Binary tree traversal ppt

Binary Tree Traversal
submitted by :-
K. Priyadarsini II-M.Sc., (CS & IT)
V. Priyanka II-M.Sc., (CS & IT)
(Nadar saraswathi college of arts & science, Theni,
TamilNadu)

• A tree is finite set of one or more
nodes.
• A binary tree is an important type of
tree structure which occurs very often.
• A binary tree traversal is perform
many operations that we often want to
perform on trees.
• A full traversal produces a linear
order for the information in a tree.

• This linear order may be familiar and
useful.
• If we let L,D,R stand for moving left,
printing the data, and moving right when
at a node then there are six possible
combinations of traversal:
 LDR
 LRD
 DLR
 DRL
 RDL
 RLD

• If we adopt the convention that we
traverse left before right then only three
traversals remain: LDR, LRD, DLR
• To these we assign the names inorder ,
postorder , preorder because there is a
natural correspondence between these
traversals and producing the infix ,
postfix , prefix forms of an expression.

This tree contains an arithmetic
expression with binary operators : add(+),
Multiply(*),divide(/),exponentiation(**) and
variables A,B,C,D, and E.
+
+
+
E*
D/
**A
CB

Inorder Traversal:
 Informally this calls for moving down
the tree towards the left until you can go
to farther.
 Then you “visit” the node, move one
node to the right and continue again.
 If you cannot move to the right, go
back one more node.
 A precise way of describing this
traversal is to write it as a recursive
procedure.

Procedure INORDER(T)
//T is a binary tree where each node has
three fields L-CHILD,DATA,R-CHILD//
If T≠0 then[call INORDER(LCHILD(T))
Print (DATA(T))
call(INORDER(RCHILD(T))]
End INORDER
Procedure PREORDER(T)
If T≠0 then[Print (DATA(T))
call PREORDER(LCHILD(T))
call(PREORDER(RCHILD(T))]
End PREORDER

Procedure POSTORDER(T)
If T≠0 then[call POSTORDER(LCHILD(T))
call(POSTORDER(RCHILD(T))
Print (DATA(T))]
End POSTORDER

Non Recursive Procedure:
 The above three algorithm using
recursion. It is very easy to produce
an equivalent non recursive
procedure.

INORDER1(T):
 A Nonrecursive version using a stack of size n
i0 //initialize the stack//
L1:if T!=0 then [i<-i+2;if i > n then call STACK_FULL
STACK(i-1)  T; STACK(i) ‘L2’
T LCHILD(T);go to L1; //traverse left subtree//
L2: Print (DATA(T))
ii+2; if i>n then call STACK__FULL
STACK(i-1)  T; STACK(i) ‘L3’
T RCHILD(T);go to L1; //traverse right subtree//
L3: if i !=0 then [//stack not empty, simulate a return//
T STACK(i-10); X STACK(i-1); x STACK(i)
i i-2; go to X]
End INORDER1

INORDER2(T):
 A simplified, nonrecursive version using a stack of size n
i0 //initialize stack//
L1: if T !=0 then [i i+1; if i>n then call STACK__FULL
stack( i )T; T LCHILD(T); go to L1
L2; print(DATA(T))
TRCHILD(T); go to L1]
if i !=0 then [//stack not empty//
T STACK(i): ii-1; go to L2]
End INORDER2

INORDER3(T):
 A nonrecursive, no go to version using a stack of size n
i0 //initialize stack//
loop
while T=0 do //move down LCHILD FIELDS//
ii+1; if i>n then call STACK__FULL
STACK( i )T; T LCHILD(T)
end
if i=0 then return
TSTACK(i); i i-1
print(DATA(T)); TRCHILD(T)
forever
End INORDER3

 Let n be the number of nodes in T. If we consider the
action of the above algorithm, we note that every node of the
tree is placed on the stack once.
 Thus, the statements STACK ( i ) ← T and T  STACK( i )
are executed n times. Moreover , T will equal zero once
for every zero link in the tree which is exactly
2n0+n1=n0+n1+n2+1=n+1
 So, every step will be executed no more than some
small constant times n or O (n).

Binary tree traversal ppt

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