Monday, April 18, 2011

Iterative Solution of Binary Tree Traversal Inorder,Preorder,PostOrder

Most problems involving binary trees can be solved by using recursion. Recursion is inherent to trees. But, keep in mind that recursion has a memory overhead because of the additional stack space required for the recursive method calls. Sometime interviewers will ask to solve problems related to trees without using recursion. This can sometimes make the problem challenging. In this problem, even though we will not use recursion explicitly, we will use the Stack data structure that emulates what recursion does.


Inorder


Algo


1) Create an empty stack S.
2) Initialize current node as root
3) Push the current node to S and set current = current->left until current is NULL
4) If current is NULL and stack is not empty then
a) Pop the top item from stack.
b) Print the popped item, set current = current->right
c) Go to step 3.
5) If current is NULL and stack is empty then we are done.



#include
#include
#define bool int

/* A binary tree tNode has data, pointer to left child
and a pointer to right child */
struct tNode
{
int data;
struct tNode* left;
struct tNode* right;
};

/* Structure of a stack node. Linked List implementation is used for
stack. A stack node contains a pointer to tree node and a pointer to
next stack node */
struct sNode
{
struct tNode *t;
struct sNode *next;
};

/* Stack related functions */
void push(struct sNode** top_ref, struct tNode *t);
struct tNode *pop(struct sNode** top_ref);
bool isEmpty(struct sNode *top);

/* Iterative function for inorder tree traversal */
void inOrder(struct tNode *root)
{
/* set current to root of binary tree */
struct tNode *current = root;
struct sNode *s = NULL; /* Initialize stack s */
bool done = 0;

while (!done)
{
/* Reach the left most tNode of the current tNode */
if(current != NULL)
{
/* place pointer to a tree node on the stack before traversing
the node's left subtree */
push(&s, current);
current = current->left;
}

/* backtrack from the empty subtree and visit the tNode
at the top of the stack; however, if the stack is empty,
you are done */
else
{
if (!isEmpty(s))
{
current = pop(&s);
printf("%d ", current->data);

/* we have visited the node and its left subtree.
Now, it's right subtree's turn */
current = current->right;
}
else
done = 1;
}
} /* end of while */
}

/* UTILITY FUNCTIONS */
/* Function to push an item to sNode*/
void push(struct sNode** top_ref, struct tNode *t)
{
/* allocate tNode */
struct sNode* new_tNode =
(struct sNode*) malloc(sizeof(struct sNode));

if(new_tNode == NULL)
{
printf("Stack Overflow \n");
getchar();
exit(0);
}

/* put in the data */
new_tNode->t = t;

/* link the old list off the new tNode */
new_tNode->next = (*top_ref);

/* move the head to point to the new tNode */
(*top_ref) = new_tNode;
}

/* The function returns true if stack is empty, otherwise false */
bool isEmpty(struct sNode *top)
{
return (top == NULL)? 1 : 0;
}

/* Function to pop an item from stack*/
struct tNode *pop(struct sNode** top_ref)
{
struct tNode *res;
struct sNode *top;

/*If sNode is empty then error */
if(isEmpty(*top_ref))
{
printf("Stack Underflow \n");
getchar();
exit(0);
}
else
{
top = *top_ref;
res = top->t;
*top_ref = top->next;
free(top);
return res;
}
}

/* Helper function that allocates a new tNode with the
given data and NULL left and right pointers. */
struct tNode* newtNode(int data)
{
struct tNode* tNode = (struct tNode*)
malloc(sizeof(struct tNode));
tNode->data = data;
tNode->left = NULL;
tNode->right = NULL;

return(tNode);
}

/* Driver program to test above functions*/
int main()
{

/* Constructed binary tree is
1
/ \
2 3
/ \
4 5
*/
struct tNode *root = newtNode(1);
root->left = newtNode(2);
root->right = newtNode(3);
root->left->left = newtNode(4);
root->left->right = newtNode(5);

inOrder(root);

getchar();
return 0;
}

Run Here https://ideone.com/bgss3

Preorder Traversal


Algo

/**
non-recursive version of Pre-order traversal
void PreOrderNonRecur(NODE *root)
Algorithm:
create a stack
PUSH the root node of the tree into the stack
While the stack is not empty
POP a node
If the node is not NULL
Print the value of the node
PUSH the node's right child into the stack
PUSH the node's left child into the stack
*/

#include
#include
#define bool int

/* A binary tree tNode has data, pointer to left child
and a pointer to right child */
struct tNode
{
int data;
struct tNode* left;
struct tNode* right;
};

/* Structure of a stack node. Linked List implementation is used for
stack. A stack node contains a pointer to tree node and a pointer to
next stack node */
struct sNode
{
struct tNode *t;
struct sNode *next;
};

/* Stack related functions */
void push(struct sNode** top_ref, struct tNode *t);
struct tNode *pop(struct sNode** top_ref);
bool isEmpty(struct sNode *top);

/* Iterative function for preorder tree traversal */
void postOrder(struct tNode *root)
{
/* set current to root of binary tree */
struct tNode *current=root;
struct sNode *s = NULL; /* Initialize stack s */


push(&s,current);

while(!isEmpty(s))
{
current=pop(&s);
printf(" %d ", current->data);
push(&s,current->right);
push(&s,current->left);

}

}

/* UTILITY FUNCTIONS */
/* Function to push an item to sNode*/
void push(struct sNode** top_ref, struct tNode *t)
{
/* allocate tNode */
struct sNode* new_tNode =
(struct sNode*) malloc(sizeof(struct sNode));

if(new_tNode == NULL)
{
printf("Stack Overflow \n");
getchar();
exit(0);
}

/* put in the data */
new_tNode->t = t;

/* link the old list off the new tNode */
new_tNode->next = (*top_ref);

/* move the head to point to the new tNode */
(*top_ref) = new_tNode;
}

/* The function returns true if stack is empty, otherwise false */
bool isEmpty(struct sNode *top)
{
return (top == NULL)? 1 : 0;
}

/* Function to pop an item from stack*/
struct tNode *pop(struct sNode** top_ref)
{
struct tNode *res;
struct sNode *top;

/*If sNode is empty then error */
if(isEmpty(*top_ref))
{
printf("Stack Underflow \n");
getchar();
exit(0);
}
else
{
top = *top_ref;
res = top->t;
*top_ref = top->next;
free(top);
return res;
}
}

/* Helper function that allocates a new tNode with the
given data and NULL left and right pointers. */
struct tNode* newtNode(int data)
{
struct tNode* tNode = (struct tNode*)
malloc(sizeof(struct tNode));
tNode->data = data;
tNode->left = NULL;
tNode->right = NULL;

return(tNode);
}

/* Driver program to test above functions*/
int main()
{

/* Constructed binary tree is
1
/ \
2 3
/ \
4 5
*/
struct tNode *root = newtNode(1);
root->left = newtNode(2);
root->right = newtNode(3);
root->left->left = newtNode(4);
root->left->right = newtNode(5);


postOrder(root);

getchar();
return 0;
}

run here https://ideone.com/YUPvS

PostOrder Traversal

Algo use Tow Stack child & Parent

* Push the root node to the child stack.
* while child stack is not empty
* Pop a node from the child stack, and push it to the parent stack.
* Push its left child followed by its right child to the child stack.
* end while
* Now the parent stack would have all the nodes ready to be traversed in post-order. Pop off the nodes from the parent stack one by one and you will have the post order traversal of the tree.


#include
#include
#define bool int

/* A binary tree tNode has data, pointer to left child
and a pointer to right child */
struct tNode
{
int data;
struct tNode* left;
struct tNode* right;
};

/* Structure of a stack node. Linked List implementation is used for
stack. A stack node contains a pointer to tree node and a pointer to
next stack node */
struct sNode
{
struct tNode *t;
struct sNode *next;
};

/* Stack related functions */
void push(struct sNode** top_ref, struct tNode *t);
struct tNode *pop(struct sNode** top_ref);
bool isEmpty(struct sNode *top);

/* Iterative function for postorder tree traversal */
void postOrder(struct tNode *root)
{
if(!root)
return;

/* set current to root of binary tree */

struct sNode *child,*parent = NULL; /* Initialize stack s */

push(&child,root);
while(!isEmpty(child))
{
struct tNode *current =pop(&child);
push(&parent,current);

if(current->left)
push(&child,current->left);
if(current->right)
push(&child,current->right);

}
while(!isEmpty(parent))
{
struct tNode *current= pop(&parent);
printf(" %d ",current->data);
}

}

/* UTILITY FUNCTIONS */
/* Function to push an item to sNode*/
void push(struct sNode** top_ref, struct tNode *t)
{
/* allocate tNode */
struct sNode* new_tNode =
(struct sNode*) malloc(sizeof(struct sNode));

if(new_tNode == NULL)
{
printf("Stack Overflow \n");
getchar();
exit(0);
}

/* put in the data */
new_tNode->t = t;

/* link the old list off the new tNode */
new_tNode->next = (*top_ref);

/* move the head to point to the new tNode */
(*top_ref) = new_tNode;
}

/* The function returns true if stack is empty, otherwise false */
bool isEmpty(struct sNode *top)
{
return (top == NULL)? 1 : 0;
}

/* Function to pop an item from stack*/
struct tNode *pop(struct sNode** top_ref)
{
struct tNode *res;
struct sNode *top;

/*If sNode is empty then error */
if(isEmpty(*top_ref))
{
printf("Stack Underflow \n");
getchar();
exit(0);
}
else
{
top = *top_ref;
res = top->t;
*top_ref = top->next;
free(top);
return res;
}
}

/* Helper function that allocates a new tNode with the
given data and NULL left and right pointers. */
struct tNode* newtNode(int data)
{
struct tNode* tNode = (struct tNode*)
malloc(sizeof(struct tNode));
tNode->data = data;
tNode->left = NULL;
tNode->right = NULL;

return(tNode);
}

/* Driver program to test above functions*/
int main()
{

/* Constructed binary tree is
1
/ \
2 3
/ \
4 5
*/
struct tNode *root = newtNode(1);
root->left = newtNode(2);
root->right = newtNode(3);
root->left->left = newtNode(4);
root->left->right = newtNode(5);
root->right->left = newtNode(6);
root->right->right = newtNode(7);
postOrder(root);

getchar();
return 0;
}


Run here https://ideone.com/uFq33

Excellent Explanation of Postorder Using Single Stack

http://www.ihas1337code.com/2010/10/binary-tree-post-order-traversal.html

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