Printing BFS (Binary Tree) in Level Order with Specific Formatting
Question:
To begin with, this question is not a dup of this one, but builds on it.
Taking the tree in that question as an example,
1
/
2 3
/ /
4 5 6
How would you modify your program to print it so,
1
2 3
4 5 6
rather than the general
1
2
3
4
5
6
I’m basically looking for intuitions on the most efficient way to do it – I’ve got a method involving appending the result to a list, and then looping through it. A more efficient way might be to store the last element in each level as it is popped, and print out a new line afterward.
Ideas?
Answers:
Sounds like breadth-first traversal to me.
Breadth-first traversal is implemented with a queue. Here, simply insert in the queue a special token that indicate that a newline must be printed. Each time the token is found, print a newline and re-insert the token in the queue (at the end — that’s the definition of a queue).
Start the algorithm with a queue containing the root followed by the special newline token.
Just build one level at a time, e.g.:
class Node(object):
def __init__(self, value, left=None, right=None):
self.value = value
self.left = left
self.right = right
def traverse(rootnode):
thislevel = [rootnode]
while thislevel:
nextlevel = list()
for n in thislevel:
print n.value,
if n.left: nextlevel.append(n.left)
if n.right: nextlevel.append(n.right)
print
thislevel = nextlevel
t = Node(1, Node(2, Node(4, Node(7))), Node(3, Node(5), Node(6)))
traverse(t)
Edit: if you’re keen to get a small saving in maximum consumed “auxiliary” memory (never having simultaneously all this level and the next level in such “auxiliary” memory), you can of course use collection.deque instead of list, and consume the current level as you go (via popleft) instead of simply looping. The idea of creating one level at a time (as you consume –or iterate on– the previous one) remains intact — when you do need to distinguish levels, it’s just more direct than using a single big deque plus auxiliary information (such as depth, or number of nodes remaining in a given level).
However, a list that is only appended to (and looped on, rather than “consumed”) is quite a bit more efficient than a deque (and if you’re after C++ solutions, quite similarly, a std::vector using just push_back for building it, and a loop for then using it, is more efficient than a std::deque). Since all the producing happens first, then all the iteration (or consuming), an interesting alternative if memory is tightly constrained might be to use a list anyway to represent each level, then .reverse it before you start consuming it (with .pop calls) — I don’t have large trees around to check by measurement, but I suspect that this approach would still be faster (and actually less memory-consuming) than deque (assuming that the underlying implementation of list [[or std::vector]] actually does recycle memory after a few calls to pop [[or pop_back]] — and with the same assumption for deque, of course;-).
A version that doesn’t require extra storage:
std::deque<Node> bfs;
bfs.push_back(start);
int nodesInThisLayer = 1;
int nodesInNextLayer = 0;
while (!bfs.empty()) {
Node front = bfs.front();
bfs.pop_front();
for (/*iterate over front's children*/) {
++nodesInNextLayer;
nodes.push_back(child);
}
std::cout << node.value;
if (0 == --nodesInThisLayer) {
std::cout << std::endl;
nodesInThisLayer = nodesInNextLayer;
nodesInNextLayer = 0;
} else {
std::cout << " ";
}
}
P.S. sorry for the C++ code, I’m not very fluent in Python yet.
why not keep sentinal in queue and check when all the nodes in current level are processed.
public void printLevel(Node n) {
Queue<Integer> q = new ArrayBlockingQueue<Integer>();
Node sentinal = new Node(-1);
q.put(n);
q.put(sentinal);
while(q.size() > 0) {
n = q.poll();
System.out.println(n.value + " ");
if (n == sentinal && q.size() > 0) {
q.put(sentinal); //push at the end again for next level
System.out.println();
}
if (q.left != null) q.put(n.left);
if (q.right != null) q.put(n.right);
}
}
A simple Version based on Bread First Search, This code is applicable for graphs in general and can be used for binary trees as well.
def printBfsLevels(graph,start):
queue=[start]
path=[]
currLevel=1
levelMembers=1
height=[(0,start)]
childCount=0
print queue
while queue:
visNode=queue.pop(0)
if visNode not in path:
if levelMembers==0:
levelMembers=childCount
childCount=0
currLevel=currLevel+1
queue=queue+graph.get(visNode,[])
if levelMembers > 0:
levelMembers=levelMembers-1
for node in graph.get(visNode,[]):
childCount=childCount+1
height.append((currLevel,node))
path=path+[visNode]
prevLevel=None
for v,k in sorted(height):
if prevLevel!=v:
if prevLevel!=None:
print "n"
prevLevel=v
print k,
return height
g={1: [2, 3,6], 2: [4, 5], 3: [6, 7],4:[8,9,13]}
printBfsLevels(g,1)
>>>
[1]
1
2 3 6
4 5 6 7
8 9 13
>>>
Another version based on Recursion, which is specific to binary tree
class BinTree:
"Node in a binary tree"
def __init__(self,val,leftChild=None,rightChild=None,root=None):
self.val=val
self.leftChild=leftChild
self.rightChild=rightChild
self.root=root
if not leftChild and not rightChild:
self.isExternal=True
def getChildren(self,node):
children=[]
if node.isExternal:
return []
if node.leftChild:
children.append(node.leftChild)
if node.rightChild:
children.append(node.rightChild)
return children
@staticmethod
def createTree(tupleList):
"Creates a Binary tree Object from a given Tuple List"
Nodes={}
root=None
for item in treeRep:
if not root:
root=BinTree(item[0])
root.isExternal=False
Nodes[item[0]]=root
root.root=root
root.leftChild=BinTree(item[1],root=root)
Nodes[item[1]]=root.leftChild
root.rightChild=BinTree(item[2],root=root)
Nodes[item[2]]=root.rightChild
else:
CurrentParent=Nodes[item[0]]
CurrentParent.isExternal=False
CurrentParent.leftChild=BinTree(item[1],root=root)
Nodes[item[1]]=CurrentParent.leftChild
CurrentParent.rightChild=BinTree(item[2],root=root)
Nodes[item[2]]=CurrentParent.rightChild
root.nodeDict=Nodes
return root
def printBfsLevels(self,levels=None):
if levels==None:
levels=[self]
nextLevel=[]
for node in levels:
print node.val,
for node in levels:
nextLevel.extend(node.getChildren(node))
print 'n'
if nextLevel:
node.printBfsLevels(nextLevel)
## 1
## 2 3
## 4 5 6 7
## 8
treeRep = [(1,2,3),(2,4,5),(3,6,7),(4,8,None)]
tree= BinTree.createTree(treeRep)
tree.printBfsLevels()
>>>
1
2 3
4 5 6 7
8 None
Here my code prints the tree level by level as well as upside down
int counter=0;// to count the toatl no. of elments in the tree
void tree::print_treeupsidedown_levelbylevel(int *array)
{
int j=2;
int next=j;
int temp=0;
while(j<2*counter)
{
if(array[j]==0)
break;
while(array[j]!=-1)
{
j++;
}
for(int i=next,k=j-1 ;i<k; i++,k--)
{
temp=array[i];
array[i]=array[k];
array[k]=temp;
}
next=j+1;
j++;
}
for(int i=2*counter-1;i>=0;i--)
{
if(array[i]>0)
printf("%d ",array[i]);
if(array[i]==-1)
printf("n");
}
}
void tree::BFS()
{
queue<node *>p;
node *leaf=root;
int array[2*counter];
for(int i=0;i<2*counter;i++)
array[i]=0;
int count=0;
node *newline=new node; //this node helps to print a tree level by level
newline->val=0;
newline->left=NULL;
newline->right=NULL;
newline->parent=NULL;
p.push(leaf);
p.push(newline);
while(!p.empty())
{
leaf=p.front();
if(leaf==newline)
{
printf("n");
p.pop();
if(!p.empty())
p.push(newline);
array[count++]=-1;
}
else
{
cout<<leaf->val<<" ";
array[count++]=leaf->val;
if(leaf->left!=NULL)
{
p.push(leaf->left);
}
if(leaf->right!=NULL)
{
p.push(leaf->right);
}
p.pop();
}
}
delete newline;
print_treeupsidedown_levelbylevel(array);
}
Here in my code the function BFS prints the tree level by level, which also fills the data in an int array for printing the tree upside down. (note there is a bit of swapping is used while printing the tree upside down which helps to achieve our goal). If the swapping is not performed then for a tree like
8
/
1 12
/
5 9
/
4 7
/
6
o/p will be
6
7 4
9 5
12 1
8
but the o/p has to be
6
4 7
5 9
1 12
8
this the reason why swapping part was needed in that array.
The following code will print each level of binary tree into new line:
public void printbylevel(node root){
int counter = 0, level = 0;
Queue<node> qu = new LinkedList<node>();
qu.add(root);
level = 1;
if(root.child1 != null)counter++;
if(root.child2 != null)counter++;
while(!qu.isEmpty()){
node temp = qu.remove();
level--;
System.out.print(temp.val);
if(level == 0 ){
System.out.println();
level = counter;
counter = 0;
}
if(temp.child1 != null){
qu.add(temp.child1);
counter++;
}
if(temp.child2 != null){
qu.add(temp.child2);
counter++;
}
}
}
My solution is similar to Alex Martelli’s, but I separate traversal of the data structure from processing the data structure. I put the meat of the code into iterLayers to keep printByLayer short and sweet.
from collections import deque
class Node:
def __init__(self, val, lc=None, rc=None):
self.val = val
self.lc = lc
self.rc = rc
def iterLayers(self):
q = deque()
q.append(self)
def layerIterator(layerSize):
for i in xrange(layerSize):
n = q.popleft()
if n.lc: q.append(n.lc)
if n.rc: q.append(n.rc)
yield n.val
while (q):
yield layerIterator(len(q))
def printByLayer(self):
for layer in self.iterLayers():
print ' '.join([str(v) for v in layer])
root = Node(1, Node(2, Node(4, Node(7))), Node(3, Node(5), Node(6)))
root.printByLayer()
which prints the following when run:
1
2 3
4 5 6
7
This is breadth first search, so you can use a queue and recursively do this in a simple and compact way …
# built-in data structure we can use as a queue
from collections import deque
def print_level_order(head, queue = deque()):
if head is None:
return
print head.data
[queue.append(node) for node in [head.left, head.right] if node]
if queue:
print_level_order(queue.popleft(), queue)
class TNode:
def __init__(self, data, left=None, right=None):
self.data = data
self.left = left
self.right = right
class BST:
def __init__(self, root):
self._root = root
def bfs(self):
list = [self._root]
while len(list) > 0:
print [e.data for e in list]
list = [e.left for e in list if e.left] +
[e.right for e in list if e.right]
bst = BST(TNode(1, TNode(2, TNode(4), TNode(5)), TNode(3, TNode(6), TNode(7))))
bst.bfs()
For those who are simply interested in visualizing binary trees (and not so much in the theory behind breadth-first search), there is a show function in the binarytree package. Applied to the example given in the question,
from binarytree import Node, show
root = Node(1)
root.left = Node(2)
root.right = Node(3)
root.left.left = Node(4)
root.right.left = Node(5)
root.right.right = Node(6)
show(root)
which prints
1
/
2 3
/ /
4 5 6
I think what you expecting is to print the nodes at each level either separated by a space or a comma and the levels be separated by a new line. This is how I would code up the algorithm. We know that when we do a breadth-first search on a graph or tree and insert the nodes in a queue, all nodes in the queue coming out will be either at the same level as the one previous or a new level which is parent level + 1 and nothing else.
So when you are at a level keep printing out the node values and as soon as you find that the level of the node increases by 1, then you insert a new line before starting to print all the nodes at that level.
This is my code which does not use much memory and only the queue is needed for everything.
Assuming the tree starts from the root.
queue = [(root, 0)] # Store the node along with its level.
prev = 0
while queue:
node, level = queue.pop(0)
if level == prev:
print(node.val, end = "")
else:
print()
print(node.val, end = "")
if node.left:
queue.append((node.left, level + 1))
if node.right:
queue.append((node.right, level + 1))
prev = level
At the end all you need is the queue for all the processing.
This is mostly the same code as provided by Alex Martelli except this is modified for python 3.
class Node(object):
def __init__(self, value, left=None, right=None):
self.value = value
self.left = left
self.right = right
def traverse(rootnode):
thislevel = [rootnode]
while thislevel:
nextlevel = list()
for n in thislevel:
print (n.value,' ', end=''),
if n.left: nextlevel.append(n.left)
if n.right: nextlevel.append(n.right)
print(" ")
thislevel = nextlevel
t = Node(1, Node(2, Node(4, Node(7))), Node(3, Node(5), Node(6)))
traverse(t)
Here is a Python gist which prints the tree by level. The idea behind it is to use BFS and keep a level marker integer which marks the end the last node of the level. This is similar to Naresh’s sentinel approach, but without the need of inserting a sentinel inside the queue, since this is accomplished by the level marker.
This algorithm has a space complexity of O(2tree_height)
# Print tree by levels - using BFS
# Time complexity of O(n)
# Space complexity: O(2^tree_height)
from collections import deque
class Node:
def __init__(self, data, left=None, right=None):
self.data = data
self.left = left
self.right = right
def print_levels_tree(root: Node):
q = deque()
q.append(root)
level, level_marker = 0, 1
while q:
if (level_marker == 0):
level, level_marker = level + 1, len(q)
print("", end = 'n')
level_marker -= 1
node = q.popleft()
if (node is None):
continue
print(node.data, " ", end = '')
q.append(node.left)
q.append(node.right)
# Some examples
tree = Node(19, Node(7, Node(3), Node(11)), Node(19))
print_levels_tree(tree)
left = Node(7, Node(3, Node(2), Node(5)), Node(11, None, Node(17, Node(13))))
tree = Node(19, left, Node(43))
print_levels_tree(tree)
left = Node(7, Node(3, Node(2), Node(5)), Node(11, None, Node(17, Node(13))))
right = Node(43, Node(23, None, Node(37, Node(29, None, Node(31)), Node(41))), Node(47, None, Node(53)) )
tree = Node(19, left, right)
print_levels_tree(tree)
Which prints something like:
19
7 43
3 11 23 47
2 5 17 37 53
If you want to use a t separator, it would look like:
19
7 43
3 11 23 47
2 5 17 37 53
This gist is available at https://gist.github.com/lopespm/993f0af88cf30b7f8c9e17982518b71b
Making use of queues(constant space complexity)
def bfs(self, queue=None):
if(queue is None):
queue = deque([self.root])
elif(not queue):
return
currNode = queue.pop()
print(currNode.data)
if currNode.left:
queue.appendleft(currNode.left)
if currNode.right:
queue.appendleft(currNode.right)
self.bfs(queue)
LEVEL ORDER TRAVERSAL of a BT / BST
In BASH, you can easily implement BT / BST without using any hash arrays/map, etc by simply creating/maintaining nodes in a .txt file.
Here’s my crack at it. 2 small functions print_level() and print_root(), will do. Script can print any level node info from any given user specified root node.
#!/bin/bash
print_level(){
echo $cs
call_flag=0
for row in $cs; do if [[ `grep "^${row}:" ~/btree-data.txt` ]]; then call_flag=1; fi; done
if [[ $call_flag == 1 ]]; then rs="$cs"; print_root; fi
}
print_root(){
if [[ ${flag} == 0 ]]; then echo "${rs}"; flag=1; fi
cs=""
for r in $rs; do cs+="$(grep "^${r}:" ~/btree-data.txt | cut -d':' -f2 | sed "s/,/ /") "; done
print_level
echo
}
flag=0
echo -e "nn
# It reads a file ~/btree-data.txt (as shown below).
# -- One can easily implement CRUD operation to maintain BT/BST using a .txt file.
#
# -- Here .txt file ROW's Format is: NODE:left_leaf_node,right_leaf_node
#
# 100:50,200
# 50:20,60
# 200:300
# 300:350
# 60:55,75
# 20:10,25
# 10:5
# 350:320
# 25:27
# 5:2
# 320:310,325
# 2:3
## ----------------- BTree Diagram -------------------------------------------------------------------------
# 100
# 50 200
# 20 60 300
# 10 25 55 75 350
# 5 27 320
# 2 310 325
# 3
## ----------------- BTree Diagram -------------------------------------------------------------------------
nn"
echo -ne "n-- Enter which root: "; read rs
print_root
echo -e "nn"
Which when you run, spits:
$ ./btree-bash-level-print.sh
# It reads a file ~/btree-data.txt (as shown below).
# -- One can easily implement CRUD operation to maintain BT/BST using a .txt file.
#
# -- Here .txt file ROW's Format is: NODE:left_leaf_node,right_leaf_node
#
# 100:50,200
# 50:20,60
# 200:300
# 300:350
# 60:55,75
# 20:10,25
# 10:5
# 350:320
# 25:27
# 5:2
# 320:310,325
# 2:3
## ----------------- BTree Diagram -------------------------------------------------------------------------
# 100
# 50 200
# 20 60 300
# 10 25 55 75 350
# 5 27 320
# 2 310 325
# 3
## ----------------- BTree Diagram -------------------------------------------------------------------------
-- Enter which root: 100
100
50 200
20 60 300
10 25 55 75 350
5 27 320
2 310 325
3
For root (300),
-- Enter which root: 300
300
350
320
310 325
For root (50),
-- Enter which root: 50
50
20 60
10 25 55 75
5 27
2
3
To begin with, this question is not a dup of this one, but builds on it.
Taking the tree in that question as an example,
1
/
2 3
/ /
4 5 6
How would you modify your program to print it so,
1
2 3
4 5 6
rather than the general
1
2
3
4
5
6
I’m basically looking for intuitions on the most efficient way to do it – I’ve got a method involving appending the result to a list, and then looping through it. A more efficient way might be to store the last element in each level as it is popped, and print out a new line afterward.
Ideas?
Sounds like breadth-first traversal to me.
Breadth-first traversal is implemented with a queue. Here, simply insert in the queue a special token that indicate that a newline must be printed. Each time the token is found, print a newline and re-insert the token in the queue (at the end — that’s the definition of a queue).
Start the algorithm with a queue containing the root followed by the special newline token.
Just build one level at a time, e.g.:
class Node(object):
def __init__(self, value, left=None, right=None):
self.value = value
self.left = left
self.right = right
def traverse(rootnode):
thislevel = [rootnode]
while thislevel:
nextlevel = list()
for n in thislevel:
print n.value,
if n.left: nextlevel.append(n.left)
if n.right: nextlevel.append(n.right)
print
thislevel = nextlevel
t = Node(1, Node(2, Node(4, Node(7))), Node(3, Node(5), Node(6)))
traverse(t)
Edit: if you’re keen to get a small saving in maximum consumed “auxiliary” memory (never having simultaneously all this level and the next level in such “auxiliary” memory), you can of course use collection.deque instead of list, and consume the current level as you go (via popleft) instead of simply looping. The idea of creating one level at a time (as you consume –or iterate on– the previous one) remains intact — when you do need to distinguish levels, it’s just more direct than using a single big deque plus auxiliary information (such as depth, or number of nodes remaining in a given level).
However, a list that is only appended to (and looped on, rather than “consumed”) is quite a bit more efficient than a deque (and if you’re after C++ solutions, quite similarly, a std::vector using just push_back for building it, and a loop for then using it, is more efficient than a std::deque). Since all the producing happens first, then all the iteration (or consuming), an interesting alternative if memory is tightly constrained might be to use a list anyway to represent each level, then .reverse it before you start consuming it (with .pop calls) — I don’t have large trees around to check by measurement, but I suspect that this approach would still be faster (and actually less memory-consuming) than deque (assuming that the underlying implementation of list [[or std::vector]] actually does recycle memory after a few calls to pop [[or pop_back]] — and with the same assumption for deque, of course;-).
A version that doesn’t require extra storage:
std::deque<Node> bfs;
bfs.push_back(start);
int nodesInThisLayer = 1;
int nodesInNextLayer = 0;
while (!bfs.empty()) {
Node front = bfs.front();
bfs.pop_front();
for (/*iterate over front's children*/) {
++nodesInNextLayer;
nodes.push_back(child);
}
std::cout << node.value;
if (0 == --nodesInThisLayer) {
std::cout << std::endl;
nodesInThisLayer = nodesInNextLayer;
nodesInNextLayer = 0;
} else {
std::cout << " ";
}
}
P.S. sorry for the C++ code, I’m not very fluent in Python yet.
why not keep sentinal in queue and check when all the nodes in current level are processed.
public void printLevel(Node n) {
Queue<Integer> q = new ArrayBlockingQueue<Integer>();
Node sentinal = new Node(-1);
q.put(n);
q.put(sentinal);
while(q.size() > 0) {
n = q.poll();
System.out.println(n.value + " ");
if (n == sentinal && q.size() > 0) {
q.put(sentinal); //push at the end again for next level
System.out.println();
}
if (q.left != null) q.put(n.left);
if (q.right != null) q.put(n.right);
}
}
A simple Version based on Bread First Search, This code is applicable for graphs in general and can be used for binary trees as well.
def printBfsLevels(graph,start):
queue=[start]
path=[]
currLevel=1
levelMembers=1
height=[(0,start)]
childCount=0
print queue
while queue:
visNode=queue.pop(0)
if visNode not in path:
if levelMembers==0:
levelMembers=childCount
childCount=0
currLevel=currLevel+1
queue=queue+graph.get(visNode,[])
if levelMembers > 0:
levelMembers=levelMembers-1
for node in graph.get(visNode,[]):
childCount=childCount+1
height.append((currLevel,node))
path=path+[visNode]
prevLevel=None
for v,k in sorted(height):
if prevLevel!=v:
if prevLevel!=None:
print "n"
prevLevel=v
print k,
return height
g={1: [2, 3,6], 2: [4, 5], 3: [6, 7],4:[8,9,13]}
printBfsLevels(g,1)
>>>
[1]
1
2 3 6
4 5 6 7
8 9 13
>>>
Another version based on Recursion, which is specific to binary tree
class BinTree:
"Node in a binary tree"
def __init__(self,val,leftChild=None,rightChild=None,root=None):
self.val=val
self.leftChild=leftChild
self.rightChild=rightChild
self.root=root
if not leftChild and not rightChild:
self.isExternal=True
def getChildren(self,node):
children=[]
if node.isExternal:
return []
if node.leftChild:
children.append(node.leftChild)
if node.rightChild:
children.append(node.rightChild)
return children
@staticmethod
def createTree(tupleList):
"Creates a Binary tree Object from a given Tuple List"
Nodes={}
root=None
for item in treeRep:
if not root:
root=BinTree(item[0])
root.isExternal=False
Nodes[item[0]]=root
root.root=root
root.leftChild=BinTree(item[1],root=root)
Nodes[item[1]]=root.leftChild
root.rightChild=BinTree(item[2],root=root)
Nodes[item[2]]=root.rightChild
else:
CurrentParent=Nodes[item[0]]
CurrentParent.isExternal=False
CurrentParent.leftChild=BinTree(item[1],root=root)
Nodes[item[1]]=CurrentParent.leftChild
CurrentParent.rightChild=BinTree(item[2],root=root)
Nodes[item[2]]=CurrentParent.rightChild
root.nodeDict=Nodes
return root
def printBfsLevels(self,levels=None):
if levels==None:
levels=[self]
nextLevel=[]
for node in levels:
print node.val,
for node in levels:
nextLevel.extend(node.getChildren(node))
print 'n'
if nextLevel:
node.printBfsLevels(nextLevel)
## 1
## 2 3
## 4 5 6 7
## 8
treeRep = [(1,2,3),(2,4,5),(3,6,7),(4,8,None)]
tree= BinTree.createTree(treeRep)
tree.printBfsLevels()
>>>
1
2 3
4 5 6 7
8 None
Here my code prints the tree level by level as well as upside down
int counter=0;// to count the toatl no. of elments in the tree
void tree::print_treeupsidedown_levelbylevel(int *array)
{
int j=2;
int next=j;
int temp=0;
while(j<2*counter)
{
if(array[j]==0)
break;
while(array[j]!=-1)
{
j++;
}
for(int i=next,k=j-1 ;i<k; i++,k--)
{
temp=array[i];
array[i]=array[k];
array[k]=temp;
}
next=j+1;
j++;
}
for(int i=2*counter-1;i>=0;i--)
{
if(array[i]>0)
printf("%d ",array[i]);
if(array[i]==-1)
printf("n");
}
}
void tree::BFS()
{
queue<node *>p;
node *leaf=root;
int array[2*counter];
for(int i=0;i<2*counter;i++)
array[i]=0;
int count=0;
node *newline=new node; //this node helps to print a tree level by level
newline->val=0;
newline->left=NULL;
newline->right=NULL;
newline->parent=NULL;
p.push(leaf);
p.push(newline);
while(!p.empty())
{
leaf=p.front();
if(leaf==newline)
{
printf("n");
p.pop();
if(!p.empty())
p.push(newline);
array[count++]=-1;
}
else
{
cout<<leaf->val<<" ";
array[count++]=leaf->val;
if(leaf->left!=NULL)
{
p.push(leaf->left);
}
if(leaf->right!=NULL)
{
p.push(leaf->right);
}
p.pop();
}
}
delete newline;
print_treeupsidedown_levelbylevel(array);
}
Here in my code the function BFS prints the tree level by level, which also fills the data in an int array for printing the tree upside down. (note there is a bit of swapping is used while printing the tree upside down which helps to achieve our goal). If the swapping is not performed then for a tree like
8
/
1 12
/
5 9
/
4 7
/
6
o/p will be
6
7 4
9 5
12 1
8
but the o/p has to be
6
4 7
5 9
1 12
8
this the reason why swapping part was needed in that array.
The following code will print each level of binary tree into new line:
public void printbylevel(node root){
int counter = 0, level = 0;
Queue<node> qu = new LinkedList<node>();
qu.add(root);
level = 1;
if(root.child1 != null)counter++;
if(root.child2 != null)counter++;
while(!qu.isEmpty()){
node temp = qu.remove();
level--;
System.out.print(temp.val);
if(level == 0 ){
System.out.println();
level = counter;
counter = 0;
}
if(temp.child1 != null){
qu.add(temp.child1);
counter++;
}
if(temp.child2 != null){
qu.add(temp.child2);
counter++;
}
}
}
My solution is similar to Alex Martelli’s, but I separate traversal of the data structure from processing the data structure. I put the meat of the code into iterLayers to keep printByLayer short and sweet.
from collections import deque
class Node:
def __init__(self, val, lc=None, rc=None):
self.val = val
self.lc = lc
self.rc = rc
def iterLayers(self):
q = deque()
q.append(self)
def layerIterator(layerSize):
for i in xrange(layerSize):
n = q.popleft()
if n.lc: q.append(n.lc)
if n.rc: q.append(n.rc)
yield n.val
while (q):
yield layerIterator(len(q))
def printByLayer(self):
for layer in self.iterLayers():
print ' '.join([str(v) for v in layer])
root = Node(1, Node(2, Node(4, Node(7))), Node(3, Node(5), Node(6)))
root.printByLayer()
which prints the following when run:
1
2 3
4 5 6
7
This is breadth first search, so you can use a queue and recursively do this in a simple and compact way …
# built-in data structure we can use as a queue
from collections import deque
def print_level_order(head, queue = deque()):
if head is None:
return
print head.data
[queue.append(node) for node in [head.left, head.right] if node]
if queue:
print_level_order(queue.popleft(), queue)
class TNode:
def __init__(self, data, left=None, right=None):
self.data = data
self.left = left
self.right = right
class BST:
def __init__(self, root):
self._root = root
def bfs(self):
list = [self._root]
while len(list) > 0:
print [e.data for e in list]
list = [e.left for e in list if e.left] +
[e.right for e in list if e.right]
bst = BST(TNode(1, TNode(2, TNode(4), TNode(5)), TNode(3, TNode(6), TNode(7))))
bst.bfs()
For those who are simply interested in visualizing binary trees (and not so much in the theory behind breadth-first search), there is a show function in the binarytree package. Applied to the example given in the question,
from binarytree import Node, show
root = Node(1)
root.left = Node(2)
root.right = Node(3)
root.left.left = Node(4)
root.right.left = Node(5)
root.right.right = Node(6)
show(root)
which prints
1
/
2 3
/ /
4 5 6
I think what you expecting is to print the nodes at each level either separated by a space or a comma and the levels be separated by a new line. This is how I would code up the algorithm. We know that when we do a breadth-first search on a graph or tree and insert the nodes in a queue, all nodes in the queue coming out will be either at the same level as the one previous or a new level which is parent level + 1 and nothing else.
So when you are at a level keep printing out the node values and as soon as you find that the level of the node increases by 1, then you insert a new line before starting to print all the nodes at that level.
This is my code which does not use much memory and only the queue is needed for everything.
Assuming the tree starts from the root.
queue = [(root, 0)] # Store the node along with its level.
prev = 0
while queue:
node, level = queue.pop(0)
if level == prev:
print(node.val, end = "")
else:
print()
print(node.val, end = "")
if node.left:
queue.append((node.left, level + 1))
if node.right:
queue.append((node.right, level + 1))
prev = level
At the end all you need is the queue for all the processing.
This is mostly the same code as provided by Alex Martelli except this is modified for python 3.
class Node(object):
def __init__(self, value, left=None, right=None):
self.value = value
self.left = left
self.right = right
def traverse(rootnode):
thislevel = [rootnode]
while thislevel:
nextlevel = list()
for n in thislevel:
print (n.value,' ', end=''),
if n.left: nextlevel.append(n.left)
if n.right: nextlevel.append(n.right)
print(" ")
thislevel = nextlevel
t = Node(1, Node(2, Node(4, Node(7))), Node(3, Node(5), Node(6)))
traverse(t)
Here is a Python gist which prints the tree by level. The idea behind it is to use BFS and keep a level marker integer which marks the end the last node of the level. This is similar to Naresh’s sentinel approach, but without the need of inserting a sentinel inside the queue, since this is accomplished by the level marker.
This algorithm has a space complexity of O(2tree_height)
# Print tree by levels - using BFS
# Time complexity of O(n)
# Space complexity: O(2^tree_height)
from collections import deque
class Node:
def __init__(self, data, left=None, right=None):
self.data = data
self.left = left
self.right = right
def print_levels_tree(root: Node):
q = deque()
q.append(root)
level, level_marker = 0, 1
while q:
if (level_marker == 0):
level, level_marker = level + 1, len(q)
print("", end = 'n')
level_marker -= 1
node = q.popleft()
if (node is None):
continue
print(node.data, " ", end = '')
q.append(node.left)
q.append(node.right)
# Some examples
tree = Node(19, Node(7, Node(3), Node(11)), Node(19))
print_levels_tree(tree)
left = Node(7, Node(3, Node(2), Node(5)), Node(11, None, Node(17, Node(13))))
tree = Node(19, left, Node(43))
print_levels_tree(tree)
left = Node(7, Node(3, Node(2), Node(5)), Node(11, None, Node(17, Node(13))))
right = Node(43, Node(23, None, Node(37, Node(29, None, Node(31)), Node(41))), Node(47, None, Node(53)) )
tree = Node(19, left, right)
print_levels_tree(tree)
Which prints something like:
19
7 43
3 11 23 47
2 5 17 37 53
If you want to use a t separator, it would look like:
19
7 43
3 11 23 47
2 5 17 37 53
This gist is available at https://gist.github.com/lopespm/993f0af88cf30b7f8c9e17982518b71b
Making use of queues(constant space complexity)
def bfs(self, queue=None):
if(queue is None):
queue = deque([self.root])
elif(not queue):
return
currNode = queue.pop()
print(currNode.data)
if currNode.left:
queue.appendleft(currNode.left)
if currNode.right:
queue.appendleft(currNode.right)
self.bfs(queue)
LEVEL ORDER TRAVERSAL of a BT / BST
In BASH, you can easily implement BT / BST without using any hash arrays/map, etc by simply creating/maintaining nodes in a .txt file.
Here’s my crack at it. 2 small functions print_level() and print_root(), will do. Script can print any level node info from any given user specified root node.
#!/bin/bash
print_level(){
echo $cs
call_flag=0
for row in $cs; do if [[ `grep "^${row}:" ~/btree-data.txt` ]]; then call_flag=1; fi; done
if [[ $call_flag == 1 ]]; then rs="$cs"; print_root; fi
}
print_root(){
if [[ ${flag} == 0 ]]; then echo "${rs}"; flag=1; fi
cs=""
for r in $rs; do cs+="$(grep "^${r}:" ~/btree-data.txt | cut -d':' -f2 | sed "s/,/ /") "; done
print_level
echo
}
flag=0
echo -e "nn
# It reads a file ~/btree-data.txt (as shown below).
# -- One can easily implement CRUD operation to maintain BT/BST using a .txt file.
#
# -- Here .txt file ROW's Format is: NODE:left_leaf_node,right_leaf_node
#
# 100:50,200
# 50:20,60
# 200:300
# 300:350
# 60:55,75
# 20:10,25
# 10:5
# 350:320
# 25:27
# 5:2
# 320:310,325
# 2:3
## ----------------- BTree Diagram -------------------------------------------------------------------------
# 100
# 50 200
# 20 60 300
# 10 25 55 75 350
# 5 27 320
# 2 310 325
# 3
## ----------------- BTree Diagram -------------------------------------------------------------------------
nn"
echo -ne "n-- Enter which root: "; read rs
print_root
echo -e "nn"
Which when you run, spits:
$ ./btree-bash-level-print.sh
# It reads a file ~/btree-data.txt (as shown below).
# -- One can easily implement CRUD operation to maintain BT/BST using a .txt file.
#
# -- Here .txt file ROW's Format is: NODE:left_leaf_node,right_leaf_node
#
# 100:50,200
# 50:20,60
# 200:300
# 300:350
# 60:55,75
# 20:10,25
# 10:5
# 350:320
# 25:27
# 5:2
# 320:310,325
# 2:3
## ----------------- BTree Diagram -------------------------------------------------------------------------
# 100
# 50 200
# 20 60 300
# 10 25 55 75 350
# 5 27 320
# 2 310 325
# 3
## ----------------- BTree Diagram -------------------------------------------------------------------------
-- Enter which root: 100
100
50 200
20 60 300
10 25 55 75 350
5 27 320
2 310 325
3
For root (300),
-- Enter which root: 300
300
350
320
310 325
For root (50),
-- Enter which root: 50
50
20 60
10 25 55 75
5 27
2
3