which traversal algorithm gives the sorted

Which traversal algorithm gives the sorted

In binary search trees, an inorder traversal algorithm gives the sorted sequence of values.
In inorder traversal, the algorithm traverses the binary search tree in a left-child-right order. Starting from the root node, the algorithm first visits the left subtree recursively until the leftmost leaf node is reached. Then it visits the current node, and finally, it recursively visits the right subtree until the rightmost leaf node is reached.

Since binary search trees follow the property of having all left child nodes smaller and all right child nodes larger than their parent node, the inorder traversal algorithm visits the nodes in ascending order of their values. Thus, the sequence obtained through an inorder traversal of a binary search tree is a sorted sequence.

Here's an example of an inorder traversal algorithm for a binary search tree in Python:

def inorder_traversal(root):

    if root is not None:

        inorder_traversal(root.left)

        print(root.val)

        inorder_traversal(root.right)

In this code, root is the root node of the binary search tree. The function recursively visits the left subtree, visits the current node, and then recursively visits the right subtree in an inorder manner. The values of the nodes are printed in the console as they are visited, producing a sorted sequence of values.

Another traversal algorithm that produces a sorted sequence is the depth-first search algorithm (DFS) using an inorder traversal strategy for traversing a graph.

In DFS, the algorithm explores as far as possible along each branch before backtracking. Using an inorder traversal strategy means visiting the left subtree, then the current node, and finally the right subtree. If the graph is a directed acyclic graph (DAG) or a tree, then the inorder traversal produces a sorted sequence of values.

Here's an example of an inorder traversal algorithm using DFS for a graph represented as an adjacency list in Python:

def inorder_traversal(graph, start, visited, output):

    visited[start] = True

    for neighbor in graph[start]:

        if not visited[neighbor]:

            inorder_traversal(graph, neighbor, visited, output)

    output.append(start)

In this code, graph is the adjacency list representation of the graph, start is the starting node for the traversal, visited is a boolean array that tracks the visited nodes, and output is a list that stores the visited nodes in the order they are visited. The function recursively visits the unvisited neighbors of the current node in an inorder manner, and appends the visited node to the output list after all its neighbors have been visited. The output list will contain the nodes in sorted order if the graph is a DAG or a tree.

It's important to note that the inorder traversal strategy only works for graphs that have a total order defined on their nodes. If the graph has cycles or there is no total order on the nodes, then an inorder traversal using DFS may not produce a sorted sequence. In such cases, other sorting algorithms or traversal strategies may be necessary.

here's an example of an inorder traversal algorithm using DFS for a binary tree in Java:

class TreeNode {

    int val;

    TreeNode left;

    TreeNode right;

    

    TreeNode(int val) {

        this.val = val;

        left = null;

        right = null;

    }

}

class BinaryTree {

    TreeNode root;

    void inorderTraversal() {

        if (root == null) {

            return;

        }

        

        Stack<TreeNode> stack = new Stack<>();

        TreeNode curr = root;

        

        while (curr != null || !stack.isEmpty()) {

            while (curr != null) {

                stack.push(curr);

                curr = curr.left;

            }

            

            curr = stack.pop();

            System.out.println(curr.val);

            

            curr = curr.right;

        }

    }

}

public class Main {

    public static void main(String[] args) {

        BinaryTree tree = new BinaryTree();

        tree.root = new TreeNode(5);

        tree.root.left = new TreeNode(3);

        tree.root.right = new TreeNode(7);

        tree.root.left.left = new TreeNode(1);

        tree.root.left.right = new TreeNode(4);

        tree.root.right.left = new TreeNode(6);

        tree.root.right.right = new TreeNode(8);

        

        tree.inorderTraversal();

    }

}

In this example, TreeNode represents a node in the binary tree, and BinaryTree represents the binary tree. The inorderTraversal method of BinaryTree performs an inorder traversal of the binary tree using an iterative approach and a stack to keep track of nodes. The traversal begins at the root node and continues down the left subtree until a leaf node is reached. The method then prints the value of the current node, pops the top node from the stack, and traverses the right subtree of the current node. This process continues until all nodes have been visited.