Question

Show a merge of the following skew heaps.  (Show each step).


         h1                  h2                                    
                               
                19                10
               /  \              /  \
             54    39          12    29
             /\    /          /  \   / \
            61 65 68        30   14 50  59

Answer 1

Steps in merging the two skew heaps:

1. Compare the roots of two heaps. The root of h1 is 19 and root of h2 is 10. The smallest among them will be the root of resulting new heap tree.Here it is 10.

10

2. The resulting new heap tree's right subtree is the left subtree of h2(as the h2's root is the smaller than h1's root).

3. Now resulting new heap tree's left subtree is computed recurively merging h2's right subtree with h1 by following the steps 1 and 2.

3.1 root node(29) of h2's right subtree is compared with root node of h1(19). 19 is smallest. Now this 19 becomes the root node of left subtree of the resulting new heap tree.

10 12 19 14 30

3.2 The left subtree of the smallest node(19) in h1 will be the right subtree of the newly added node(19) in the new heap tree.

4.1 root node(39) of h1's right subtree is compared with root node of h2's right subtree (29). 29 is smallest. Now this 29 becomes the root node of left subtree of node 19 in the resulting new heap tree.

4.2 The left subtree of the smallest node(29) in h2 will be the right subtree of the newly added node(29) in the new heap tree.

5.1 root node(59) of right subtree of node having 29(which is added newly in the resulting tree) in h2 is compared with root node(39) of right subtree h1. 39 is smallest. Now this 39 becomes the root node of left subtree of node 29 in the resulting new heap tree.

5.2  The left subtree of the smallest node(39) in h1 will be the right subtree of the newly added node(39) in the new heap tree.

6. The left out node is 59 in the tree h2. This will become the left subtree for the node 29 in the resulting new heap tree.

This is the final merged heap tree.