feat: add Fusion Tree

docs/source/pydatastructs/trees/binary_trees.rst

@@ -18,3 +18,5 @@ Binary Trees
 .. autoclass:: pydatastructs.RedBlackTree
 
 .. autoclass:: pydatastructs.BinaryTreeTraversal
+
+.. autoclass:: pydatastructs.FusionTree

pydatastructs/trees/__init__.py

@@ -17,7 +17,8 @@
     CartesianTree,
     Treap,
     SplayTree,
-    RedBlackTree
+    RedBlackTree,
+    FusionTree
 )
 __all__.extend(binary_trees.__all__)
 

pydatastructs/trees/binary_trees.py

@@ -1,4 +1,5 @@
 import random
+import math
 from collections import deque as Queue
 from pydatastructs.utils import TreeNode, CartesianTreeNode, RedBlackTreeNode
 from pydatastructs.miscellaneous_data_structures import Stack
@@ -17,7 +18,8 @@
     'CartesianTree',
     'Treap',
     'SplayTree',
-    'RedBlackTree'
+    'RedBlackTree',
+    'FusionTree',
 ]
 
 class BinaryTree(object):
@@ -1887,3 +1889,160 @@ def get_sum(self, left_index, right_index):
                    self.get_prefix_sum(left_index - 1)
         else:
             return self.get_prefix_sum(right_index)
+
+class FusionTree(object):
+    """
+    Implements a Fusion Tree, a multi-way search tree optimized for integer keys.
+
+    Parameters
+    ==========
+
+    key: int
+        The integer key to insert.
+    root_data: Any
+        Optional data to store with the key.
+    backend: pydatastructs.Backend
+        The backend to be used. Available backends: Python and C++
+        Optional, by default, the Python backend is used. For faster execution, use the C++ backend.
+    word_size: int
+        The size of the integer keys in bits.
+        Optional, by default, set to 64.
+
+    Examples
+    ========
+
+    >>> from pydatastructs import FusionTree
+    >>> ft = FusionTree()
+    >>> ft.insert(1, 1)
+    >>> ft.insert(2, 2)
+    >>> ft.search(1)
+    0
+    >>> ft.delete(1)
+    True
+    >>> ft.search(1)
+
+
+    References:
+    - https://en.wikipedia.org/wiki/Fusion_tree
+    - Fredman & Willard (1990): "Fusion Trees"
+    """
+
+    __slots__ = ['root_idx', 'tree', 'size', 'B',
+                 'sketch_mask', 'fingerprint_multiplier']
+
+    def __new__(cls, key=None, root_data=None, **kwargs):
+        backend = kwargs.get('backend', Backend.PYTHON)
+        raise_if_backend_is_not_python(cls, backend)
+
+        obj = object.__new__(cls)
+        key = None if root_data is None else key
+        root = TreeNode(key, root_data)
+        root.is_root = True
+        obj.root_idx = 0
+        obj.tree, obj.size = ArrayForTrees(TreeNode, [root]), 1
+        obj.B = int(math.log2(kwargs.get('word_size', 64))
+                    ** (1/5))  # Multi-way branching factor
+        obj.sketch_mask = 0  # Computed dynamically
+        obj.fingerprint_multiplier = 2654435761  # Prime multiplier for fingerprinting
+        return obj
+
+    def _compute_sketch_mask(self):
+        """
+        Computes a sketch mask for efficient parallel comparisons.
+        """
+        keys = [node.key for node in self.tree if node is not None]
+        if len(keys) > 1:
+            significant_bits = [max(k.bit_length() for k in keys)]
+            self.sketch_mask = sum(1 << b for b in significant_bits)
+
+    def insert(self, key, data=None):
+        """
+        Inserts a key into the Fusion Tree.
+
+        Parameters
+        ==========
+
+        key: int
+            The integer key to insert.
+        data: Any
+            Optional data to store with the key.
+        """
+        # Edge case for root node if not intially inserted
+        if self.size == 1 and self.tree[0].key is None:
+            self.tree[0] = TreeNode(key, data)
+            self.tree[0].is_root = True
+            return
+
+        node = TreeNode(key, data)
+        self.tree.append(node)
+        self.size += 1
+        if self.size > 1:
+            self._compute_sketch_mask()
+
+    def _sketch_key(self, key):
+        """
+        Applies the sketch mask to compress the key for fast comparison.
+        """
+        return key & self.sketch_mask
+
+    def _fingerprint(self, key):
+        """
+        Uses multiplication-based fingerprinting to create a unique identifier
+        for the key, allowing fast parallel searches.
+        """
+        return (key * self.fingerprint_multiplier) & ((1 << 64) - 1)
+
+    def search(self, key):
+        """
+        Searches for a key in the Fusion Tree using bitwise sketching and fingerprinting.
+
+        Parameters
+        ==========
+
+        key: int
+            The integer key to search.
+
+        Returns
+        =======
+
+        int: The index of the key in the tree, or None if not found.
+        """
+        sketch = self._sketch_key(key)
+        fingerprint = self._fingerprint(key)
+        for i in range(self.size):
+            if self._sketch_key(self.tree[i].key) == sketch and self._fingerprint(self.tree[i].key) == fingerprint:
+                return i
+        return None
+
+    def delete(self, key):
+        """
+        Deletes a key from the Fusion Tree.
+
+        Parameters
+        ==========
+
+        key: int
+            The integer key to delete.
+
+        Returns
+        =======
+
+        bool: True if the key was successfully deleted, False otherwise.
+
+        """
+        index = self.search(key)
+        if index is not None:
+            self.tree[index] = None  # Soft delete
+            # Compact tree
+            self.tree = [node for node in self.tree if node is not None]
+            self.size -= 1
+            if self.size > 1:
+                self._compute_sketch_mask()
+            return True
+        return False
+
+    def __str__(self):
+        """
+        Returns a string representation of the Fusion Tree.
+        """
+        return str([(node.key, node.data) for node in self.tree if node is not None])

pydatastructs/trees/tests/test_binary_trees.py

@@ -1,5 +1,5 @@
 from pydatastructs.trees.binary_trees import (
-    BinaryTree, BinarySearchTree, BinaryTreeTraversal, AVLTree,
+    BinaryTree, BinarySearchTree, BinaryTreeTraversal, AVLTree, FusionTree,
     ArrayForTrees, BinaryIndexedTree, SelfBalancingBinaryTree, SplayTree, CartesianTree, Treap, RedBlackTree)
 from pydatastructs.utils.raises_util import raises
 from pydatastructs.utils.misc_util import TreeNode
@@ -818,3 +818,90 @@ def test_RedBlackTree():
 
 def test_cpp_RedBlackTree():
     _test_RedBlackTree(Backend.CPP)
+
+
+def _test_FusionTree(backend):
+    FT = FusionTree
+    f_tree = FT(backend=backend)
+
+    f_tree.insert(8, 8)
+    f_tree.insert(3, 3)
+    f_tree.insert(10, 10)
+    f_tree.insert(1, 1)
+    f_tree.insert(6, 6)
+    f_tree.insert(4, 4)
+    f_tree.insert(7, 7)
+    f_tree.insert(14, 14)
+    f_tree.insert(13, 13)
+
+    assert f_tree.search(10) is not None
+    assert f_tree.search(-1) is None
+
+    assert f_tree.delete(13) is True
+    assert f_tree.search(13) is None
+    assert f_tree.delete(10) is True
+    assert f_tree.search(10) is None
+    assert f_tree.delete(3) is True
+    assert f_tree.search(3) is None
+    assert f_tree.delete(13) is False  # Already deleted
+
+    expected_str = '[(8, 8), (1, 1), (6, 6), (4, 4), (7, 7), (14, 14)]'
+    assert str(f_tree) == expected_str
+
+    f_tree.insert(8, 9)
+    assert f_tree.search(8) is not None
+
+    large_key = 10**9
+    f_tree.insert(large_key, large_key)
+    assert f_tree.search(large_key) is not None
+
+    expected_str = '[(8, 8), (1, 1), (6, 6), (4, 4), (7, 7), (14, 14), (8, 9), (1000000000, 1000000000)]'
+    assert str(f_tree) == expected_str
+    assert f_tree.delete(8) is True
+
+    expected_str = '[(1, 1), (6, 6), (4, 4), (7, 7), (14, 14), (8, 9), (1000000000, 1000000000)]'
+    assert str(f_tree) == expected_str
+
+    FT = FusionTree
+    f_tree = FT(8, 8, backend=backend)
+
+    f_tree.insert(8, 8)
+    f_tree.insert(3, 3)
+    f_tree.insert(10, 10)
+    f_tree.insert(1, 1)
+    f_tree.insert(6, 6)
+    f_tree.insert(4, 4)
+    f_tree.insert(7, 7)
+    f_tree.insert(14, 14)
+    f_tree.insert(13, 13)
+
+    assert f_tree.search(10) is not None
+    assert f_tree.search(-1) is None
+
+    assert f_tree.delete(13) is True
+    assert f_tree.search(13) is None
+    assert f_tree.delete(10) is True
+    assert f_tree.search(10) is None
+    assert f_tree.delete(3) is True
+    assert f_tree.search(3) is None
+    assert f_tree.delete(13) is False  # Already deleted
+
+    expected_str = '[(8, 8), (8, 8), (1, 1), (6, 6), (4, 4), (7, 7), (14, 14)]'
+    assert str(f_tree) == expected_str
+
+    f_tree.insert(8, 9)
+    assert f_tree.search(8) is not None
+
+    large_key = 10**9
+    f_tree.insert(large_key, large_key)
+    assert f_tree.search(large_key) is not None
+
+    expected_str = '[(8, 8), (8, 8), (1, 1), (6, 6), (4, 4), (7, 7), (14, 14), (8, 9), (1000000000, 1000000000)]'
+    assert str(f_tree) == expected_str
+    assert f_tree.delete(8) is True
+
+    expected_str = '[(8, 8), (1, 1), (6, 6), (4, 4), (7, 7), (14, 14), (8, 9), (1000000000, 1000000000)]'
+    assert str(f_tree) == expected_str
+
+def test_FusionTree():
+    _test_FusionTree(Backend.PYTHON)