving)
return self.result(self)
# Calculating proof and disproof numbers
def set_pn_dpn(self, node):
# Internal Node
if node.expanded:
# AND Node
# PN = sum of children PN; DPN = minimum of children DPN
if node.node_type == "AND":
node.pn = sum(c.pn for c in node.children)
node.dpn = min(c.dpn for c in node.children)
# OR Node
# PN = minimum of children PN; DPN = sum of children DPN
else:
node.pn = min(c.pn for c in node.children)
node.dpn = sum(c.dpn for c in node.children)
# Leaf node
else:
evaluation = node.value
# Lost
if evaluation == FALSE:
node.pn = float("inf")
node.dpn = 0
# Won
elif evaluation == TRUE:
node.pn = 0
node.dpn = float("inf")
# Unknown
elif evaluation == UNKNOWN:
node.pn, node.dpn = self.get_pn_dpn(node)
def select_most_proving_node(self, node):
while node.expanded:
# Lowest DPN
if node.node_type == "AND":
vals = [c.dpn for c in node.children]
# Lowest PN
else:
vals = [c.pn for c in node.children]
node = node.children[vals.index(min(vals))]
return node
def expand_node(self, node):
if node.pn == 0 or node.dpn == 0: return
# Check whether evaluation added children to node
if node.expanded: return
# generate all children
child_type = "AND" if node.node_type == "OR" else "OR"
for a in node.state.allowed_actions():
new_state = node.state.perform_action(a)
# Node(Type,State,Parent,Action)
child_node = Node(node_type=child_type,
state=new_state,
parent=node,
depth=node.depth + 1,
action=a)
self.add_child(child_node, node)
if self.immediateEvaluation:
self.evaluate_node(child_node)
self.set_pn_dpn(child_node)
if child_node.pn == 0 and node.node_type == "OR": break # won
if child_node.dpn == 0 and node.node_type == "AND": break # lost
node.expanded = True
def update_ancestors(self, node):
while True:
old_pn = node.pn
old_dpn = node.dpn
# Check in case of delayed evaluation
if old_pn == 0 or old_dpn == 0:
if node == self.root:
return self.root
node = node.parent
continue
self.set_pn_dpn(node)
# No change on the path
if node.pn == old_pn and node.dpn == old_dpn:
return node
# delete disproved subtrees
if self.delete_subtrees and (node.pn == 0 or node.dpn == 0):
self.delete_subtree(node)
if node == self.root:
return self.root
node = node.parent
return node
def delete_subtree(self, node):
self.pn_tree.delete_subtree(node)
def add_child(self, child_node, node):
self.pn_tree.add_child(child_node, node)
def test(self):
tree = Tree()
tree.add_child(5)
assert (tree.tree[5]["left"] is None)
assert (tree.tree[5]["right"] is None)
def test(self):
tree = Tree()
tree.add_child(5)
tree.add_child(3)
assert (tree.tree[5]["left"] == 3)
def GenerateAST(self, ins):
self._statement_num += 1
AST = Tree()
try:
l.info("[insn] op %s" % (ins.opname))
AST.op=ins.op
AST.opname = ins.opname
if ins.op == idaapi.cit_block:
self.dump_block(ins.ea, ins.cblock, AST)
elif ins.op == idaapi.cit_expr:
AST.add_child(self.dump_expr(ins.cexpr))
elif ins.op == idaapi.cit_if:
l.info("[if]"+spliter)
cif = ins.details
cexpr = cif.expr
ithen = cif.ithen
ielse = cif.ielse
AST.add_child(self.dump_expr(cexpr))
if ithen:
AST.add_child(self.GenerateAST(ithen))
if ielse:
AST.add_child(self.GenerateAST(ielse))
elif ins.op == idaapi.cit_while:
cwhile = ins.details
self.dump_while(cwhile,AST)
elif ins.op == idaapi.cit_return:
creturn = ins.details
AST.add_child( self.dump_return(creturn) )
elif ins.op == idaapi.cit_for:
l.info( '[for]'+spliter)
cfor = ins.details
AST.add_child(self.dump_expr(cfor.init))
AST.add_child(self.dump_expr(cfor.step))
AST.add_child(self.dump_expr(cfor.expr))
AST.add_child(self.GenerateAST(cfor.body))
elif ins.op == idaapi.cit_switch:
l.info('[switch]'+spliter)
cswitch = ins.details
cexpr = cswitch.expr
ccases = cswitch.cases #Switch cases: values and instructions.
cnumber = cswitch.mvnf #Maximal switch value and number format.
AST.add_child(self.dump_expr(cexpr))
self.dump_ccases(ccases, AST)
elif ins.op == idaapi.cit_do:
l.info('[do]'+spliter)
cdo = ins.details
cbody = cdo.body
cwhile = cdo.expr
AST.add_child(self.GenerateAST(cbody))
AST.add_child(self.dump_expr(cwhile))
elif ins.op == idaapi.cit_break or ins.op == idaapi.cit_continue:
pass
elif ins.op == idaapi.cit_goto:
pass
else:
l.warning('[error] not handled op type %s' % ins.opname)
except:
l.warning("[E] exception here ! ")
return AST
def dump_expr(self, cexpr):
'''
l.info the expression
:return: AST with two nodes op and oprand : op Types.NODETYPE.OPTYPE, oprand : list[]
'''
# l.info "dumping expression %x" % (cexpr.ea)
#操作数
oprand =[] # a list of Tree()
l.info("[expr] op %s" % cexpr.opname)
if cexpr.op == idaapi.cot_call:
# oprand = args
# get the function call arguments
self._get_callee(cexpr.ea)
l.info('[call]'+spliter)
args = cexpr.a
for arg in args:
oprand.append(self.dump_expr(arg))
elif cexpr.op == idaapi.cot_idx:
l.info('[idx]'+spliter)
oprand.append(self.dump_expr(cexpr.x))
oprand.append(self.dump_expr(cexpr.y))
elif cexpr.op == idaapi.cot_memptr:
l.info('[memptr]'+spliter)
#TODO
AST=Tree()
AST.op = idaapi.cot_num #consider the mem size pointed by memptr
AST.value = cexpr.ptrsize
AST.opname = "value"
oprand.append(AST)
# oprand.append(cexpr.m) # cexpr.m : member offset
# oprand.append(cexpr.ptrsize)
elif cexpr.op == idaapi.cot_memref:
l.info('[memref]'+spliter)
# oprand.append(cexpr.m)
elif cexpr.op == idaapi.cot_num:
l.info ('[num]' + str(cexpr.n._value))
AST = Tree()
AST.op = idaapi.cot_num # consider the mem size pointed by memptr
AST.value = cexpr.n._value
AST.opname = "value"
oprand.append(AST)
elif cexpr.op == idaapi.cot_var:
# var : cexpr.v
l.info ('[var]' + str(cexpr.v.idx))
# oprand.append(cexpr.v.idx) # which var (index for var)
# TODO handle array type
elif cexpr.op == idaapi.cot_str:
# string constant
l.info( '[str]' + cexpr.string)
AST =Tree()
AST.opname = "string"
AST.op = cexpr.op
AST.value = cexpr.string
oprand.append(AST)
elif cexpr.op == idaapi.cot_obj:
l.info ('[cot_obj]' + hex(cexpr.obj_ea))
# oprand.append(cexpr.obj_ea)
# Many strings are defined as 'obj'
# I wonder if 'obj' still points to other types of data?
# notice that the address of 'obj' is not in .text segment
if get_segm_name(getseg(cexpr.obj_ea)) not in ['.text']:
AST = Tree()
AST.opname = "string"
AST.op = cexpr.op
AST.value = GetString(cexpr.obj_ea)
oprand.append(AST)
elif cexpr.op <= idaapi.cot_fdiv and cexpr.op >= idaapi.cot_comma:
#All binocular operators
oprand.append(self.dump_expr(cexpr.x))
oprand.append(self.dump_expr(cexpr.y))
elif cexpr.op >= idaapi.cot_fneg and cexpr.op <= idaapi.cot_call:
# All unary operators
l.info( '[single]' + spliter)
oprand.append(self.dump_expr(cexpr.x))
else:
l.warning ('[error] %s not handled ' % cexpr.opname)
AST = Tree()
AST.opname=cexpr.opname
AST.op=cexpr.op
for tree in oprand:
AST.add_child(tree)
return AST
from Tree import Tree from bfs import bfs tree1 = Tree(3) tree2 = Tree(9) tree3 = Tree(20) tree4 = Tree(15) tree5 = Tree(7) tree1.add_child(tree2) tree1.add_child(tree3) tree3.add_child(tree4) tree3.add_child(tree5) goal_queue = bfs(tree1) print(goal_queue)
def test(self):
tree = Tree()
tree.add_child(5)
tree.add_child(6)
assert (tree.tree[5]["right"] == 6)
def test(self):
tree = Tree()
tree.add_child(5)
assert (tree.parent == 5)
def test(self):
tree = Tree()
children = [5, 4, 6]
[tree.add_child(child) for child in children]
assert (tree.tree[5]["left"] == 4 and tree.tree[5]["right"] == 6)
class TreeTest(unittest.TestCase):
"""docstring for TreeTest"""
def setUp(self):
self.tree = Tree(root=5)
def test_tree_data(self):
# print()
# print("*** test_tree_data")
# print(self.tree.data)
self.assertEqual(self.tree.data, 5)
# print("***end test_tree_data")
# print()
def test_tree_string_representation(self):
# print(str(self.tree))
self.assertEqual(str(self.tree), str(self.tree.data))
def test_tree_children_exist(self):
# print()
# print("*** test test_tree_children_exist")
self.tree.add_child(5, 4)
self.tree.add_child(5, 7)
self.tree.add_child(5, 9)
# print(self.tree.children)
self.assertTrue(len(self.tree.children) > 0)
# print("***end test test_tree_children_exist")
# print()
def test_has_children(self):
# print()
# print("*** has_children")
self.tree.add_child(5, 4)
self.tree.add_child(5, 8)
self.tree.add_child(6, 9)
# print(self.tree.has_children())
self.assertTrue(str(self.tree.children) == "[4, 8]")
# print("***end has_children")
# print()
def test_find_proper_node(self):
# print()
# print("*** test_find_proper_node")
# print(self.tree.has_children())
self.assertFalse(self.tree.find_proper_node(9, 6))
self.tree.add_child(5, 19)
# print(self.tree.has_children())
# print("***end test_find_proper_node")
# print()
def test_find_proper_node_when_children(self):
# print()
# print("*** test_find_proper_node_when_children")
self.tree.add_child(5, 4)
self.tree.add_child(5, 8)
self.tree.add_child(5, 9)
# add children to the children
self.tree.add_child(8, 7)
self.tree.add_child(8, 3)
self.tree.add_child(8, 45)
self.tree.add_child(9, 62)
self.tree.add_child(9, 68)
self.tree.add_child(9, 93)
self.tree.add_child(4, 41)
self.tree.add_child(4, 42)
self.tree.add_child(4, 43)
self.tree.add_child(4, 44)
# print(self.tree.children[1].children)
# print(self.tree.children[2].children)
# print(self.tree.children[0].children)
self.assertEqual(str(self.tree.children[1].children), "[7, 3, 45]")
self.assertEqual(str(self.tree.children[2].children), "[62, 68, 93]")
self.assertEqual(str(self.tree.children[0].children),
"[41, 42, 43, 44]")
# print("***end test_find_proper_node_when_children")
def test_find(self):
# print()
# print("*** test_find")
self.tree.add_child(5, 4)
self.tree.add_child(5, 8)
self.tree.add_child(5, 9)
# print(self.tree.find(5))
self.assertEqual(self.tree.find(5), True)
self.assertEqual(self.tree.find(6), False)
self.tree.add_child(4, 41)
self.tree.add_child(4, 42)
self.tree.add_child(4, 43)
self.tree.add_child(4, 44)
self.tree.add_child(8, 82)
self.tree.add_child(8, 87)
self.tree.add_child(8, 83)
self.tree.add_child(9, 92)
self.tree.add_child(9, 98)
self.tree.add_child(9, 93)
# print(self.tree.find(4))
# print(self.tree.find(8))
# print(self.tree.find(9))
# print(self.tree.find(41))
# print(self.tree.find(42))
# print(self.tree.find(43))
# print(self.tree.find(44))
# print(self.tree.find(82))
# print(self.tree.find(87))
# print(self.tree.find(83))
# print(self.tree.find(92))
# print(self.tree.find(98))
# print(self.tree.find(93))
self.assertEqual(self.tree.find(4), True)
self.assertEqual(self.tree.find(8), True)
self.assertEqual(self.tree.find(9), True)
self.assertEqual(self.tree.find(41), True)
self.assertEqual(self.tree.find(42), True)
self.assertEqual(self.tree.find(43), True)
self.assertEqual(self.tree.find(44), True)
self.assertEqual(self.tree.find(82), True)
self.assertEqual(self.tree.find(87), True)
self.assertEqual(self.tree.find(83), True)
self.assertEqual(self.tree.find(92), True)
self.assertEqual(self.tree.find(98), True)
self.assertEqual(self.tree.find(93), True)
# print(self.tree.find(28))
# print(self.tree.find(13))
# print(self.tree.find(87))
# print(self.tree.find(46))
self.assertEqual(self.tree.find(28), False)
self.assertEqual(self.tree.find(13), False)
self.assertEqual(self.tree.find(87), True)
self.assertEqual(self.tree.find(46), False)
# print("***end test_find")
# print()
def test_height(self):
# print()
# print("*** test_height")
# self.assertEqual(self.tree.height(), 1)
# test when only root
self.assertEqual(self.tree.height(), 1)
# test when tree is with greater height than 1
self.tree.add_child(5, 4)
self.tree.add_child(5, 8)
self.tree.add_child(5, 9)
self.tree.add_child(4, 41)
self.tree.add_child(4, 42)
self.tree.add_child(4, 43)
self.tree.add_child(4, 44)
self.tree.add_child(44, 441)
self.tree.add_child(44, 442)
self.tree.add_child(44, 443)
self.tree.add_child(443, "a")
self.tree.add_child(443, "b")
self.tree.add_child(443, "c")
self.assertEqual(self.tree.height(), 5)
self.tree.children = []
# test after we have reset the tree's children to []
self.assertEqual(self.tree.height(), 1)
self.tree.add_child(5, 8)
self.assertEqual(self.tree.height(), 2)
self.tree.add_child(8, 14)
self.assertEqual(self.tree.height(), 3)
self.tree.add_child(14, 62)
self.assertEqual(self.tree.height(), 4)
# print("***end test_height")
# print()
def test_attr_count(self):
self.tree.add_child(5, 4)
self.tree.add_child(5, 8)
self.tree.add_child(5, 9)
self.tree.add_child(4, 41)
self.tree.add_child(4, 42)
self.tree.add_child(4, 43)
self.tree.add_child(4, 44)
self.tree.add_child(8, 82)
self.tree.add_child(8, 87)
self.tree.add_child(8, 83)
self.tree.add_child(9, 92)
self.tree.add_child(9, 98)
self.tree.add_child(9, 93)
self.assertEqual(self.tree.count_nodes(), 14)
def test_tree_levels_method(self):
# if only root
self.assertEqual(self.tree.tree_levels(), [[5]])
# add more nodes
self.tree.add_child(5, 4)
self.tree.add_child(5, 8)
self.tree.add_child(5, 9)
self.assertEqual(self.tree.tree_levels(), [[5], [4, 8, 9]])
self.tree.add_child(4, 41)
self.tree.add_child(4, 42)
self.tree.add_child(4, 43)
self.assertEqual(self.tree.tree_levels(),
[[5], [41, 42, 43], [4, 8, 9]])
self.tree.add_child(8, 82)
self.tree.add_child(8, 87)
self.tree.add_child(8, 83)
self.assertEqual(self.tree.tree_levels(),
[[5], [41, 42, 43], [82, 87, 83], [4, 8, 9]])
self.tree.add_child(9, 92)
self.tree.add_child(9, 97)
self.tree.add_child(9, 93)
self.assertEqual(
self.tree.tree_levels(),
[[5], [41, 42, 43], [82, 87, 83], [92, 97, 93], [4, 8, 9]])