From e7ec541c715f591bbbeb5cf2a08ed78fa1529bc8 Mon Sep 17 00:00:00 2001
From: BEaANIKET <aniketchaturvedi309@gmail.com>
Date: Thu, 3 Oct 2024 20:17:52 +0530
Subject: [PATCH] Added Morris In-Order Traversal algorithm

---
 C++/morrisTraversal.cpp | 101 ++++++++++++++++++++++++++++++++++++++++
 1 file changed, 101 insertions(+)
 create mode 100644 C++/morrisTraversal.cpp

diff --git a/C++/morrisTraversal.cpp b/C++/morrisTraversal.cpp
new file mode 100644
index 00000000..6c26e4e3
--- /dev/null
+++ b/C++/morrisTraversal.cpp
@@ -0,0 +1,101 @@
+/*
+Problem statements:
+
+Implement Morris In-Order Traversal for a Binary Search Tree in C++. The traversal should be done without using recursion or a stack, ensuring O(1) space complexity.
+
+
+
+Time Complexity: O(n), where n is the number of nodes in the tree. Each node is visited twice (once to create a thread and once to remove it).
+
+Space Complexity: O(1), since no additional space (stack or recursion) is used apart from the tree itself.
+
+*/
+
+#include <iostream>
+using namespace std;
+
+// Definition of TreeNode
+struct TreeNode
+{
+    int val;
+    TreeNode *left;
+    TreeNode *right;
+
+    // Constructor to initialize node with a value
+    TreeNode(int x) : val(x), left(nullptr), right(nullptr) {}
+};
+
+// Function to perform Morris In-Order Traversal
+void morrisInOrderTraversal(TreeNode *root)
+{
+    TreeNode *current = root; // Initialize current node to the root of the tree
+
+    while (current != nullptr)
+    {
+        // Case 1: If current has no left child, visit this node and move to the right
+        if (current->left == nullptr)
+        {
+            cout << current->val << " "; // Print the current node's value
+            current = current->right;    // Move to the right subtree
+        }
+        // Case 2: If current has a left child, find the in-order predecessor
+        else
+        {
+            TreeNode *predecessor = current->left;
+
+            // Find the rightmost node in the left subtree (in-order predecessor)
+            while (predecessor->right != nullptr && predecessor->right != current)
+            {
+                predecessor = predecessor->right;
+            }
+
+            // Case 2a: If the predecessor's right child is null, establish a thread
+            if (predecessor->right == nullptr)
+            {
+                predecessor->right = current; // Create a temporary link (thread)
+                current = current->left;      // Move to the left subtree
+            }
+            // Case 2b: If the predecessor's right child is already current, remove the thread
+            else
+            {
+                predecessor->right = nullptr; // Remove the thread
+                cout << current->val << " ";  // Visit the current node
+                current = current->right;     // Move to the right subtree
+            }
+        }
+    }
+}
+
+// Helper function to create a new TreeNode
+TreeNode *createNode(int val)
+{
+    return new TreeNode(val);
+}
+
+// Main function to test the Morris In-Order Traversal
+int main()
+{
+    /* Construct the following Binary Search Tree (BST):
+                 4
+               /   \
+              2     6
+             / \   / \
+            1   3 5   7
+    */
+
+    TreeNode *root = createNode(4);
+    root->left = createNode(2);
+    root->right = createNode(6);
+    root->left->left = createNode(1);
+    root->left->right = createNode(3);
+    root->right->left = createNode(5);
+    root->right->right = createNode(7);
+
+    // Print the in-order traversal of the BST using Morris Traversal
+    cout << "In-Order Traversal of the BST using Morris Traversal: ";
+    morrisInOrderTraversal(root);
+    cout << endl;
+
+    return 0;
+}
+