Binary Search Trees (BSTs) are a popular data structure used in computer science and programming. They are efficient in searching, inserting, and deleting elements. One way to traverse a BST is through the Zig Zag Traversal method, which can be implemented in C++.
The Zig Zag Traversal method is a variation of the in-order traversal method. In-order traversal visits the left subtree, then the root, and finally the right subtree. The Zig Zag Traversal method, on the other hand, visits the nodes in a zig-zag pattern, alternating between the left and right subtrees.
To implement the Zig Zag Traversal method in C++, we first need to create a BST. A BST is a tree where each node has at most two children, the left child and the right child. The left child of a node is smaller than the node, and the right child of a node is greater than the node.
Here is an example of a C++ class for a BST node:
class Node { public: int data; Node* left; Node* right; Node(int data) { this->data = data; this->left = nullptr; this->right = nullptr; }
};
Once we have our BST class, we can implement the Zig Zag Traversal method. The first step is to use a stack to keep track of the nodes that need to be visited. We will use two stacks, one for the left subtree and one for the right subtree.
void zigzagTraversal(Node* root) { stack<Node*> leftStack; stack<Node*> rightStack; leftStack.push(root); while (!leftStack.empty() || !rightStack.empty()) { while (!leftStack.empty()) { Node* current = leftStack.top(); leftStack.pop(); cout << current->data << " "; if (current->left != nullptr) { rightStack.push(current->left); } if (current->right != nullptr) { rightStack.push(current->right); }
} while (!rightStack.empty()) { Node* current = rightStack.top(); rightStack.pop(); cout << current->data << " "; if (current->right != nullptr) { leftStack.push(current->right); } if (current->left != nullptr) { leftStack.push(current->left); }
}
}
}
In the above code, we start by pushing the root of the tree onto the leftStack. We then enter a while loop that continues as long as either the leftStack or the rightStack is not empty. Within the while loop, we first check if the leftStack is not empty. If it is not, we pop the top element off the stack and print its value. We then check if the popped node has a left and right child. If it does, we push these children onto the rightStack.
Once the leftStack is empty, we then check if the rightStack is not empty. If it is not, we pop the top element off the stack and print its value. We then check if the
popped node has a left and right child. If it does, we push these children onto the leftStack.
This process of alternating between the leftStack and rightStack continues until both stacks are empty, resulting in a zig-zag pattern of traversing the tree. This method can also be implemented using a queue instead of stacks, but using stacks allows for reversing the order of the traversal if needed.
It is important to note that the Zig Zag Traversal method does not have a specific order of visiting the nodes. It does not visit the nodes in increasing or decreasing order like the in-order or post-order traversal methods. Instead, it visits the nodes in a zig-zag pattern, alternating between the left and right subtrees.
In addition, the Zig Zag Traversal method can also be used for other types of trees, such as a binary tree. The same process of using two stacks and alternating between the left and right subtrees can be applied, but it will not maintain the sorted property of a BST.
Overall, the Zig Zag Traversal method is a useful variation of the in-order traversal method for traversing a BST in C++. It can be implemented using stacks or queues and can also be applied to other types of trees. It is important to keep in mind that the Zig Zag Traversal method does not have a specific order of visiting the nodes, and the sorted property of a BST is not maintained.
