feat(datastructures, binary-tree): connect all siblings

algorithms/graphs/alien_dictionary/test_alien_dictionary.py

@@ -73,5 +73,6 @@ def is_valid_alien_order(self, words: List[str], order: str) -> bool:
                     return False
         return True
 
+
 if __name__ == "__main__":
     unittest.main()

datastructures/trees/binary/README.md

@@ -65,3 +65,80 @@ entire height of the tree, including `h` steps.
 The space complexity of this solution is `O(1)` as there is no additional space being used. Only two pointers are being 
 maintained requiring constant space.
 
+---
+
+## Connect All Siblings of a Binary Tree
+
+Given the root of a perfect binary tree, where each node is equipped with an additional pointer, next, connect all nodes
+from left to right. Do so in such a way that the next pointer of each node points to its immediate right sibling except
+for the rightmost node, which points to the first node of the next level.
+
+The next pointer of the last node of the binary tree (i.e., the rightmost node of the last level) should be set to NULL.
+
+> A binary tree in which all the levels are completely filled with nodes, and all leaf nodes (nodes with no children)
+> are at the same level.
+
+### Constraints
+
+- The number of nodes in the tree is in the range [0,500].
+- 1000 <= `node.data` <= 1000
+
+### Examples
+
+![Example 1](./images/examples/connect_all_siblings_of_binary_tree_example_1.png)
+![Example 2](./images/examples/connect_all_siblings_of_binary_tree_example_2.png)
+
+### Solution
+
+The algorithm connects all nodes by utilizing the structure of the perfect binary tree, where each non-leaf node has
+exactly two children. Using this property, the algorithm connects nodes without needing extra space. It uses two pointers:
+one to traverse the current level and another to connect nodes at the next level. Starting from the root, the algorithm
+links each node’s left child to its right child and then connects the right child to the next node’s left child on the
+same level, continuing this process across all nodes at that level. If no adjacent node is on the same level, the right
+child’s next pointer is connected to the first node on the next lower level. This process continues until all nodes are
+connected in a manner that reflects level-order traversal.
+
+The steps of the algorithm are given below:
+
+1. If the root is None, the tree is empty. In this case, return immediately.
+2. Initialize two pointers current and last to the root node. The current pointer traverses the nodes level by level,
+   while the last keeps track of the last node connected via the next pointer.
+3. The loop continues as long as current.left exists. In a perfect binary tree, all non-leaf nodes have a left child,
+   so this condition ensures that the loop continues until all levels are processed.
+   - First connection: last.next = current.left connects the last node (initially the root) to the current.left child.
+     After this, last is updated to current.left.
+   - Second connection: last.next = current.right connects current.left (now pointed to by last) to current.right. last
+     is then updated to current.right.
+   - Move to the next node: current = current.next moves the current pointer to the next node.
+4. Finally, return the modified root of the tree, where all nodes are connected to their next sibling in the level-order
+   traversal.
+
+Let’s look at the following illustration(s) to get a better understanding of the solution:
+
+![Solution 1](./images/solutions/connect_all_siblings_of_binary_tree_solution_1.png)
+![Solution 2](./images/solutions/connect_all_siblings_of_binary_tree_solution_2.png)
+![Solution 3](./images/solutions/connect_all_siblings_of_binary_tree_solution_3.png)
+![Solution 4](./images/solutions/connect_all_siblings_of_binary_tree_solution_4.png)
+![Solution 5](./images/solutions/connect_all_siblings_of_binary_tree_solution_5.png)
+![Solution 6](./images/solutions/connect_all_siblings_of_binary_tree_solution_6.png)
+![Solution 7](./images/solutions/connect_all_siblings_of_binary_tree_solution_7.png)
+![Solution 8](./images/solutions/connect_all_siblings_of_binary_tree_solution_8.png)
+![Solution 9](./images/solutions/connect_all_siblings_of_binary_tree_solution_9.png)
+![Solution 10](./images/solutions/connect_all_siblings_of_binary_tree_solution_10.png)
+![Solution 11](./images/solutions/connect_all_siblings_of_binary_tree_solution_11.png)
+![Solution 12](./images/solutions/connect_all_siblings_of_binary_tree_solution_12.png)
+![Solution 13](./images/solutions/connect_all_siblings_of_binary_tree_solution_13.png)
+![Solution 14](./images/solutions/connect_all_siblings_of_binary_tree_solution_14.png)
+![Solution 15](./images/solutions/connect_all_siblings_of_binary_tree_solution_15.png)
+![Solution 16](./images/solutions/connect_all_siblings_of_binary_tree_solution_16.png)
+![Solution 17](./images/solutions/connect_all_siblings_of_binary_tree_solution_17.png)
+
+#### Time Complexity
+
+The time complexity of the solution is O(N), where N is the number of nodes in the binary tree. The algorithm traverses
+each node exactly once, connecting the left and right children as it moves through the tree.
+
+#### Space Complexity
+
+The space complexity of the solution is O(1) because the algorithm uses only a constant amount of extra space,
+specifically the pointers current and last, regardless of the size of the tree.

datastructures/trees/binary/node.py

@@ -17,6 +17,7 @@ def __init__(
         right: Optional["BinaryTreeNode"] = None,
         key: Optional[Any] = None,
         parent: Optional["BinaryTreeNode"] = None,
+        next: Optional["BinaryTreeNode"] = None,
     ) -> None:
         """
         Constructor for BinaryTreeNode class. This will create a new node with the provided data and optional
@@ -29,10 +30,19 @@ def __init__(
             right (Optional[BinaryTreeNode]): Right child of the node
             key (Optional[Any]): Key for the node, if not provided a hash of the data is used
             parent (Optional[BinaryTreeNode]): Parent of the node
+            next (Optional[BinaryTreeNode]): Next child of the node which is the sibling of the node. The sibling is the
+            node on the same level as this node. If this is the rightmost node in the tree that is not on the last level
+            of the tree, then this is the next node on the next level starting from the left. If this is the last node
+            in the tree, then this is None.
         """
         super().__init__(data, key, parent)
         self.left: Optional[BinaryTreeNode] = left
         self.right: Optional[BinaryTreeNode] = right
+        # Next is a pointer that connects this node to it's right sibling in the tree. If this node is the right most
+        # node on a given level, then it is connected to the first node on the next level. If this node is the last node
+        # in the tree on the last node, then it is pointed to None. By default, it is set to None.
+        # Note that if this is the root node, it is connected to the left most node on the next level.
+        self.next: Optional[BinaryTreeNode] = next
 
     def insert_node(self, data: T) -> None:
         """
@@ -181,7 +191,7 @@ def height(self) -> int:
         pass
 
     def __repr__(self):
-        return f"BinaryTreeNode(data={self.data}, key={self.key}, left={self.left}, right={self.right})"
+        return f"BinaryTreeNode(data={self.data}, key={self.key}, left={self.left}, right={self.right}, parent={self.parent}, next={self.next})"
 
     def __eq__(self, other: "BinaryTreeNode") -> bool:
         """Checks if this node is equal to another node based on the data they contain
@@ -193,7 +203,11 @@ def __eq__(self, other: "BinaryTreeNode") -> bool:
         if other is None:
             return False
 
-        if other.data == self.data:
+        if (
+            other.data == self.data
+            and self.left == other.left
+            and self.right == other.right
+        ):
             return True
 
         return False

datastructures/trees/binary/test_utils.py

@@ -1,7 +1,10 @@
 import unittest
+from parameterized import parameterized
 from datastructures.trees.binary.utils import (
     lowest_common_ancestor,
     lowest_common_ancestor_ptr,
+    connect_all_siblings,
+    connect_all_siblings_ptr,
 )
 from datastructures.trees.binary.node import BinaryTreeNode
 
@@ -182,5 +185,60 @@ def test_4(self):
         self.assertEqual(expected, actual)
 
 
+CONNECT_ALL_SIBLINGS_TEST_CASES = [
+    (
+        BinaryTreeNode(
+            data=100,
+            left=BinaryTreeNode(
+                data=50, left=BinaryTreeNode(data=25), right=BinaryTreeNode(data=75)
+            ),
+            right=BinaryTreeNode(
+                data=200, left=BinaryTreeNode(data=300), right=BinaryTreeNode(data=10)
+            ),
+        ),
+        BinaryTreeNode(
+            data=100,
+            left=BinaryTreeNode(
+                data=50, left=BinaryTreeNode(data=25), right=BinaryTreeNode(data=75)
+            ),
+            right=BinaryTreeNode(
+                data=200, left=BinaryTreeNode(data=300), right=BinaryTreeNode(data=10)
+            ),
+            next=BinaryTreeNode(
+                data=50,
+                left=BinaryTreeNode(data=300),
+                right=BinaryTreeNode(data=10),
+                next=BinaryTreeNode(
+                    data=200,
+                    left=BinaryTreeNode(data=300),
+                    right=BinaryTreeNode(data=10),
+                    next=BinaryTreeNode(
+                        data=25,
+                        next=BinaryTreeNode(
+                            data=75,
+                            next=BinaryTreeNode(data=300, next=BinaryTreeNode(data=10)),
+                        ),
+                    ),
+                ),
+            ),
+        ),
+    ),
+]
+
+
+class ConnectAllSiblingsTestCase(unittest.TestCase):
+    @parameterized.expand(CONNECT_ALL_SIBLINGS_TEST_CASES)
+    def test_connect_all_siblings(self, root: BinaryTreeNode, expected: BinaryTreeNode):
+        actual = connect_all_siblings(root)
+        self.assertEqual(expected, actual)
+
+    @parameterized.expand(CONNECT_ALL_SIBLINGS_TEST_CASES)
+    def test_connect_all_siblings_ptr(
+        self, root: BinaryTreeNode, expected: BinaryTreeNode
+    ):
+        actual = connect_all_siblings_ptr(root)
+        self.assertEqual(expected, actual)
+
+
 if __name__ == "__main__":
     unittest.main()

datastructures/trees/binary/tree/binary_tree.py

@@ -86,10 +86,10 @@ def level_order_traversal(self) -> List[Any]:
             return []
 
         current_level: List[BinaryTreeNode] = [self.root]
-        levels: List[List[T]] = []
+        levels: List[List[Any]] = []
 
         while current_level:
-            level: List[T] = []
+            level: List[Any] = []
             next_level: List[BinaryTreeNode] = []
 
             for node in current_level:

datastructures/trees/binary/utils.py

@@ -1,3 +1,5 @@
+from typing import Optional, Deque, List
+from collections import deque
 from datastructures.trees.binary.node import BinaryTreeNode
 
 
@@ -67,3 +69,96 @@ def lowest_common_ancestor_ptr(
         ptr2 = ptr2.parent if ptr2.parent else node_one
 
     return ptr1
+
+
+def connect_all_siblings(root: BinaryTreeNode) -> Optional[BinaryTreeNode]:
+    """
+    Connects all siblings of a binary tree given the root, such that, the right most node is connected to the first node
+    on the next level using a 'next' pointer forming a kind of linked list data structure. The right most node on the
+    last level is set to None. On each level the nodes are pointed to each other via the next pointer
+    This assumes that the provided root is part of a perfect binary tree.
+
+    This uses a level order traversal utilizing a queue to traverse the nodes from the first level to the last level
+    adding the nodes to a list for further traversal. The levels list is then traversed connecting nodes to the next
+    node in the list via the next pointer. At this point the levels list will have the nodes in the correct order using
+    the level order traversal technique.
+
+    After the traversal, the root node will be the first element in the levels list and we simply return that which
+    will contain the modified tree with all siblings connected
+
+    This uses Space of O(n) as the levels list is required to handle the final iteration for the connections.
+    Time complexity is O(n) as we travers all the nodes in the tree.
+
+    Args:
+        root(BinaryTreeNode): root of a perfect binary tree
+    Returns:
+        BinaryTreeNode root such that the next pointer has been set to point to siblings
+    """
+    if not root:
+        return root
+
+    # Queue will have the root node initially
+    queue: Deque[BinaryTreeNode] = deque([root])
+    levels: List[BinaryTreeNode] = [root]
+
+    while queue:
+        node = queue.popleft()
+        if node.left:
+            queue.append(node.left)
+            levels.append(node.left)
+        if node.right:
+            queue.append(node.right)
+            levels.append(node.right)
+
+    for idx in range(len(levels) - 1):
+        levels[idx].next = levels[idx + 1]
+
+    return levels[0]
+
+
+def connect_all_siblings_ptr(
+    root: Optional[BinaryTreeNode],
+) -> Optional[BinaryTreeNode]:
+    """
+    Connects all siblings of a binary tree given the root, such that, the right most node is connected to the first node
+    on the next level using a 'next' pointer forming a kind of linked list data structure. The right most node on the
+    last level is set to None. On each level the nodes are pointed to each other via the next pointer
+    This assumes that the provided root is part of a perfect binary tree.
+
+    This performs a level order traversal using two pointers to traverse the tree utilizing constant space in the process
+    making it efficient in terms of space. However, this incurs a time complexity of O(n) as all the nodes in the tree
+     have to be traversed from the root to make the connections
+
+    Args:
+        root(BinaryTreeNode): root of a perfect binary tree
+    Returns:
+        BinaryTreeNode root such that the next pointer has been set to point to siblings
+
+    """
+    # If the tree is empty, there's nothing to connect
+    if root is None:
+        return root
+
+    # Initialize two pointers:
+    # 'current' points to the current node being processed
+    # 'last' keeps track of the last node that was connected
+    current = root
+    last = root
+
+    # Loop continues until there are no more left children in the current level
+    while current.left:
+        # Connect the last node's 'next' to the current node's left child
+        last.next = current.left
+        # Update 'last' to point to this left child
+        last = last.next
+
+        # Connect the last node's 'next' to the current node's right child
+        last.next = current.right
+        # Update 'last' to point to this right child
+        last = last.next
+
+        # Move 'current' to the next node at the same level
+        current = current.next
+
+    # Return the root of the modified tree
+    return root