Question

Write the following method in the class BinaryTree

1) int numberOfLeaves()
The method returns the number of leaves in the tree

Answer 1

The method `numberOfLeaves` in a `BinaryTree` class counts the tree leaves by recursively traversing the tree and checking for nodes that have no children. A working example of this method was demonstrated using the Java programming language.

Step-by-step explanation:

Implementing the numberOfLeaves Method

To write a method numberOfLeaves in a BinaryTree class, you would perform a recursive traversal of the tree, counting the leaves as you go. A leaf is defined as a node that has no children (neither left child nor right child).

Example in Java:

Assuming the class BinaryTree has a nested node class Node with left and right children, here's how you might implement numberOfLeaves:

class BinaryTree {

class Node {
Node left;
Node right;
// additional fields like value, etc.
}

Node root;

public int numberOfLeaves() {
return countLeaves(root);
}

private int countLeaves(Node node) {
if (node == null) {
// No node means no leaf
return 0;
} else if (node.left == null && node.right == null) {
// No children means this is a leaf
return 1;
} else {
// Recursively count the leaves in both subtrees and sum them
return countLeaves(node.left) + countLeaves(node.right);
}
}
}

This is a typical depth-first approach to count the leaves.