def str_tree(atree,indent_char ='.',indent_delta=2):
def str_tree_1(indent,atree):
if atree == None:
return ''
else:
answer = ''
answer += str_tree_1(indent+indent_delta,atree.right)
answer += indent*indent_char+str(atree.value)+'\n'
answer += str_tree_1(indent+indent_delta,atree.left)
return answer
return str_tree_1(0,atree)
def build_balanced_bst(l):
d = []
if len(l) == 0:
return None
else:
mid = (len(l)-1)//2
if mid >= 1:
d.append(build_balanced_bst(l[:mid]))
d.append(build_balanced_bst(l[mid:]))
else:
return d
The build_balanced_bst(l) takes in a list of unique values that are sorted in increasing order. It returns a reference to the root of a well-balanced binary search tree. For example, calling build_ballanced_bst( list(irange(1,10)) returns a binary search tree of height 3 that would print as:
......10
....9
..8
......7
....6
5
......4
....3
..2
....1
The str_tree function prints what the build_balanced_bst function returns
I am working on the build_balanced_bst(l) function to make it apply to the str_tree function. I used the middle value in the list as the root’s value.
But when I call the function as the way below:
l = list(irange(1,10))
t = build_balanced_bst(l)
print('Tree is\n',str_tree(t),sep='')
it doesn't print anything. Can someone help me to fix my build_balanced_bst(l) function?
Keeping the str_tree method as it is, here's the remaining code.
class Node:
"""Represents a single node in the tree"""
def __init__(self, value, left=None, right=None):
self.value = value
self.left = left
self.right = right
def build_balanced_bst(lt):
"""
Find the middle element in the sorted list
and make it root.
Do same for left half and right half recursively.
"""
if len(lt) == 1:
return Node(lt[0])
if len(lt) == 0:
return None
mid = (len(lt)-1)//2
left = build_balanced_bst(lt[:mid])
right = build_balanced_bst(lt[mid+1:])
root = Node(lt[mid], left, right)
return root
ordered_list = list(range(1,11))
bst=build_balanced_bst(ordered_list)
bst_repr = str_tree(bst)
print(bst_repr)
The output comes out as follows:
......10
....9
..8
......7
....6
5
......4
....3
..2
....1
Related
I have to count nodes in a binary tree recursively. I'm new to python and can't find any solution for my problem to finish my code.
This is what I have already tried. As you can see it is not complete, and I can't figure out where to go.
class Tree:
def __init__(self, root):
self.root = root
def add(self, subtree):
self.root.children.append(subtree)
class Node:
def __init__(self, value, children=None):
self.value = value
self.children = children if children is not None else []
def check_root(tree):
if tree.root is None:
return 0
if tree.root is not None:
return count_nodes(tree)
def count_nodes(tree):
if tree.root.children is not None:
j = 0
for i in tree.root.children:
j = 1 + count_nodes(tree)
return j
print(count_nodes(Tree(None))) # 0
print(count_nodes(Tree(Node(10)))) # 1
print(count_nodes(Tree(Node(5, [Node(6), Node(17)])))) #3
With every new step I'm getting different error. E.g. with this code I have exceeded maximum recursion depth.
Thank you for your time reading this. Any hint or help what to do next would be greatly appreciated.
I would start by passing the root node to the count_nodes function -
print(count_nodes(Tree(None)).root) # 0
print(count_nodes(Tree(Node(10))).root) # 1
print(count_nodes(Tree(Node(5, [Node(6), Node(17)]))).root) #3
or make a helper function for that.
Then the count_nodes function can simply look like this
def count_nodes(node):
return 1 + sum(count_nodes(child) for child in node.children)
EDIT: I have just noticed, you can have a None root, this means, you should also handle that:
def count_nodes(node):
if node is None:
return 0
return 1 + sum(count_nodes(child) for child in node.children)
And if you really want to handle tree or node in one function, you can make it a bit uglier:
def count_nodes(tree_or_node):
if isinstance(tree_or_node, Tree):
return count_nodes(tree_or_node.root)
if tree_or_node is None:
return 0
return 1 + sum(count_nodes(child) for child in tree_or_node.children)
and then you can call it like you originally did.
Your problem is that you're counting the same tree infinitely. Take a look at this line:
j = 1 + count_nodes(tree)
An Easy Way:
Lets assume, A is a binary tree with children or nodes which are not NULL. e.g.
3
/ \
7 5
\ \
6 9
/ \ /
1 11 4
Now in order to count number of nodes, we have a simple workaround.
Recursive Method: >>> get_count(root)
For a binary tree, the basic idea of Recursion is to traverse the tree in Post-Order. Here, if the current node is full, we increment result by 1 and add returned values of the left and right sub-trees such as:
class TestNode():
def __init__(self, data):
self.data = data
self.left = None
self.right = None
Now we move forward to get the count of full nodes in binary tree by using the method below:
def get_count(root):
if (root == None):
return 0
res = 0
if (root.left and root.right):
res += 1
res += (get_count(root.left) +
get_count(root.right))
return res
At the end, in order to run the code, we'll manage a main scope:
Here we create our binary tree A as given above:
if __name__ == '__main__':
root = TestNode(3)
root.left = TestNode(7)
root.right = TestNode(5)
root.left.right = TestNode(6)
root.left.right.left = TestNode(1)
root.left.right.right = TestNode(4)
Now at the end, inside main scope we will print count of binary tree nodes such as:
print(get_Count(root))
Here is the time complexity of this recursive function to get_count for binary tree A.
Time Complexity: O(n)
def str_tree(atree,indent_char ='.',indent_delta=2):
def str_tree_1(indent,atree):
if atree == None:
return ''
else:
answer = ''
answer += str_tree_1(indent+indent_delta,atree.right)
answer += indent*indent_char+str(atree.value)+'\n'
answer += str_tree_1(indent+indent_delta,atree.left)
return answer
return str_tree_1(0,atree)
def build_balanced_bst(l):
if len(l) == 0:
return None
else:
mid = (len(l)-1)/2
if mid >= 1:
build_balanced_bst(l[:mid])
build_balanced_bst(l[mid:])
else:
return
I am working on the build_balanced_bst(l), the build_balanced_bst(l) takes a list of unique values that are sorted in increasing order. calling build_ballanced_bst( list(irange(1,10)) returns a binary search tree of height 3 that would print as:
......10
....9
..8
......7
....6
5
......4
....3
..2
....1
the str_tree function is used to print what the build_balanced_bst() function returns. my str_tree function is correct, I cannot change it. I can only change the build_balanced_bst() function.
I used the middle value in the list as the root’s value. when I try to call the build_balanced_bst(l) in the below, it does not print anything.
l = list(irange(1,10))
t = build_balanced_bst(l)
print('Tree is\n',str_tree(t),sep='')
can someone help me to fix my build_balanced_bst(l) function? many thanks.
str_tree() doesn't do anything: It just defines a nested function and implicitly returns None.
As a start, you can have str_tree do something:
def str_tree(atree, indent_char ='.', indent_delta=2):
def str_tree_1(indent, atree):
# Note that str_tree_1 doesn't use the indent argument
if atree == None:
return ''
return str_tree_1(indent_delta, atree)
But this is just a start.
The objective of my code is to get each seperate word from a txt file and put it into a list and then making a binary search tree using that list to count the frequency of each word and printing each word in alphabetical order along with its frequency. Each word in the can only contain letters, numbers, -, or ' The part that I am unable to do with my beginner programming knowledge is to make the Binary Search Tree using the list I have (I am only able to insert the whole list in one Node instead of putting each word in a Node to make the tree). The code I have so far is this:
def read_words(filename):
openfile = open(filename, "r")
templist = []
letterslist = []
for lines in openfile:
for i in lines:
ii = i.lower()
letterslist.append(ii)
for p in letterslist:
if p not in ['a','b','c','d','e','f','g','h','i','j','k','l','m','n','o','p','q','r','s','t','u','v','w','x','y','z',"'","-",' '] and p.isdigit() == False:
letterslist.remove(p)
wordslist = list("".join(letterslist).split())
return wordslist
class BinaryTree:
class _Node:
def __init__(self, value, left=None, right=None):
self._left = left
self._right = right
self._value = value
self._count = 1
def __init__(self):
self.root = None
def isEmpty(self):
return self.root == None
def insert(self, value) :
if self.isEmpty() :
self.root = self._Node(value)
return
parent = None
pointer = self.root
while (pointer != None) :
if value == pointer._value:
pointer._count += 1
return
elif value < pointer._value:
parent = pointer
pointer = pointer._left
else :
parent = pointer
pointer = pointer._right
if (value <= parent._value) :
parent._left = self._Node(value)
else :
parent._right = self._Node(value)
def printTree(self):
pointer = self.root
if pointer._left is not None:
pointer._left.printTree()
print(str(pointer._value) + " " + str(pointer._count))
if pointer._right is not None:
pointer._right.printTree()
def createTree(self,words):
if len(words) > 0:
for word in words:
BinaryTree().insert(word)
return BinaryTree()
else:
return None
def search(self,tree, word):
node = tree
depth = 0
count = 0
while True:
print(node.value)
depth += 1
if node.value == word:
count = node.count
break
elif word < node.value:
node = node.left
elif word > node.value:
node = node.right
return depth, count
def main():
words = read_words('sample.txt')
b = BinaryTree()
b.insert(words)
b.createTree(words)
b.printTree()
Since you're a beginner I'd advice to implement the tree methods with recursion instead of iteration since this will result to simpler implementation. While recursion might seem a bit difficult concept at first often it is the easiest approach.
Here's a draft implementation of a binary tree which uses recursion for insertion, searching and printing the tree, it should support the functionality you need.
class Node(object):
def __init__(self, value):
self.value = value
self.left = None
self.right = None
self.count = 1
def __str__(self):
return 'value: {0}, count: {1}'.format(self.value, self.count)
def insert(root, value):
if not root:
return Node(value)
elif root.value == value:
root.count += 1
elif value < root.value:
root.left = insert(root.left, value)
else:
root.right = insert(root.right, value)
return root
def create(seq):
root = None
for word in seq:
root = insert(root, word)
return root
def search(root, word, depth=1):
if not root:
return 0, 0
elif root.value == word:
return depth, root.count
elif word < root.value:
return search(root.left, word, depth + 1)
else:
return search(root.right, word, depth + 1)
def print_tree(root):
if root:
print_tree(root.left)
print root
print_tree(root.right)
src = ['foo', 'bar', 'foobar', 'bar', 'barfoo']
tree = create(src)
print_tree(tree)
for word in src:
print 'search {0}, result: {1}'.format(word, search(tree, word))
# Output
# value: bar, count: 2
# value: barfoo, count: 1
# value: foo, count: 1
# value: foobar, count: 1
# search foo, result: (1, 1)
# search bar, result: (2, 2)
# search foobar, result: (2, 1)
# search bar, result: (2, 2)
# search barfoo, result: (3, 1)
To answer your direct question, the reason why you are placing all of the words into a single node is because of the following statement inside of main():
b.insert(words)
The insert function creates a Node and sets the value of the node to the item you pass in. Instead, you need to create a node for each item in the list which is what your createTree() function does. The preceeding b.insert is not necessary.
Removing that line makes your tree become correctly formed, but reveals a fundamental problem with the design of your data structure, namely the printTree() method. This method seems designed to traverse the tree and recursively call itself on any child. In your initial version this function worked, because there the tree was mal-formed with only a single node of the whole list (and the print function simply printed that value since right and left were empty).
However with a correctly formed tree the printTree() function now tries to invoke itself on the left and right descendants. The descendants however are of type _Node, not of type BinaryTree, and there is no methodprintTree() declared for _Node objects.
You can salvage your code and solve this new error in one of two ways. First you can implement your BinaryTree.printTree() function as _Node.printTree(). You can't do a straight copy and paste, but the logic of the function won't have to change much. Or you could leave the method where it is at, but wrap each _left or _right node inside of a new BinaryTree so that they would have the necessary printTree() method. Doing this would leave the method where it is at, but you will still have to implement some kind of helper traversal method inside of _Node.
Finally, you could change all of your _Node objects to be _BinaryTree objects instead.
The semantic difference between a node and a tree is one of scope. A node should only be aware of itself, its direct children (left and right), and possibly its parent. A tree on the other hand can be aware of any of its descendents, no matter how far removed. This is accomplished by treating any child node as its own tree. Even a leaf, without any children at all can be thought of as a tree with a depth of 0. This behavior is what lets a tree work recursively. Your code is mixing the two together.
here this is the node definition
class Node(object):
def __init__(self,value=None):
self.value = value
self.next = None
this is the conversion for the code a number to linked list
def number_to_list(number):
head,tail = None,None
p = True
for x in str(number):
if x=='-':
p = False
continue
else:
if p:
node = Node(int(x))
else:
node = Node(int("-"+x))
if head:
tail.next = node
else:
head = node
tail = node
return head
pass
this is code for conversion of linked list to number
def list_to_number(head):
neg = False
num = ''
for number in head:
val = str(number)
if (val.find('-')!= -1):
neg = True
num=num+val.replace('-','')
if (neg==False):
return int(num)
else:
return -1*int(num)
pass
here it is the test cases
def test_number_to_list():
import listutils
head = number_to_list(120)
assert [1,2,0] == listutils.from_linked_list(head)
assert 120 == list_to_number(head)
head = number_to_list(0)
assert [0] == listutils.from_linked_list(head)
assert 0 == list_to_number(head)
head = number_to_list(-120)
assert [-1, -2, 0] == listutils.from_linked_list(head)
assert -120 == list_to_number(head)
here from_linked_list means
# avoids infinite loops
def from_linked_list(head):
result = []
counter = 0
while head and counter < 100: # tests don't use more than 100 nodes, so bail if you loop 100 times.
result.append(head.value)
head = head.next
counter += 1
return result
at last in this the problem is while converting the linked list to single number it is encountering an error i.e.,node object is not iterable
please help me out of this to write the code
def list_to_number(head):
neg = False
num = ''
for number in head:
val = str(number)
TypeError: 'Node' object is not iterable
here this is the traceback
The
for number in head:
is not a correct way to iterate of the list.
You need to start from head and then follow the chain of next references.
Note that if __iter__ is defined on Node like this:
class Node(object):
def __init__(self,value=None):
self.value = value
self.next = None
def __iter__(self):
that = self
while that is not None:
yield that.value
that = that.next
Then:
for number in head:
Would actually work.
I am trying to find the kth smallest element of binary search tree and I have problems using recursion. I understand how to print the tree inorder/postorder etc. but I fail to return the rank of the element. Can someone point where I am making a mistake? In general, I am having hard time understanding recursion in trees.
Edit: this is an exercise, so I am not looking for using built-in functions. I have another solution where I keep track of number of left and right children as I insert nodes and that code is working fine. I am wondering if it is possible to do this using inorder traversal because it seems to be a simpler solution.
class BinaryTreeNode:
def __init__(self, data, left=None, right=None):
self.data = data
self.left = left
self.right = right
def traverseInOrder(root,order):
if root == None:
return
traverseInOrder(root.left,order+1)
print root.data,
print order
traverseInOrder(root.right,order)
"""
a
/ \
b c
/ \ / \
d e f g
/ \
h i
"""
h = BinaryTreeNode("h")
i = BinaryTreeNode("i")
d = BinaryTreeNode("d", h, i)
e = BinaryTreeNode("e")
f = BinaryTreeNode("f")
g = BinaryTreeNode("g")
b = BinaryTreeNode("b", d, e)
c = BinaryTreeNode("c", f, g)
a = BinaryTreeNode("a", b, c)
print traverseInOrder(a,0)
If this is an academic exercise, make traverseInOrder (or similar method tailored to the purpose) return the number of children it visited. From there things get simpler.
If this isn't academic, have a look at http://stromberg.dnsalias.org/~dstromberg/datastructures/ - the dictionary-like objects are all trees, and support iterators - so finding the nth is a matter of zip(tree, range(n)).
You could find the smallets element in the binary search tree first. Then from that element call a method to give you the next element k times.
For find_smallest_node method, note that you can traverse all the nodes "in-order" until reach to smallest. But that approach takes O(n) time.
However, you do not need a recursion to find the smallest node, because in BST smallest node is simply the left most node, so you can traverse the nodes until finding a node that has no left child and it takes O(log n) time:
class BST(object):
def find_smallest_node(self):
if self.root == None:
return
walking_node = self.root
smallest_node = self.root
while walking_node != None:
if walking_node.data <= smallest_node.data:
smallest_node = walking_node
if walking_node.left != None:
walking_node = walking_node.left
elif walking_node.left == None:
walking_node = None
return smallest_node
def find_k_smallest(self, k):
k_smallest_node = self.find_smallest_node()
if k_smallest_node == None:
return
else:
k_smallest_data = k_smallest_node.data
count = 1
while count < k:
k_smallest_data = self.get_next(k_smallest_data)
count += 1
return k_smallest_data
def get_next (self, key):
...
It just requires to keep the parent of the nodes when inserting them to the tree.
class Node(object):
def __init__(self, data, left=None, right=None, parent=None):
self.data = data
self.right = right
self.left = left
self.parent = parent
An implementation of the bst class with the above methods and also def get_next (self, key) function is here. The upper folder contains the test cases for it and it worked.