Chapter 8, Problem 47E

Program Plan Intro

Binary search tree:

• Binary search tree is a tree; the nodes are sorted in the semantic order.
• Binary search tree nodes can have zero, one, or two children.
• Node without children is called a leaf or end node.
• A node that does not have a superior node is called a root node or starting node.
  • In binary search tree, the left subtree contains the nodes lesser than the root node.
  • The right subtree contains the nodes greater than the root node.
• The binary search will performed until finding a search node or reaching the end of the tree.

Explanation of Solution

Insertion of elements in the binary search tree:

Given elements to construct a binary search tree are as follows:

50, 72, 96, 107, 26, 12, 11, 9, 2, 10, 25, 51, 16, 17, 95.

Step 1:

Insert the element 50, which is the root node of a binary search tree.

Step 2:

Next element is 72, which is greater than root node element 50, so insert the element 72 as the right child of the root node.

Step 3:

• Next element is 96, which is greater than root node element 50, so insert the element 96 as the right child of the root node.
• The root node already contains the element 72 as the right child and the element 96 is greater than the element 72.
• So, insert the element 96 as the right child of 72.

Step 4:

• Next element is 107, which is greater than root node element 50, so insert the element 107 as the right child of the root node.
• The root node already contains the element 72 as the right child and the element 107 is greater than the element 72.
• The element 72 already contains the element 96 as the right child and the element 107 is greater than the element 96.
• So, insert the element 107 as the right child of 96.

Step 5:

Next element is 26, which is less than root node value 50, so insert the element 26 as the left child of the root node.

Step 6:

• Next element is 12, which is less than the root node value 50, so insert the element 12 as left child of the root node.
• The root node already contains the element 26 as the left child and the element 12 is less than the element 26.
• So, insert the element 12 as left child of the element 26.

Step 7:

• Next element is 11, which is less than the root node value 50, so insert the element 11 as left child of the root node.
• The root node already contains the element 26 as the left child and the element 11 is less than the element 26.
• The element 26 already contains the element 12 as the left child and the element 11 is lesser than the element 12.
• So, insert the element 11 as left child of the element 12.

Step 8:

• Next element is 9, which is less than the root node value 50, so insert the element 9 as left child of the root node.
• The root node already contains the element 26 as the left child and the element 9 is less than the element 26.
• The element 26 already contains the element 12 as the left child and the element 9 is lesser than the element 12.
• The element 12 already contains the element 11 as the left child and the element 9 is lesser than the element 11.
• So, insert the element 9 as left child of the element 11.

Step 9:

• Next element is 2, which is less than the root node value 50, so insert the element 2 as left child of the root node.
• The root node already contains the element 26 as the left child and the element 2 is less than the element 26.
• The element 26 already contains the element 12 as the left child and the element 2 is lesser than the element 12.
• The element 12 already contains the element 11 as the left child and the element 2 is lesser than the element 11.
• The element 11 already contains the element 9 as the left child and the element 2 is lesser than the element 9.
• So, insert the element 2 as left child of the element 9.

Step 10:

• Next element is 10, which is less than the root node value 50, so insert the element 10 as left child of the root node.
• The root node already contains the element 26 as the left child and the element 10 is less than the element 26.
• The element 26 already contains the element 12 as the left child and the element 10 is lesser than the element 12.
• The element 12 already contains the element 11 as the left child and the element 10 is lesser than the element 11.
• The element 11 already contains the element 9 as the left child and the element 10 is greater than the element 9.
• So, insert the element 10 as right child of the element 9.

Step 11:

• Next element is 25, which is less than the root node value 50, so insert the element 25 as left child of the root node.
• The root node already contains the element 26 as the left child and the element 25 is less than the element 26.
• The element 26 already contains the element 12 as the left child and the element 25 is greater than the element 12.
• So, insert the element 25 as right child of the element 12.

Step 12:

• Next element is 51, which is greater than root node element 50, so insert the element 51 as the right child of the root node.
• The root node already contains the element 72 as the right child and the element 51 is lesser than the element 72.
• So, insert the element 51 as the left child of 72.

Step 13:

• Next element is 16, which is less than the root node value 50, so insert the element 16 as left child of the root node.
• The root node already contains the element 26 as the left child and the element 16 is less than the element 26.
• The element 26 already contains the element 12 as the left child and the element 16 is greater than the element 12.
• The element 12 already contains the element 25 as the right child and the element 16 is lesser than the element 25.
• So, insert the element 16 as left child of the element 25.

Step 14:

• Next element is 17, which is less than the root node value 50, so insert the element 17 as left child of the root node.
• The root node already contains the element 26 as the left child and the element 17 is less than the element 26.
• The element 26 already contains the element 12 as the left child and the element 17 is greater than the element 12.
• The element 12 already contains the element 25 as the right child and the element 17 is lesser than the element 25.
• The element 25 already contains the element 16 as the left child and the element 17 is greater than the element 16.
• So, insert the element 17 as right child of the element 16.

Step 15:

• Next element is 95, which is greater than root node element 50, so insert the element 95 as the right child of the root node.
• The root node already contains the element 72 as the right child and the element 95 is greater than the element 72.
• The element 72 already contains the element 96 as the right child and the element 95 is lesser than the element 96.
• So, insert the element 95 as the left child of 96.

Therefore, the above tree is the final constructed binary search tree for the given elements.