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Wednesday, June 11, 2014

Diameter of a Binary Tree

The diameter of a tree (sometimes called the width) is the number of nodes on the longest path between two leaves in the tree. The diagram below shows two trees each with diameter nine, the leaves that form the ends of a longest path are shaded (note that there is more than one path in each tree of length nine, but no path longer than nine nodes).(reference geeksforgeeks.org)


The diameter of a tree T is the largest of the following quantities:
* the diameter of T’s left subtree
* the diameter of T’s right subtree
* the longest path between leaves that goes through the root of T (this can be computed from the heights of the subtrees of T)

Implementation:
#include<stdio.h>
#include<iostream>
#include<conio.h>

using namespace std;

struct node
{
    int val,leftVal,rightVal;
    node *left;
    node *right;
}*root;

void make_tree(node **temp,int i)
{
    if((*temp) == NULL)
    {
        (*temp) = new node;
        (*temp)->val = i;
        (*temp)->leftVal = (*temp)->rightVal = 0;
        (*temp)->right = (*temp)->left = NULL;
    }

    else if((*temp)->val > i)
    {
        make_tree(&(*temp)->left,i);
    }

    else
    {
        make_tree(&(*temp)->right,i);
    }
}

void post_order(node *temp)
{
    if(temp == NULL)
        return;

    post_order(temp->left);
    post_order(temp->right);
    printf("%i\t",temp->val);
}

void del(node **temp)
{
    if((*temp) == NULL)
        return;

    del(&(*temp)->left);
    del(&(*temp)->right);

    node *ptr = (*temp);
    *temp = NULL;

    getch();

    cout<<ptr->val<<endl;
    delete ptr;

}

void diameter(node *temp, int *max)
{
    if(temp == NULL)
        return;

    else
    {
        diameter(temp->left,max);
        diameter(temp->right,max);

        if(temp->left)
            temp->leftVal = (temp->left->leftVal > temp->left->rightVal) 
? temp->left->leftVal + 1 : temp->left->rightVal + 1;
        else
            temp->leftVal = 0;

        if(temp->right)
            temp->rightVal = (temp->right->leftVal > temp->right->rightVal)
 ? temp->right->leftVal + 1 : temp->right->rightVal + 1;
        else
            temp->rightVal = 0;

        if( *max < temp->rightVal + temp->leftVal + 1)
            *max = temp->rightVal + temp->leftVal + 1;
    }
}
int main()
{
    int n,i,max = -1234;

    cin>>n;

    while(n--)
    {
        cin>>i;

        make_tree(&root,i);
    }

    cout<<"Post - Order Traversal   :   ";

    post_order(root);

    diameter(root,&max);

    cout<<"\nThe Diameter of Given Tree :   "<<max<<"\n";

    cout<<"\nNow, Deleting Nodes :   ";

    del(&root);

    return 0;
}