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In-order, Pre-order and Post-order Tree Traversal Explain : using C and c++ Programming

Unlike linear data structures (Array, Linked List, Queues, Stacks, etc) which have only one logical way to traverse them, trees can be traversed in different ways. Following are the generally used ways for traversing trees.



depth First Traversals:
(a) Inorder
(b) Preorder
(c) Postorder
Breadth First or Level Order Traversal
Inorder Traversal:
Algorithm Inorder(tree)
   1. Traverse the left subtree, i.e., call Inorder(left-subtree)
   2. Visit the root.
   3. Traverse the right subtree, i.e., call Inorder(right-subtree)
Uses of Inorder
In case of binary search trees (BST), Inorder traversal gives nodes in non-decreasing order. To get nodes of BST in non-increasing order, a variation of Inorder traversal where Inorder itraversal s reversed, can be used.
Example: Inorder traversal for the above given figure is 4 2 5 1 3.

Practice Inorder Traversal

Preorder Traversal:
Algorithm Preorder(tree)
   1. Visit the root.
   2. Traverse the left subtree, i.e., call Preorder(left-subtree)
   3. Traverse the right subtree, i.e., call Preorder(right-subtree) 
Uses of Preorder
Preorder traversal is used to create a copy of the tree. Preorder traversal is also used to get prefix expression on of an expression tree. Please see http://en.wikipedia.org/wiki/Polish_notation to know why prefix expressions are useful.
Example: Preorder traversal for the above given figure is 1 2 4 5 3.

Practice Preorder Traversal

Postorder Traversal:
Algorithm Postorder(tree)
   1. Traverse the left subtree, i.e., call Postorder(left-subtree)
   2. Traverse the right subtree, i.e., call Postorder(right-subtree)
   3. Visit the root.
Uses of Postorder
Postorder traversal is used to delete the tree. Please see the question for deletion of tree for details. Postorder traversal is also useful to get the postfix expression of an expression tree. Please seehttp://en.wikipedia.org/wiki/Reverse_Polish_notation to for the usage of postfix expression.



In-order traversal method:
1. Visit Left Sub-Tree
2. Process Current Node
3. Visit Right Sub-Tree

Pre-order traversal method:
1. Process Current Node
2. Visit Left Sub-Tree
3. Visit Right Sub-Tree

Post-order traversal method:
1. Visit Left Sub-Tree
2. Visit Right Sub-Tree
3. Process Current Node

C/C++ Implementation with full program:

#include <stdio.h>
#include <stdlib.h>

struct node
{
    int value;
    node* left;
    node* right;
};


struct node* root;

struct node* insert(struct node* r, int data);
void inOrder(struct node* r);
void preOrder(struct node* r);
void postOrder(struct node* r);

int main()
{
    root = NULL;
    int n, v;

    printf("How many data's do you want to insert ?\n");
    scanf("%d", &n);

    for(int i=0; i<n; i++){
        printf("Data %d: ", i+1);
        scanf("%d", &v);
        root = insert(root, v);
    }

    printf("Inorder Traversal: ");
    inOrder(root);
    printf("\n");

    printf("Preorder Traversal: ");
    preOrder(root);
    printf("\n");

    printf("Postorder Traversal: ");
    postOrder(root);
    printf("\n");


    return 0;
}

struct node* insert(struct node* r, int data)
{
    if(r==NULL)
    {
        r = (struct node*) malloc(sizeof(struct node));
        r->value = data;
        r->left = NULL;
        r->right = NULL;
    }
    else if(data < r->value){
        r->left = insert(r->left, data);
    }
    else {
        r->right = insert(r->right, data);
    }
    return r;

}

void inOrder(struct node* r)
{
    if(r!=NULL){
        inOrder(r->left);
        printf("%d ", r->value);
        inOrder(r->right);
    }
}

void preOrder(struct node* r)
{
    if(r!=NULL){
        printf("%d ", r->value);
        preOrder(r->left);
        preOrder(r->right);
    }
}

void postOrder(struct node* r)
{
    if(r!=NULL){
        postOrder(r->left);
        postOrder(r->right);
        printf("%d ", r->value);

    }
}