Added implementation for M-ary tree

Added M_aryTreeNode for use in M_ary tree and an implementation for
M_ary Tree. The work is in reference with issue codezonediitj#101.

pydatastructs/trees/m_ary_trees.py

@@ -0,0 +1,168 @@
+from pydatastructs.utils import M_AryTreeNode, BinomialTreeNode
+from pydatastructs.linear_data_structures.arrays import ArrayForTrees
+
+__all__ = [
+    'M_AryTree'
+]
+
+class M_AryTree(object):
+    """
+    Abstract m-ary tree.
+
+    Parameters
+    ==========
+
+    max_children
+        Optional, specifies the maximum number of children 
+        a node can have. Defaults to 2 in case nothing is 
+        specified.
+    root_data
+        Optional, the root node of the binary tree.
+        If not of type M_AryTreeNode, it will consider
+        root as data and a new root node will
+        be created.
+    key
+        Required if tree is to be instantiated with
+        root otherwise not needed.
+    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.
+    is_order_statistic: bool
+        Set it to True, if you want to use the
+        order statistic features of the tree.
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/M-ary_tree
+    """
+
+    __slots__ = ['root_idx', 'max_children', 'comparator', 'tree', 'size',
+                 'is_order_statistic']
+
+
+    def __new__(cls, max_children=2, key=None, root_data=None, comp=None,
+                is_order_statistic=False):
+        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 = M_AryTreeNode(key, root_data)
+        root.is_root = True
+        obj.root_idx = 0
+        obj.max_children = max_children
+        obj.tree, obj.size = ArrayForTrees(M_AryTreeNode, [root]), 1
+        obj.comparator = lambda key1, key2: key1 < key2 \
+                        if comp is None else comp
+        obj.is_order_statistic = is_order_statistic
+        return obj
+
+    def insert(self, key, data):
+        """
+        Inserts data by the passed key using iterative
+        algorithm.
+
+        Parameters
+        ==========
+
+        key
+            The key for comparison.
+        data
+            The data to be inserted.
+
+        Returns
+        =======
+
+        None
+        """
+        raise NotImplementedError("This is an abstract method.")
+
+    def delete(self, key, **kwargs):
+        """
+        Deletes the data with the passed key
+        using iterative algorithm.
+
+        Parameters
+        ==========
+
+        key
+            The key of the node which is
+            to be deleted.
+        balancing_info: bool
+            Optional, by default, False
+            The information needed for updating
+            the tree is returned if this parameter
+            is set to True. It is not meant for
+            user facing APIs.
+
+        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.
+        """
+        raise NotImplementedError("This is an abstract method.")
+
+    def search(self, key, **kwargs):
+        """
+        Searches for the data in the binary search 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.
+        """
+        raise NotImplementedError("This is an abstract method.")
+
+    def to_binary_tree(self):
+        """
+        Converts an m-ary tree to a binary tree. 
+
+        Returns
+        =======
+
+        TreeNode
+            The root of the newly created binary tree. 
+        """
+        raise NotImplementedError("This is an abstract method.")
+
+
+    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)
+                for j in node.children:
+                    if j is not None:
+                        to_be_printed[i].append(j)
+        return str(to_be_printed)

pydatastructs/utils/__init__.py

@@ -3,6 +3,7 @@
 from . import misc_util
 from .misc_util import (
     TreeNode,
+    M_AryTreeNode,
     LinkedListNode,
     BinomialTreeNode,
     AdjacencyListGraphNode,

pydatastructs/utils/misc_util.py

@@ -1,5 +1,6 @@
 __all__ = [
     'TreeNode',
+    'M_AryTreeNode',
     'LinkedListNode',
     'BinomialTreeNode',
     'AdjacencyListGraphNode',
@@ -104,6 +105,54 @@ def __str__(self):
         """
         return str((self.key, self.data))
 
+class M_AryTreeNode(TreeNode):
+    """
+    Represents node in an M-ary trees.
+
+    Parameters
+    ==========
+
+    data
+        Any valid data to be stored in the node.
+    key
+        Required for comparison operations.
+
+    Note
+    ====
+
+    The following are the data members of the class:
+
+    children: DynamicOneDimensionalArray
+        An array of indices which stores the children of 
+        this node in the M-ary tree array
+    is_root: bool, by default, False
+        If the current node is a root of the tree then
+        set it to True otherwise False.
+    """
+    __slots__ = ['key', 'children', 'data', 'is_root']
+
+    def __new__(cls, key, data):
+        from pydatastructs.linear_data_structures.arrays import DynamicOneDimensionalArray
+        obj = Node.__new__(cls)
+        obj.data = data
+        obj.key = key
+        obj.is_root = False
+        obj.children = DynamicOneDimensionalArray(int, 0)
+        return obj
+
+    def add_children(self, *children):
+        """
+        Adds children of current node.
+        """
+        for child in children:
+            self.children.append(child)
+
+    def __str__(self):
+        """
+        For printing the key and data.
+        """
+        return str((self.key, self.data))
+
 class LinkedListNode(Node):
     """
     Represents node in linked lists.