In an improper binary tree, the minimum and maximum number of internal and external nodes can be determined based on the number of nodes (n) in the tree.

• An improper binary tree is a binary tree where a node can have any number of children (including zero, one, or two). In this case, the terms "internal node" and "external node" are used instead of "internal node" and "leaf node" in a proper binary tree.

Let's consider the minimum and maximum scenarios for an improper binary tree with n nodes:

Minimum Scenario: In the minimum scenario, the tree will be a linear tree, also known as a chain or linked list. Each node except the last one will have exactly one child.

• Minimum number of internal nodes: 0
• Minimum number of external nodes (leaves): n

Maximum Scenario: In the maximum scenario, the tree will be a completely balanced tree, where each internal node has two children (except possibly the last level). This is achieved when the tree is a complete binary tree.

• Maximum number of internal nodes: n - 1
• Maximum number of external nodes (leaves): 1

To summarize:

• Minimum number of internal nodes: 0 Maximum number of internal nodes: n - 1
• Minimum number of external nodes (leaves): n Maximum number of external nodes (leaves): 1

Please note that these values assume that the tree is non-empty (n > 0). If n = 0, the number of internal and external nodes would be 0.