1.Consider two binary search trees A and B. BST A has m nodes, and BST B has n n

Question

1.Consider two binary search trees A and B. BST A has m nodes, and BST B has n nodes. Assume m is much greater than n. We wish to find the intersection of values from the two trees; i.e., we wish to identify all values in BST A which are also found in BST B. Give the most efficient answer in each case and show your work.

a) We will perform an inorder traversal of BST A, and for each value we will perform a search in BST B for that value. What is the worst-case running time of this approach?

b) We will perform an inorder traversal of BST A, dumping the values into a list. We will do the same for BST B. Then we will find the intersection of the two lists. What is the worst-case running time?

Now assume A and B are AVL trees.

c) We will perform an inorder traversal of AVL tree A, and for each value we will perform a search in AVL tree B for that value. What is the worst-case running time of this approach?

d) We will perform an inorder traversal of AVL tree A, dumping the values into a list. We will do the same for AVL tree B. Then we will find the intersection of the two lists. What is the worst-case running time?

Explanation / Answer

#include <stdio.h>

#include <stdlib.h>

struct node

{

    int data;

    struct node* left, *right;

};

/* Function to find LCA of n1 and n2. The function assumes that both

   n1 and n2 are present in BST */

struct node *lca(struct node* root, int n1, int n2)

{

    if (root == NULL) return NULL;

    // If both n1 and n2 are smaller than root, then LCA lies in left

    if (root->data > n1 && root->data > n2)

        return lca(root->left, n1, n2);

    // If both n1 and n2 are greater than root, then LCA lies in right

    if (root->data < n1 && root->data < n2)

        return lca(root->right, n1, n2);

    return root;

}

/* Helper function that allocates a new node with the given data.*/

struct node* newNode(int data)

{

    struct node* node = (struct node*)malloc(sizeof(struct node));

    node->data = data;

    node->left = node->right = NULL;

    return(node);

}

/* Driver program to test mirror() */

int main()

{

    // Let us construct the BST shown in the above figure

    struct node *root        = newNode(20);

    root->left               = newNode(8);

    root->right              = newNode(22);

    root->left->left         = newNode(4);

    root->left->right        = newNode(12);

    root->left->right->left = newNode(10);

    root->left->right->right = newNode(14);

    int n1 = 10, n2 = 14;

    struct node *t = lca(root, n1, n2);

    printf("LCA of %d and %d is %d ", n1, n2, t->data);

    n1 = 14, n2 = 8;

    t = lca(root, n1, n2);

    printf("LCA of %d and %d is %d ", n1, n2, t->data);

    n1 = 10, n2 = 22;

    t = lca(root, n1, n2);

    printf("LCA of %d and %d is %d ", n1, n2, t->data);

    getchar();

    return 0;

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