feat: fenwick tree (#16)

Add FenwickTree implementation and tests

Author: rubenperezm

README.md

@@ -3,10 +3,10 @@
 [![Build](https://github.com/rubenperezm/pystrukts/actions/workflows/test.yml/badge.svg)](https://github.com/rubenperezm/pystrukts/actions/workflows/test.yml/badge.svg)
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-<!-- [![Python Versions](https://img.shields.io/pypi/pyversions/pystrukts.svg)](https://pypi.org/project/pystrukts) -->
+[![Python Versions](https://img.shields.io/pypi/pyversions/pystrukts.svg)](https://pypi.org/project/pystrukts)
 
 
-A Python library for data structures. This library provides more than 20 advanced data structures not available in the Python standard library.
+A Python library for data structures. This library provides more than 10 advanced data structures not available in the Python standard library.
 
 ## Installation
 
@@ -21,23 +21,12 @@ pip install pystrukts
 - [x] Doubly Linked Node
 - [x] Doubly Linked List
 - [x] Circular Linked List (Single, Double)
-- [ ] Skip List
 
 ### Trees
 - [x] Binary Tree
 - [x] Generic Tree
 - [x] Binary Search Tree
-- [ ] Ternary Search Tree
-- [ ] Suffix Tree
-- [ ] AVL Tree
-- [ ] Red-Black Tree
-- [ ] Splay Tree
-- [ ] B-Tree
-- [ ] B+ Tree
-- [ ] R-Tree
-- [ ] Interval Tree
-- [ ] Segment Tree
-- [ ] Fenwick Tree
+- [x] Fenwick Trees (RUPQ, RURQ)
 - [x] Trie
 
 ### Graphs

pystrukts/tree/__init__.py

@@ -3,4 +3,5 @@
 from .trie import Trie, TrieNode
 from .generic_tree import GenericTree
 from .binary_tree import BinaryTree
-from .binary_search_tree import BinarySearchTree
+from .binary_search_tree import BinarySearchTree
+from .fenwick_tree import FenwickTree, RUPQ, RURQ

pystrukts/tree/fenwick_tree.py

@@ -0,0 +1,193 @@
+'''
+Fenwick Tree implementation in Python.
+
+This module contains the implementation of Fenwick Trees, as well as two extensions of it:
+- Range Update Point Query (RUPQ)
+- Range Update Range Query (RURQ)
+'''
+
+from typing import List
+
+class FenwickTree:
+    '''
+    Fenwick Tree implementation in Python.
+
+    Attributes:
+    - n: int - the size of the Fenwick Tree
+    - ftree: list - the Fenwick Tree itself
+
+    Methods:
+    - lsone(s: int) -> int: returns the least significant bit of s
+    - query(i: int, j: int) -> int: returns the sum of the elements in the range [i, j]
+    - update(i: int, v: int): updates the element at index i with value v
+    - select(k: int) -> int: returns the index of the k-th element in the Fenwick Tree
+    '''
+    def __init__(self, f: List[int]):
+        self.n = len(f)
+        self.ftree = [0] * (self.n + 1)
+
+        for i in range(1, self.n + 1):
+            self.ftree[i] += f[i - 1]
+            if i + self._lsone(i) <= self.n:
+                self.ftree[i + self._lsone(i)] += self.ftree[i]
+
+    def _lsone(self, s: int) -> int:
+        '''
+        Returns the least significant bit of s.
+
+        Args:
+            s (int): The number to get the least significant bit from.
+
+        Returns:
+            out (int): The least significant bit of s.
+        '''
+        return s & -s
+
+    def query(self, i: int, j: int) -> int:
+        '''
+        Queries the Fenwick Tree for the sum of the elements in the range [i, j].
+
+        Args:
+            i (int): The lower bound of the range.
+            j (int): The upper bound of the range.
+
+        Returns:
+            s (int): The sum of the elements in the range [i, j].
+        '''
+        if i > 1:
+            return self.query(1, j) - self.query(1, i - 1)
+
+        s = 0
+        while j > 0:
+            s += self.ftree[j]
+            j -= self._lsone(j)
+
+        return s
+
+    def update(self, i: int, v: int):
+        '''
+        Updates the element at index i with value v.
+
+        Args:
+            i (int): The index of the element to update.
+            v (int): The new value of the element.
+        '''
+
+        while i <= self.n:
+            self.ftree[i] += v
+            i += self._lsone(i)
+
+    def select(self, k: int) -> int:
+        '''
+        Returns the index of the k-th element in the Fenwick Tree.
+
+        Args:
+            k (int): The index of the element to return.
+
+        Returns:
+            i (int): The index of the k-th element in the Fenwick Tree.
+        '''
+
+        p = 1
+        while p*2 <= self.n:
+            p *= 2
+
+        i = 0
+        while p > 0:
+            if k > self.ftree[i + p]:
+                k -= self.ftree[i + p]
+                i += p
+            p //= 2
+
+        return i + 1
+
+class RUPQ:
+    '''
+    Range Update Point Query (RUPQ) implementation.
+
+    This class extends the Fenwick Tree to support range updates and point queries.
+
+    Attributes:
+    - ftree: FenwickTree - the Fenwick Tree used for the range updates
+
+    Methods:
+    - query(i: int) -> int: returns the value of the element at index i
+    - update(i: int, j: int, v: int): updates the elements in the range [i, j] with value v
+    '''
+    def __init__(self, n: int):
+        self.ftree = FenwickTree([0] * n)
+
+    def query(self, i: int) -> int:
+        '''
+        Queries the Fenwick Tree for the value of the element at index i.
+        
+        Args:
+            i (int): The index of the element to query.
+
+        Returns:
+            s (int): The value of the element at index i.
+        '''
+
+        return self.ftree.query(1, i)
+
+    def update(self, i: int, j: int, v: int):
+        '''
+        Updates the elements in the range [i, j] with value v.
+
+        Args:
+            i (int): The lower bound of the range.
+            j (int): The upper bound of the range.
+            v (int): The value to update the elements with.
+        '''
+
+        self.ftree.update(i, v)
+        self.ftree.update(j + 1, -v)
+
+class RURQ:
+    '''
+    Range Update Range Query (RURQ) implementation.
+
+    This class extends the Fenwick Tree to support range updates and range queries.
+
+    Attributes:
+    - f: FenwickTree - the Fenwick Tree used for the range updates
+    - r: RUPQ - the RUPQ used for the range queries
+
+    Methods:
+    - query(i: int, j: int) -> int: returns the sum of the elements in the range [i, j]
+    - update(i: int, j: int, v: int): updates the elements in the range [i, j] with value v
+    '''
+
+    def __init__(self, n: int):
+        self.ftree = FenwickTree([0] * n)
+        self.rupq = RUPQ(n)
+
+    def query(self, i: int, j: int) -> int:
+        '''
+        Queries the Fenwick Tree for the sum of the elements in the range [i, j].
+
+        Args:
+            i (int): The lower bound of the range.
+            j (int): The upper bound of the range.
+
+        Returns:
+            s (int): The sum of the elements in the range [i, j].
+        '''
+
+        if i > 1:
+            return self.query(1, j) - self.query(1, i - 1)
+        return self.rupq.query(j) * j - self.ftree.query(1, j)
+
+    def update(self, i: int, j: int, v: int):
+        '''
+        Updates the elements in the range [i, j] with value v.
+
+        Args:
+            i (int): The lower bound of the range.
+            j (int): The upper bound of the range.
+            v (int): The value to update the elements with.
+        '''
+
+        self.rupq.update(i, j, v)
+        self.ftree.update(i, v * (i - 1))
+        self.ftree.update(j + 1, -1 * v * j)

tests/test_fenwick_tree.py

@@ -0,0 +1,36 @@
+import pytest
+from pystrukts.tree import FenwickTree, RUPQ, RURQ
+
+
+def test_initialization_ftree():
+    f = [0, 1, 0, 1, 2, 3, 2, 1, 1, 0]
+    ft = FenwickTree(f)
+    assert ft.n == 10
+    assert ft.ftree == [0, 0, 1, 0, 2, 2, 5, 2, 10, 1, 1]
+    assert ft.query(1, 6) == 7
+    assert ft.query(1, 3) == 1
+    assert ft.select(7) == 6
+    ft.update(5, 1)
+    assert ft.query(1, 10) == 12
+
+def test_rupq():
+    r = RUPQ(10)
+    r.update(2, 9, 7)
+    r.update(6, 7, 3)
+    assert r.query(1) == 0
+    assert r.query(2) == 7
+    assert r.query(3) == 7
+    assert r.query(4) == 7
+    assert r.query(5) == 7
+    assert r.query(6) == 10
+    assert r.query(7) == 10
+    assert r.query(8) == 7
+    assert r.query(9) == 7
+    assert r.query(10) == 0
+
+def test_rurq():
+    r = RURQ(10)
+    r.update(2, 9, 7)
+    r.update(6, 7, 3)
+    assert r.query(3, 5) == 21
+    assert r.query(7, 8) == 17