GATE | GATE-CS-2014-(Set-1) | Question 21

Consider a rooted Binary tree represented using pointers. The best upper bound on the time required to determine the number of subtrees having having exactly 4 nodes O(n^a Logn ^b). Then the value of a + 10b is ________
(A) 1
(B) 11
(C) 12
(D) 21


Answer: (A)

Explanation: We can find the subtree with 4 nodes in O(n) time. Following can be a simple approach.
1) Traverse the tree in bottom up manner and find size of subtree rooted with current node
2) If size becomes 4, then print the current node.

Following is C implementation

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

struct Node
{
    int data;
    struct Node *left, *right;
};

// A utility function to create a new Binary Tree Node
struct Node *newNode(int item)
{
    struct Node *temp =  (struct Node *)malloc(sizeof(struct Node));
    temp->data = item;
    temp->left = temp->right = NULL;
    return temp;
}

int print4Subtree(struct Node *root)
{
    if (root == NULL)
      return 0;
    int l =  print4Subtree(root->left);
    int r =   print4Subtree(root->right);
    if ((l + r + 1) == 4)
       printf("%d ", root->data);
    return (l + r + 1);
}

// Driver Program to test above functions
int main()
{
    struct Node *root = newNode(1);
    root->left = newNode(2);
    root->right = newNode(3);
    root->left->left = newNode(4);
    root->left->right = newNode(5);
    root->right->left = newNode(6);
    root->right->right = newNode(7);
    root->right->left->right = newNode(8);

    print4Subtree(root);

    return 0;
}

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