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Recursive Call
Recall that a stack is used during function
calls.
The caller function places the arguments
on the stack and passes control to the
called function.
Local variables are allocated storage on
the call stack.
Calling a function itself makes no
difference as far as the call stack is
concerned.
Stack Layout during a call
Here is stack layout when function F calls
function F (recursively):
Parameters(F)
Local variables(F)
Return address(F)
Parameters(F)
Parameters(F)
Local variables(F)
Return address(F)
Parameters(F)
Local variables(F)
Return address(F)
Parameters(F)
Local variables(F)
Return address(F)
At point of call During execution of F After call
sp
sp
sp
Recursion: preorder
..preorder(15)
....preorder(null)
....preorder(18)
......preorder(16)
........preorder(null)
........preorder(17)
..........preorder(null)
..........preorder(null)
......preorder(20)
........preorder(null)
........preorder(null)
14 4 9 7 3 5 15 16 17 18 20
Recursion: inorder
inorder(14)
..inorder(4)
....inorder(3)
......inorder(null)
......inorder(null)
....inorder(9)
......inorder(7)
........inorder(5)
..........inorder(null)
..........inorder(null)
........inorder(null)
......inorder(null)
14 4 9 7 3 5 15 16 17 18 20
Non Recursive Traversal
We can implement non-recursive versions
of the preorder, inorder and postorder
traversal by using an explicit stack.
The stack will be used to store the tree
nodes in the appropriate order.
Here, for example, is the routine for
inorder traversal that uses a stack.
Non Recursive Traversal
void inorder(TreeNode* root)
Stack<TreeNode* > stack;
TreeNode* p;
p = root;
do
while( p != NULL )
stack.push( p );
p = p->getLeft();
// at this point, left tree is empty
Non Recursive Traversal
void inorder(TreeNode* root)
Stack<TreeNode* > stack;
TreeNode* p;
p = root;
do
while( p != NULL )
stack.push( p );
p = p->getLeft();
// at this point, left tree is empty
Non Recursive Traversal
if( !stack.empty() )
p = stack.pop();
cout << *(p->getInfo()) << " ";
// go back & traverse right subtree
p = p->getRight();
} while ( !stack.empty() || p != NULL );
Non Recursive Traversal
if( !stack.empty() )
p = stack.pop();
cout << *(p->getInfo()) << " ";
// go back & traverse right subtree
p = p->getRight();
} while ( !stack.empty() || p != NULL );
Non Recursive Traversal
if( !stack.empty() )
p = stack.pop();
cout << *(p->getInfo()) << " ";
// go back & traverse right subtree
p = p->getRight();
} while ( !stack.empty() || p != NULL );
Traversal Trace
recursive inorder
inorder(14) ..inorder(4) ....inorder(3) 3 4 ..inorder(9) ....inorder(7) ......inorder(5) 5 7 9 14 inorder(15) 15 inorder(18) ..inorder(16) 16 ..inorder(17) 17 18 inorder(20) 20
nonrecursive inorder
push(14) ..push(4) ....push(3) 3 4 ..push(9) ....push(7) ......push(5) 5 7 9 14 push(15) 15 push(18) ..push(16) 16 ..push(17) 17 18 push(20) 20
Traversal Trace
recursive inorder
inorder(14) ..inorder(4) ....inorder(3) 3 4 ..inorder(9) ....inorder(7) ......inorder(5) 5 7 9 14 inorder(15) 15 inorder(18) ..inorder(16) 16 ..inorder(17) 17 18 inorder(20) 20
nonrecursive inorder
push(14) ..push(4) ....push(3) 3 4 ..push(9) ....push(7) ......push(5) 5 7 9 14 push(15) 15 push(18) ..push(16) 16 ..push(17) 17 18 push(20) 20
Traversal Trace
recursive inorder
inorder(14) ..inorder(4) ....inorder(3) 3 4 ..inorder(9) ....inorder(7) ......inorder(5) 5 7 9 14 inorder(15) 15 inorder(18) ..inorder(16) 16 ..inorder(17) 17 18 inorder(20) 20
nonrecursive inorder
push(14) ..push(4) ....push(3) 3 4 ..push(9) ....push(7) ......push(5) 5 7 9 14 push(15) 15 push(18) ..push(16) 16 ..push(17) 17 18 push(20) 20
Level-order Traversal
There is yet another way of traversing a
binary tree that is not related to recursive
traversal procedures discussed previously.
In level-order traversal, we visit the nodes
at each level before proceeding to the next
level.
At each level, we visit the nodes in a left-
to-right order.
