From 6f688cd87e65e95071bb0021c15fd895091a9843 Mon Sep 17 00:00:00 2001
From: FamALouiz <fam@awadlouis.com>
Date: Fri, 14 Mar 2025 20:35:44 +0100
Subject: [PATCH 1/8] Added parent pointer tree node for python backend

---
 pydatastructs/utils/__init__.py  |  1 +
 pydatastructs/utils/misc_util.py | 34 ++++++++++++++++++++++++++++++++
 2 files changed, 35 insertions(+)

diff --git a/pydatastructs/utils/__init__.py b/pydatastructs/utils/__init__.py
index 20a8c750c..7ea5689dd 100644
--- a/pydatastructs/utils/__init__.py
+++ b/pydatastructs/utils/__init__.py
@@ -13,6 +13,7 @@
     BinomialTreeNode,
     AdjacencyListGraphNode,
     AdjacencyMatrixGraphNode,
+    ParentPointerTreeNode,
     GraphEdge,
     Set,
     CartesianTreeNode,
diff --git a/pydatastructs/utils/misc_util.py b/pydatastructs/utils/misc_util.py
index 4c7ca7faa..1cc43811b 100644
--- a/pydatastructs/utils/misc_util.py
+++ b/pydatastructs/utils/misc_util.py
@@ -13,6 +13,7 @@
     'Set',
     'CartesianTreeNode',
     'RedBlackTreeNode',
+    'ParentPointerTreeNode',
     'TrieNode',
     'SkipNode',
     'minimum',
@@ -275,6 +276,39 @@ def add_children(self, *children):
     def __str__(self):
         return str((self.key, self.data))
 
+class ParentPointerTreeNode(TreeNode):
+    """
+    Represents node in trees with parent pointers.
+
+    Parameters
+    ==========
+
+    key
+        Required for comparison operations.
+    data
+        Any valid data to be stored in the node.
+    parent
+        Reference to the parent node.
+    backend: pydatastructs.Backend
+        The backend to be used.
+        Optional, by default, the best available
+        backend is used.
+    """
+    __slots__ = ['key', 'data', 'parent']
+
+    @classmethod
+    def methods(cls):
+        return ['__new__', '__str__']
+
+    def __new__(cls, key, data=None, parent=None, **kwargs):
+        raise_if_backend_is_not_python(
+            cls, kwargs.get('backend', Backend.PYTHON))
+        obj = Node.__new__(cls)
+        obj.data, obj.key, obj.parent = data, key, parent
+        return obj
+
+    def __str__(self):
+        return str((self.key, self.data))
 
 class LinkedListNode(Node):
     """

From 9563a44280d399880b559bd3da23eb4d6717cdf7 Mon Sep 17 00:00:00 2001
From: FamALouiz <fam@awadlouis.com>
Date: Wed, 19 Mar 2025 12:25:01 +0100
Subject: [PATCH 2/8] Added basic skeleton for parent pointer tree

---
 pydatastructs/trees/m_ary_trees.py | 154 ++++++++++++++++++++++++++++-
 pydatastructs/utils/misc_util.py   |   2 +-
 2 files changed, 154 insertions(+), 2 deletions(-)

diff --git a/pydatastructs/trees/m_ary_trees.py b/pydatastructs/trees/m_ary_trees.py
index a06fda9ee..4382282af 100644
--- a/pydatastructs/trees/m_ary_trees.py
+++ b/pydatastructs/trees/m_ary_trees.py
@@ -1,4 +1,4 @@
-from pydatastructs.utils import MAryTreeNode
+from pydatastructs.utils import MAryTreeNode, ParentPointerTreeNode
 from pydatastructs.linear_data_structures.arrays import ArrayForTrees
 from pydatastructs.utils.misc_util import (
     Backend, raise_if_backend_is_not_python)
@@ -170,3 +170,155 @@ def __str__(self):
                     if j is not None:
                         to_be_printed[i].append(j)
         return str(to_be_printed)
+
+class ParentPointerTree(object):
+    """
+    Implements a tree with parent pointers.
+
+    Parameters
+    ==========
+
+    key
+        Required if tree is to be instantiated with
+        root otherwise not needed.
+    root_data
+        Optional, the root node of the tree.
+        If not of type TreeNode, it will consider
+        root as data and a new root node will
+        be created.
+    comp: lambda
+        Optional, A lambda function which will be used
+        for comparison of keys. Should return a
+        bool value. By default it implements less
+        than operator.
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Tree_(data_structure)#Parent_pointer_tree
+    """
+
+    __slots__ = ['root_idx', 'comparator', 'tree', 'size']
+
+    def __new__(cls, key=None, root_data=None, comp=None, **kwargs):
+        raise_if_backend_is_not_python(
+            cls, kwargs.get('backend', Backend.PYTHON))
+        obj = object.__new__(cls)
+        if key is None and root_data is not None:
+            raise ValueError('Key required.')
+        key = None if root_data is None else key
+        root = ParentPointerTreeNode(key, root_data)
+        root.is_root = True
+        obj.root_idx = 0
+        obj.tree, obj.size = ArrayForTrees(ParentPointerTreeNode, [root]), 1
+        obj.comparator = lambda key1, key2: key1 < key2 \
+            if comp is None else comp
+
+        return obj
+
+    @classmethod
+    def methods(cls):
+        return ['__new__', '__str__']
+
+    def insert(self, parent_key, key, data=None):
+        """
+        Inserts data by the passed key using iterative
+        algorithm.
+
+        Parameters
+        ==========
+
+        key
+            The key for comparison.
+        data
+            The data to be inserted.
+
+        Returns
+        =======
+
+        None
+        """
+        if parent_key is None:
+            raise ValueError("Parent key is required.")
+        if key is None:
+            raise ValueError("Key is required.")
+        if self.search(key) is not None:
+            raise ValueError("Key already exists.")
+        
+        parent_node = self.search(parent_key, parent=True)
+        new_node = ParentPointerTreeNode(key, data, parent_node)
+                
+        self.tree.append(new_node)
+        self.size += 1
+
+    def delete(self, key):
+        """
+        Deletes the data with the passed key
+        using iterative algorithm.
+
+        Parameters
+        ==========
+
+        key
+            The key of the node which is
+            to be deleted.
+
+        Returns
+        =======
+
+        True
+            If the node is deleted successfully.
+
+        None
+            If the node to be deleted doesn't exists.
+
+        Note
+        ====
+
+        The node is deleted means that the connection to that
+        node are removed but the it is still in tree.
+        """
+        for idx in range(self.size): 
+            if self.tree[idx].key == key:
+                self.tree.delete(idx)
+                return True
+            
+        return None
+
+    def search(self, key, **kwargs):
+        """
+        Searches for the data in the tree
+        using iterative algorithm.
+
+        Parameters
+        ==========
+
+        key
+            The key for searching.
+        parent: bool
+            If true then returns index of the
+            parent of the node with the passed
+            key.
+            By default, False
+
+        Returns
+        =======
+
+        int
+            If the node with the passed key is
+            in the tree.
+        tuple
+            The index of the searched node and
+            the index of the parent of that node.
+        None
+            In all other cases.
+        """
+        
+
+    def __str__(self):
+        to_be_printed = ['' for i in range(self.tree._last_pos_filled + 1)]
+        for i in range(self.tree._last_pos_filled + 1):
+            if self.tree[i] is not None:
+                node = self.tree[i]
+                to_be_printed[i] = (node.key, node.data, node.parent)
+        return str(to_be_printed)
diff --git a/pydatastructs/utils/misc_util.py b/pydatastructs/utils/misc_util.py
index 1cc43811b..81aae1d3c 100644
--- a/pydatastructs/utils/misc_util.py
+++ b/pydatastructs/utils/misc_util.py
@@ -300,7 +300,7 @@ class ParentPointerTreeNode(TreeNode):
     def methods(cls):
         return ['__new__', '__str__']
 
-    def __new__(cls, key, data=None, parent=None, **kwargs):
+    def __new__(cls, key, data=None, parent: 'ParentPointerTreeNode' = None, **kwargs):
         raise_if_backend_is_not_python(
             cls, kwargs.get('backend', Backend.PYTHON))
         obj = Node.__new__(cls)

From 7c731fd8e6bb61cb4661ca072bb2f7a2cf90d4a4 Mon Sep 17 00:00:00 2001
From: FamALouiz <fam@awadlouis.com>
Date: Wed, 19 Mar 2025 15:37:04 +0100
Subject: [PATCH 3/8] Immplemented search and least common ancestor of parent
 pointer tree

---
 pydatastructs/trees/m_ary_trees.py | 65 ++++++++++++++++++++++++++----
 1 file changed, 58 insertions(+), 7 deletions(-)

diff --git a/pydatastructs/trees/m_ary_trees.py b/pydatastructs/trees/m_ary_trees.py
index 4382282af..de0b92c4e 100644
--- a/pydatastructs/trees/m_ary_trees.py
+++ b/pydatastructs/trees/m_ary_trees.py
@@ -171,7 +171,7 @@ def __str__(self):
                         to_be_printed[i].append(j)
         return str(to_be_printed)
 
-class ParentPointerTree(object):
+class ParentPointerTree(MAryTree):
     """
     Implements a tree with parent pointers.
 
@@ -296,7 +296,7 @@ def search(self, key, **kwargs):
         key
             The key for searching.
         parent: bool
-            If true then returns index of the
+            If true then returns node of the
             parent of the node with the passed
             key.
             By default, False
@@ -304,17 +304,68 @@ def search(self, key, **kwargs):
         Returns
         =======
 
-        int
-            If the node with the passed key is
+        ParentPointerTreeNode
+            The tree node if it was found
             in the tree.
-        tuple
-            The index of the searched node and
-            the index of the parent of that node.
         None
             In all other cases.
         """
+        parent = kwargs.get('parent', False)
+
+        for idx in range(self.size):
+            node = self.tree[idx]
+            if node is not None and node.key == key:
+                if parent:
+                    return node.parent
+                return node
+
+        return None
         
 
+    def least_common_ancestor(self, first_child_key, second_child_key):
+        """
+        Finds the least common ancestor of two nodes in 
+        the tree.
+
+        Parameters
+        ==========
+
+        first_child_key
+            The key of the first child node.
+        second_child_key
+            The key of the second child node.
+
+        Returns
+        =======
+
+        ParentPointerTreeNode
+            The least common ancestor node.
+        None
+            If either of the nodes doesn't exist in the tree.
+        """
+        first_node_idx = self.search(first_child_key)
+        second_node_idx = self.search(second_child_key)
+
+        # One or both nodes do not exist
+        if first_node_idx is None or second_node_idx is None:
+            return None  
+
+        first_node = self.tree[first_node_idx]
+        second_node = self.tree[second_node_idx]
+        
+        first_ancestors = set()
+
+        while first_node is not None:
+            first_ancestors.add(first_node)
+            first_node = first_node.parent
+
+        while second_node is not None:
+            if second_node in first_ancestors:
+                return second_node  # Found the least common ancestor
+            second_node = second_node.parent
+
+        return None  # No common ancestor found
+
     def __str__(self):
         to_be_printed = ['' for i in range(self.tree._last_pos_filled + 1)]
         for i in range(self.tree._last_pos_filled + 1):

From baaa06da58b75f0d9a6b1b13b08fe7c4100f38a3 Mon Sep 17 00:00:00 2001
From: FamALouiz <fam@awadlouis.com>
Date: Wed, 19 Mar 2025 15:40:15 +0100
Subject: [PATCH 4/8] Added parent pointer tree skeleton tests

---
 pydatastructs/trees/tests/test_m_ary_trees.py | 4 ++++
 1 file changed, 4 insertions(+)

diff --git a/pydatastructs/trees/tests/test_m_ary_trees.py b/pydatastructs/trees/tests/test_m_ary_trees.py
index 6cbc84ace..b289a7ead 100644
--- a/pydatastructs/trees/tests/test_m_ary_trees.py
+++ b/pydatastructs/trees/tests/test_m_ary_trees.py
@@ -1,5 +1,9 @@
 from pydatastructs import MAryTree
+from pydatastructs.trees.m_ary_trees import ParentPointerTree
 
 def test_MAryTree():
     m = MAryTree(1, 1)
     assert str(m) == '[(1, 1)]'
+
+def test_ParentPointerTree(): 
+    pass
\ No newline at end of file

From 77b7a362b00a75c42e9247c4798866544ebee2e9 Mon Sep 17 00:00:00 2001
From: FamALouiz <fam@awadlouis.com>
Date: Wed, 19 Mar 2025 19:19:02 +0100
Subject: [PATCH 5/8] Added parent pointer tree tests

---
 pydatastructs/trees/tests/test_m_ary_trees.py | 68 +++++++++++++++++--
 1 file changed, 64 insertions(+), 4 deletions(-)

diff --git a/pydatastructs/trees/tests/test_m_ary_trees.py b/pydatastructs/trees/tests/test_m_ary_trees.py
index b289a7ead..a85f45f26 100644
--- a/pydatastructs/trees/tests/test_m_ary_trees.py
+++ b/pydatastructs/trees/tests/test_m_ary_trees.py
@@ -1,9 +1,69 @@
-from pydatastructs import MAryTree
-from pydatastructs.trees.m_ary_trees import ParentPointerTree
+from pydatastructs.utils.misc_util import Backend
+from pydatastructs.trees.m_ary_trees import MAryTree, ParentPointerTree
+
 
 def test_MAryTree():
     m = MAryTree(1, 1)
     assert str(m) == '[(1, 1)]'
 
-def test_ParentPointerTree(): 
-    pass
\ No newline at end of file
+
+def _test_ParentPointerTree(backend):
+    PPT = ParentPointerTree
+
+    tree = PPT(1, "root", backend=backend)
+    assert tree.root_idx == 0
+    assert tree.tree[0].key == 1
+    assert tree.tree[0].data == "root"
+    assert tree.tree[0].parent is None
+
+    tree.insert(1, 2, "child_1")
+    tree.insert(1, 3, "child_2")
+    tree.insert(1, 4, "child_3")
+    assert tree.size == 4
+    assert tree.tree[1].key == 2
+    assert tree.tree[1].data == "child_1"
+    assert tree.tree[1].parent == tree.tree[0]
+    assert tree.tree[2].key == 3
+    assert tree.tree[2].data == "child_2"
+    assert tree.tree[2].parent == tree.tree[0]
+    assert tree.tree[3].key == 4
+    assert tree.tree[3].data == "child_3"
+    assert tree.tree[3].parent == tree.tree[0]
+
+    assert tree.search(2).data == "child_1"
+    assert tree.search(3).data == "child_2"
+    assert tree.search(4).data == "child_3"
+    assert tree.search(5) is None
+    assert tree.search(2, parent=True) == tree.tree[0]
+
+    tree.insert(2, 5, "child_4")
+    tree.insert(2, 6, "child_5")
+    assert tree.least_common_ancestor(5, 6) == tree.tree[1]
+    assert tree.least_common_ancestor(5, 3) == tree.tree[0]
+    assert tree.least_common_ancestor(2, 4) == tree.tree[0]
+    assert tree.least_common_ancestor(5, 7) is None
+
+    assert tree.delete(5) is True
+    assert tree.search(5) is None
+    assert tree.size == 5
+    assert tree.delete(6) is True
+    assert tree.search(6) is None
+    assert tree.size == 4
+    assert tree.delete(10) is None
+
+    expected = '''[(1, 'root', 'None'), (2, 'child_1', "(1, 'root')"), (3, 'child_2', "(1, 'root')"), (4, 'child_3', "(1, 'root')")]'''
+    assert str(tree) == expected
+
+    empty_tree = PPT(backend=backend)
+    assert empty_tree.size == 0
+    assert empty_tree.search(1) is None
+    assert empty_tree.delete(1) is None
+    assert empty_tree.least_common_ancestor(1, 2) is None
+
+    empty_tree.insert(None, 7, "child_6")
+
+    expected = '''[(7, 'child_6', 'None')]'''
+    assert str(empty_tree) == expected
+
+def test_ParentPointerTree():
+    _test_ParentPointerTree(Backend.PYTHON)

From 1bb35f02936c923efdc40475d5214251a7243724 Mon Sep 17 00:00:00 2001
From: FamALouiz <fam@awadlouis.com>
Date: Wed, 19 Mar 2025 19:19:26 +0100
Subject: [PATCH 6/8] Fixed bugs with parent pointer tree insert and search
 functions

---
 pydatastructs/trees/m_ary_trees.py | 65 +++++++++++++++++++-----------
 1 file changed, 41 insertions(+), 24 deletions(-)

diff --git a/pydatastructs/trees/m_ary_trees.py b/pydatastructs/trees/m_ary_trees.py
index de0b92c4e..b9ac3b20e 100644
--- a/pydatastructs/trees/m_ary_trees.py
+++ b/pydatastructs/trees/m_ary_trees.py
@@ -204,9 +204,15 @@ def __new__(cls, key=None, root_data=None, comp=None, **kwargs):
         raise_if_backend_is_not_python(
             cls, kwargs.get('backend', Backend.PYTHON))
         obj = object.__new__(cls)
-        if key is None and root_data is not None:
-            raise ValueError('Key required.')
-        key = None if root_data is None else key
+
+        # Empty tree
+        if key is None:
+            obj.root_idx = None
+            obj.tree, obj.size = ArrayForTrees(ParentPointerTreeNode, []), 0
+            obj.comparator = lambda key1, key2: key1 < key2 \
+                if comp is None else comp
+            return obj
+
         root = ParentPointerTreeNode(key, root_data)
         root.is_root = True
         obj.root_idx = 0
@@ -238,16 +244,29 @@ def insert(self, parent_key, key, data=None):
 
         None
         """
-        if parent_key is None:
-            raise ValueError("Parent key is required.")
         if key is None:
             raise ValueError("Key is required.")
+
+        # Empty tree
+        if self.size == 0:
+            if parent_key is not None:
+                raise ValueError("Parent key should be None.")
+
+            root = ParentPointerTreeNode(key, data)
+            root.is_root = True
+            self.tree.append(root)
+            self.size += 1
+            return
+
+        if parent_key is None:
+            raise ValueError("Parent key is required.")
+
         if self.search(key) is not None:
             raise ValueError("Key already exists.")
-        
-        parent_node = self.search(parent_key, parent=True)
+
+        parent_node = self.search(parent_key)
         new_node = ParentPointerTreeNode(key, data, parent_node)
-                
+
         self.tree.append(new_node)
         self.size += 1
 
@@ -278,11 +297,12 @@ def delete(self, key):
         The node is deleted means that the connection to that
         node are removed but the it is still in tree.
         """
-        for idx in range(self.size): 
-            if self.tree[idx].key == key:
+        for idx in range(self.tree._last_pos_filled + 1):
+            if self.tree[idx] and self.tree[idx].key == key:
                 self.tree.delete(idx)
+                self.size -= 1
                 return True
-            
+
         return None
 
     def search(self, key, **kwargs):
@@ -295,7 +315,7 @@ def search(self, key, **kwargs):
 
         key
             The key for searching.
-        parent: bool
+        get_parent: bool
             If true then returns node of the
             parent of the node with the passed
             key.
@@ -312,7 +332,7 @@ def search(self, key, **kwargs):
         """
         parent = kwargs.get('parent', False)
 
-        for idx in range(self.size):
+        for idx in range(self.tree._last_pos_filled + 1):
             node = self.tree[idx]
             if node is not None and node.key == key:
                 if parent:
@@ -320,11 +340,11 @@ def search(self, key, **kwargs):
                 return node
 
         return None
-        
+
 
     def least_common_ancestor(self, first_child_key, second_child_key):
         """
-        Finds the least common ancestor of two nodes in 
+        Finds the least common ancestor of two nodes in
         the tree.
 
         Parameters
@@ -343,16 +363,13 @@ def least_common_ancestor(self, first_child_key, second_child_key):
         None
             If either of the nodes doesn't exist in the tree.
         """
-        first_node_idx = self.search(first_child_key)
-        second_node_idx = self.search(second_child_key)
+        first_node = self.search(first_child_key)
+        second_node = self.search(second_child_key)
 
         # One or both nodes do not exist
-        if first_node_idx is None or second_node_idx is None:
-            return None  
+        if first_node is None or second_node is None:
+            return None
 
-        first_node = self.tree[first_node_idx]
-        second_node = self.tree[second_node_idx]
-        
         first_ancestors = set()
 
         while first_node is not None:
@@ -367,9 +384,9 @@ def least_common_ancestor(self, first_child_key, second_child_key):
         return None  # No common ancestor found
 
     def __str__(self):
-        to_be_printed = ['' for i in range(self.tree._last_pos_filled + 1)]
+        to_be_printed = []
         for i in range(self.tree._last_pos_filled + 1):
             if self.tree[i] is not None:
                 node = self.tree[i]
-                to_be_printed[i] = (node.key, node.data, node.parent)
+                to_be_printed.append((node.key, node.data, str(node.parent)))
         return str(to_be_printed)

From 19c09202bc09ba9fea6d720f5020790f4e37dbcc Mon Sep 17 00:00:00 2001
From: FamALouiz <fam@awadlouis.com>
Date: Thu, 20 Mar 2025 11:33:59 +0100
Subject: [PATCH 7/8] Added parent pointer tree to trees subpackage

---
 pydatastructs/trees/__init__.py    | 4 +++-
 pydatastructs/trees/m_ary_trees.py | 3 ++-
 2 files changed, 5 insertions(+), 2 deletions(-)

diff --git a/pydatastructs/trees/__init__.py b/pydatastructs/trees/__init__.py
index 1c99cca25..2eaf1100d 100644
--- a/pydatastructs/trees/__init__.py
+++ b/pydatastructs/trees/__init__.py
@@ -22,7 +22,9 @@
 __all__.extend(binary_trees.__all__)
 
 from .m_ary_trees import (
-    MAryTreeNode, MAryTree
+    MAryTreeNode,
+    MAryTree,
+    ParentPointerTree
 )
 
 __all__.extend(m_ary_trees.__all__)
diff --git a/pydatastructs/trees/m_ary_trees.py b/pydatastructs/trees/m_ary_trees.py
index b9ac3b20e..17ee71005 100644
--- a/pydatastructs/trees/m_ary_trees.py
+++ b/pydatastructs/trees/m_ary_trees.py
@@ -4,7 +4,8 @@
     Backend, raise_if_backend_is_not_python)
 
 __all__ = [
-    'MAryTree'
+    'MAryTree',
+    'ParentPointerTree'
 ]
 
 class MAryTree(object):

From 8f2c68d399fea320fcbdb8ffc41f873a87d5f611 Mon Sep 17 00:00:00 2001
From: FamALouiz <fam@awadlouis.com>
Date: Thu, 20 Mar 2025 11:34:06 +0100
Subject: [PATCH 8/8] Updated trees docs

---
 docs/source/pydatastructs/trees/m_ary_trees.rst | 1 +
 1 file changed, 1 insertion(+)

diff --git a/docs/source/pydatastructs/trees/m_ary_trees.rst b/docs/source/pydatastructs/trees/m_ary_trees.rst
index a191643f3..ada8bf794 100644
--- a/docs/source/pydatastructs/trees/m_ary_trees.rst
+++ b/docs/source/pydatastructs/trees/m_ary_trees.rst
@@ -1,3 +1,4 @@
 M-ary Trees
 ===========
 
+.. autoclass:: pydatastructs.ParentPointerTree