Answer and Explanation:
To draw the binary search tree based on the given inorder and postorder traversals, we can follow these steps:
1. Identify the root node:
- The last element in the postorder traversal is the root of the binary search tree. In this case, the root is 56.
2. Divide the inorder traversal into two parts:
- Elements to the left of the root node in the inorder traversal represent the left subtree.
- Elements to the right of the root node in the inorder traversal represent the right subtree.
In this case, the inorder traversal can be divided as follows:
- Left subtree: 13, 23, 31, 49, 50, 54, 55.
- Right subtree: 57, 58, 70, 80, 83, 99, 100.
3. Divide the postorder traversal into two parts:
- The elements to the left of the root node in the postorder traversal represent the left subtree.
- The elements to the right of the root node in the postorder traversal represent the right subtree.
In this case, the postorder traversal can be divided as follows:
- Left subtree: 13, 31, 23, 50, 55, 54, 49.
- Right subtree: 57, 70, 58, 83, 100, 99, 80.
4. Recursively apply steps 1 to 3 to construct the left and right subtrees.
Using the above steps, we can construct the binary search tree as follows:
```
56
/ \
23 99
/ \ \
13 50 100
/ \ /
31 54 83
/ \
49 80
\
55
\
57
\
58
\
70
```
Based on the given information, this binary search tree can be called a "balanced binary search tree." A balanced binary search tree is a type of binary search tree where the height of the left and right subtrees of any node differs by at most one. In this case, the tree is balanced because the height difference between any two subtrees is at most one.