From aa21b2545fd1ef7a7c2499808d885c0dded8fff1 Mon Sep 17 00:00:00 2001
From: AmirMohammad Hosseini Nasab <awmirhn@gmail.com>
Date: Fri, 12 Aug 2022 10:40:22 +0430
Subject: [PATCH 01/14] Enhance fenwick_tree.py

---
 data_structures/binary_tree/fenwick_tree.py | 80 +++++++++++++++------
 1 file changed, 58 insertions(+), 22 deletions(-)

diff --git a/data_structures/binary_tree/fenwick_tree.py b/data_structures/binary_tree/fenwick_tree.py
index 54f0f07ac68d..ec9df75c9345 100644
--- a/data_structures/binary_tree/fenwick_tree.py
+++ b/data_structures/binary_tree/fenwick_tree.py
@@ -1,28 +1,64 @@
 class FenwickTree:
-    def __init__(self, SIZE):  # create fenwick tree with size SIZE
-        self.Size = SIZE
-        self.ft = [0 for i in range(0, SIZE)]
+    """
+    Fenwick Tree
 
-    def update(self, i, val):  # update data (adding) in index i in O(lg N)
-        while i < self.Size:
-            self.ft[i] += val
-            i += i & (-i)
+    More info: https://en.wikipedia.org/wiki/Fenwick_tree
 
-    def query(self, i):  # query cumulative data from index 0 to i in O(lg N)
-        ret = 0
-        while i > 0:
-            ret += self.ft[i]
-            i -= i & (-i)
-        return ret
+    >>> f = FenwickTree(10)
+    >>> f.query(10)
+    0
+    >>> f.update(1, 20)
+    >>> f.query(1)
+    0
+    >>> f.query(2)
+    20
+    >>> f.query(3)
+    20
+    >>> f.update(2, 10)
+    >>> f.query(2)
+    20
+    >>> f.query(3)
+    30
+    >>> f.query(10)
+    30
+    """
+
+    def __init__(self, size: int):
+        """
+        Initialize a Fenwick tree with size elements
+        """
+        self.size = size
+        self.tree = [0] * (size + 1)
+
+    @staticmethod
+    def next(index: int):
+        return index + (index & (-index))
+
+    @staticmethod
+    def prev(index: int):
+        return index - (index & (-index))
+
+    def update(self, index: int, value: int):
+        """
+        Add a value to index in O(lg N)
+        """
+        index += 1  # 1-indexed
+        while index < self.size:
+            self.tree[index] += value
+            index = self.next(index)
+
+    def query(self, right: int):
+        """
+        Query the sum of all elements in [0, right) in O(lg N)
+        """
+        result = 0
+        while right > 0:
+            result += self.tree[right]
+            right = self.prev(right)
+        return result
 
 
 if __name__ == "__main__":
-    f = FenwickTree(100)
-    f.update(1, 20)
-    f.update(4, 4)
-    print(f.query(1))
-    print(f.query(3))
-    print(f.query(4))
-    f.update(2, -5)
-    print(f.query(1))
-    print(f.query(3))
+    import doctest
+
+    doctest.testmod()

From 85e2ef9682536170380ddf7bb9c418f82c094735 Mon Sep 17 00:00:00 2001
From: AmirMohammad Hosseini Nasab <awmirhn@gmail.com>
Date: Fri, 12 Aug 2022 10:40:55 +0430
Subject: [PATCH 02/14] Change update to add in fenwick_tree.py

---
 data_structures/binary_tree/fenwick_tree.py | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/data_structures/binary_tree/fenwick_tree.py b/data_structures/binary_tree/fenwick_tree.py
index ec9df75c9345..4d01644ac733 100644
--- a/data_structures/binary_tree/fenwick_tree.py
+++ b/data_structures/binary_tree/fenwick_tree.py
@@ -7,14 +7,14 @@ class FenwickTree:
     >>> f = FenwickTree(10)
     >>> f.query(10)
     0
-    >>> f.update(1, 20)
+    >>> f.add(1, 20)
     >>> f.query(1)
     0
     >>> f.query(2)
     20
     >>> f.query(3)
     20
-    >>> f.update(2, 10)
+    >>> f.add(2, 10)
     >>> f.query(2)
     20
     >>> f.query(3)
@@ -38,7 +38,7 @@ def next(index: int):
     def prev(index: int):
         return index - (index & (-index))
 
-    def update(self, index: int, value: int):
+    def add(self, index: int, value: int):
         """
         Add a value to index in O(lg N)
         """

From 251cf3ed26fcf6717ed5851f76bd2546d969287c Mon Sep 17 00:00:00 2001
From: AmirMohammad Hosseini Nasab <awmirhn@gmail.com>
Date: Fri, 12 Aug 2022 10:46:20 +0430
Subject: [PATCH 03/14] Some changes

---
 data_structures/binary_tree/fenwick_tree.py | 64 +++++++++++++++++----
 1 file changed, 53 insertions(+), 11 deletions(-)

diff --git a/data_structures/binary_tree/fenwick_tree.py b/data_structures/binary_tree/fenwick_tree.py
index 4d01644ac733..8ad8ad5cf9a4 100644
--- a/data_structures/binary_tree/fenwick_tree.py
+++ b/data_structures/binary_tree/fenwick_tree.py
@@ -5,27 +5,30 @@ class FenwickTree:
     More info: https://en.wikipedia.org/wiki/Fenwick_tree
 
     >>> f = FenwickTree(10)
-    >>> f.query(10)
+    >>> f.query(0, 10)
     0
     >>> f.add(1, 20)
-    >>> f.query(1)
+    >>> f.query(0, 1)
     0
-    >>> f.query(2)
+    >>> f.query(1, 10)
     20
-    >>> f.query(3)
+    >>> f.query(0, 10)
     20
-    >>> f.add(2, 10)
-    >>> f.query(2)
+    >>> f.update(2, 10)
+    >>> f.query(0, 2)
     20
-    >>> f.query(3)
-    30
-    >>> f.query(10)
+    >>> f.query(2, 3)
+    10
+    >>> f.query(0, 10)
     30
     """
 
     def __init__(self, size: int):
         """
         Initialize a Fenwick tree with size elements
+
+        Parameters:
+            size (int): size of the Fenwick tree
         """
         self.size = size
         self.tree = [0] * (size + 1)
@@ -41,15 +44,41 @@ def prev(index: int):
     def add(self, index: int, value: int):
         """
         Add a value to index in O(lg N)
+
+        Parameters:
+            index (int): index to add value to
+            value (int): value to add to index
+
+        Returns:
+            None
         """
         index += 1  # 1-indexed
         while index < self.size:
             self.tree[index] += value
             index = self.next(index)
 
-    def query(self, right: int):
+    def update(self, index: int, value: int):
+        """
+        Set the value of index in O(lg N)
+
+        Parameters:
+            index (int): index to set value to
+            value (int): value to set in index
+
+        Returns:
+            None
+        """
+        self.add(index, value - self.query(index, index + 1))
+
+    def prefix(self, right: int):
         """
-        Query the sum of all elements in [0, right) in O(lg N)
+        Prefix sum of all elements in [0, right) in O(lg N)
+
+        Parameters:
+            right (int): right bound of the query (exclusive)
+
+        Returns:
+            int: sum of all elements in [0, right)
         """
         result = 0
         while right > 0:
@@ -57,6 +86,19 @@ def query(self, right: int):
             right = self.prev(right)
         return result
 
+    def query(self, left: int, right: int):
+        """
+        Query the sum of all elements in [left, right) in O(lg N)
+
+        Parameters:
+            left (int): left bound of the query (inclusive)
+            right (int): right bound of the query (exclusive)
+
+        Returns:
+            int: sum of all elements in [left, right)
+        """
+        return self.prefix(right) - self.prefix(left)
+
 
 if __name__ == "__main__":
     import doctest

From fe1f8ae3330e18d0b2b34cd4963ca1a7aadfa2d8 Mon Sep 17 00:00:00 2001
From: AmirMohammad Hosseini Nasab <awmirhn@gmail.com>
Date: Fri, 12 Aug 2022 10:53:58 +0430
Subject: [PATCH 04/14] Fix bug

---
 data_structures/binary_tree/fenwick_tree.py | 6 +++++-
 1 file changed, 5 insertions(+), 1 deletion(-)

diff --git a/data_structures/binary_tree/fenwick_tree.py b/data_structures/binary_tree/fenwick_tree.py
index 8ad8ad5cf9a4..4a6e6e719612 100644
--- a/data_structures/binary_tree/fenwick_tree.py
+++ b/data_structures/binary_tree/fenwick_tree.py
@@ -7,6 +7,10 @@ class FenwickTree:
     >>> f = FenwickTree(10)
     >>> f.query(0, 10)
     0
+    >>> f.add(9, 10)
+    >>> f.prefix(10)
+    10
+    >>> f.add(9, -10)
     >>> f.add(1, 20)
     >>> f.query(0, 1)
     0
@@ -53,7 +57,7 @@ def add(self, index: int, value: int):
             None
         """
         index += 1  # 1-indexed
-        while index < self.size:
+        while index < self.size + 1:
             self.tree[index] += value
             index = self.next(index)
 

From 015d3f3d4c8d85fb453f40319f53d2fcea25f958 Mon Sep 17 00:00:00 2001
From: AmirMohammad Hosseini Nasab <awmirhn@gmail.com>
Date: Fri, 12 Aug 2022 10:59:36 +0430
Subject: [PATCH 05/14] Add O(N) initializer to FenwickTree

---
 data_structures/binary_tree/fenwick_tree.py | 47 ++++++++++++++++++---
 1 file changed, 41 insertions(+), 6 deletions(-)

diff --git a/data_structures/binary_tree/fenwick_tree.py b/data_structures/binary_tree/fenwick_tree.py
index 4a6e6e719612..d11898913a97 100644
--- a/data_structures/binary_tree/fenwick_tree.py
+++ b/data_structures/binary_tree/fenwick_tree.py
@@ -1,10 +1,13 @@
+from typing import List
+
+
 class FenwickTree:
     """
     Fenwick Tree
 
     More info: https://en.wikipedia.org/wiki/Fenwick_tree
 
-    >>> f = FenwickTree(10)
+    >>> f = FenwickTree(size=10)
     >>> f.query(0, 10)
     0
     >>> f.add(9, 10)
@@ -27,15 +30,47 @@ class FenwickTree:
     30
     """
 
-    def __init__(self, size: int):
+    def __init__(self, arr: List[int] = None, size: int = None):
+        """
+        Constructor for the Fenwick tree
+
+        Parameters:
+            arr (list): list of elements to initialize the tree with (optional)
+            size (int): size of the Fenwick tree (if arr is None)
+        """
+
+        if arr is None and size is not None:
+            self.size = size
+            self.tree = [0] * (size + 1)
+        elif arr is not None:
+            self.init(arr)
+        else:
+            raise ValueError("Either arr or size must be specified")
+
+    def init(self, arr: List[int]):
         """
-        Initialize a Fenwick tree with size elements
+        Initialize the Fenwick tree with arr in O(N)
 
         Parameters:
-            size (int): size of the Fenwick tree
+            arr (list): list of elements to initialize the tree with
+
+        Returns:
+            None
+
+        >>> a = [1, 2, 3, 4, 5]
+        >>> f1 = FenwickTree(a)
+        >>> f2 = FenwickTree(size=len(a))
+        >>> for index, value in enumerate(a):
+        ...     f2.add(index, value)
+        >>> f1.tree == f2.tree
+        True
         """
-        self.size = size
-        self.tree = [0] * (size + 1)
+        self.size = len(arr)
+        self.tree = [0] + arr
+        for i in range(1, self.size + 1):
+            j = self.next(i)
+            if j < self.size + 1:
+                self.tree[j] += self.tree[i]
 
     @staticmethod
     def next(index: int):

From a45e744afbf69de8883d55410fe87baf97919394 Mon Sep 17 00:00:00 2001
From: AmirMohammad Hosseini Nasab <awmirhn@gmail.com>
Date: Fri, 12 Aug 2022 11:10:21 +0430
Subject: [PATCH 06/14] Add get method to Fenwick Tree

---
 data_structures/binary_tree/fenwick_tree.py | 28 +++++++++++++++------
 1 file changed, 20 insertions(+), 8 deletions(-)

diff --git a/data_structures/binary_tree/fenwick_tree.py b/data_structures/binary_tree/fenwick_tree.py
index d11898913a97..3a4bfa84d60c 100644
--- a/data_structures/binary_tree/fenwick_tree.py
+++ b/data_structures/binary_tree/fenwick_tree.py
@@ -47,7 +47,7 @@ def __init__(self, arr: List[int] = None, size: int = None):
         else:
             raise ValueError("Either arr or size must be specified")
 
-    def init(self, arr: List[int]):
+    def init(self, arr: List[int]) -> None:
         """
         Initialize the Fenwick tree with arr in O(N)
 
@@ -73,14 +73,14 @@ def init(self, arr: List[int]):
                 self.tree[j] += self.tree[i]
 
     @staticmethod
-    def next(index: int):
+    def next(index: int) -> int:
         return index + (index & (-index))
 
     @staticmethod
-    def prev(index: int):
+    def prev(index: int) -> int:
         return index - (index & (-index))
 
-    def add(self, index: int, value: int):
+    def add(self, index: int, value: int) -> None:
         """
         Add a value to index in O(lg N)
 
@@ -96,7 +96,7 @@ def add(self, index: int, value: int):
             self.tree[index] += value
             index = self.next(index)
 
-    def update(self, index: int, value: int):
+    def update(self, index: int, value: int) -> None:
         """
         Set the value of index in O(lg N)
 
@@ -107,9 +107,9 @@ def update(self, index: int, value: int):
         Returns:
             None
         """
-        self.add(index, value - self.query(index, index + 1))
+        self.add(index, value - self.get(index))
 
-    def prefix(self, right: int):
+    def prefix(self, right: int) -> int:
         """
         Prefix sum of all elements in [0, right) in O(lg N)
 
@@ -125,7 +125,7 @@ def prefix(self, right: int):
             right = self.prev(right)
         return result
 
-    def query(self, left: int, right: int):
+    def query(self, left: int, right: int) -> int:
         """
         Query the sum of all elements in [left, right) in O(lg N)
 
@@ -138,6 +138,18 @@ def query(self, left: int, right: int):
         """
         return self.prefix(right) - self.prefix(left)
 
+    def get(self, index: int) -> int:
+        """
+        Get value at index in O(lg N)
+
+        Parameters:
+            index (int): index to get the value
+
+        Returns:
+            int: Value of element at index
+        """
+        return self.query(index, index + 1)
+
 
 if __name__ == "__main__":
     import doctest

From 6423a1ba8ad2e681e9e6f073f74fa2355bbf5ac8 Mon Sep 17 00:00:00 2001
From: AmirMohammad Hosseini Nasab <awmirhn@gmail.com>
Date: Fri, 12 Aug 2022 11:19:42 +0430
Subject: [PATCH 07/14] Change tree in Fenwick Tree

---
 data_structures/binary_tree/fenwick_tree.py | 21 +++++++++++++--------
 1 file changed, 13 insertions(+), 8 deletions(-)

diff --git a/data_structures/binary_tree/fenwick_tree.py b/data_structures/binary_tree/fenwick_tree.py
index 3a4bfa84d60c..7de76999af34 100644
--- a/data_structures/binary_tree/fenwick_tree.py
+++ b/data_structures/binary_tree/fenwick_tree.py
@@ -30,7 +30,7 @@ class FenwickTree:
     30
     """
 
-    def __init__(self, arr: List[int] = None, size: int = None):
+    def __init__(self, arr: List[int] = None, size: int = None) -> None:
         """
         Constructor for the Fenwick tree
 
@@ -41,7 +41,7 @@ def __init__(self, arr: List[int] = None, size: int = None):
 
         if arr is None and size is not None:
             self.size = size
-            self.tree = [0] * (size + 1)
+            self.tree = [0] * size
         elif arr is not None:
             self.init(arr)
         else:
@@ -66,10 +66,10 @@ def init(self, arr: List[int]) -> None:
         True
         """
         self.size = len(arr)
-        self.tree = [0] + arr
-        for i in range(1, self.size + 1):
+        self.tree = deepcopy(arr)
+        for i in range(1, self.size):
             j = self.next(i)
-            if j < self.size + 1:
+            if j < self.size:
                 self.tree[j] += self.tree[i]
 
     @staticmethod
@@ -91,8 +91,10 @@ def add(self, index: int, value: int) -> None:
         Returns:
             None
         """
-        index += 1  # 1-indexed
-        while index < self.size + 1:
+        if index == 0:
+            self.tree[0] += value
+            return
+        while index < self.size:
             self.tree[index] += value
             index = self.next(index)
 
@@ -119,7 +121,10 @@ def prefix(self, right: int) -> int:
         Returns:
             int: sum of all elements in [0, right)
         """
-        result = 0
+        if right == 0:
+            return 0
+        result = self.tree[0]
+        right -= 1  # make right inclusive
         while right > 0:
             result += self.tree[right]
             right = self.prev(right)

From 92bca3aa1a4ba8ca395a9594a375f506b2a4db57 Mon Sep 17 00:00:00 2001
From: AmirMohammad Hosseini Nasab <awmirhn@gmail.com>
Date: Fri, 12 Aug 2022 11:30:18 +0430
Subject: [PATCH 08/14] Add rank query to FenwickTree

---
 data_structures/binary_tree/fenwick_tree.py | 46 +++++++++++++++++++++
 1 file changed, 46 insertions(+)

diff --git a/data_structures/binary_tree/fenwick_tree.py b/data_structures/binary_tree/fenwick_tree.py
index 7de76999af34..061eacf1ef4c 100644
--- a/data_structures/binary_tree/fenwick_tree.py
+++ b/data_structures/binary_tree/fenwick_tree.py
@@ -1,3 +1,4 @@
+from copy import deepcopy
 from typing import List
 
 
@@ -155,6 +156,51 @@ def get(self, index: int) -> int:
         """
         return self.query(index, index + 1)
 
+    def rank_query(self, value: int) -> int:
+        """
+        Find the largest index with prefix(i) <= value in O(lg N)
+        NOTE: Requires that all values are non-negative!
+
+        Parameters:
+            value (int): value to find the largest index of
+
+        Returns:
+            -1: if value is smaller than all elements in prefix sum
+            int: largest index with prefix(i) <= value
+
+        >>> f = FenwickTree([1, 2, 0, 3, 0, 5])
+        >>> f.rank_query(0)
+        -1
+        >>> f.rank_query(2)
+        0
+        >>> f.rank_query(1)
+        0
+        >>> f.rank_query(3)
+        2
+        >>> f.rank_query(5)
+        2
+        >>> f.rank_query(6)
+        4
+        >>> f.rank_query(11)
+        5
+        """
+        value -= self.tree[0]
+        if value < 0:
+            return -1
+
+        j = 1  # Largest power of 2 <= size
+        while j * 2 < self.size:
+            j *= 2
+
+        i = 0
+
+        while j > 0:
+            if i + j < self.size and self.tree[i + j] <= value:
+                value -= self.tree[i + j]
+                i += j
+            j //= 2
+        return i
+
 
 if __name__ == "__main__":
     import doctest

From 6bd20fa63675db9e37284fd36fb0a18da3ee6a88 Mon Sep 17 00:00:00 2001
From: AmirMohammad Hosseini Nasab <awmirhn@gmail.com>
Date: Fri, 12 Aug 2022 11:41:30 +0430
Subject: [PATCH 09/14] Add get_array method to FenwickTree

---
 data_structures/binary_tree/fenwick_tree.py | 19 +++++++++++++++++++
 1 file changed, 19 insertions(+)

diff --git a/data_structures/binary_tree/fenwick_tree.py b/data_structures/binary_tree/fenwick_tree.py
index 061eacf1ef4c..849638c79799 100644
--- a/data_structures/binary_tree/fenwick_tree.py
+++ b/data_structures/binary_tree/fenwick_tree.py
@@ -73,6 +73,25 @@ def init(self, arr: List[int]) -> None:
             if j < self.size:
                 self.tree[j] += self.tree[i]
 
+    def get_array(self) -> List[int]:
+        """
+        Get the Normal Array of the Fenwick tree in O(N)
+
+        Returns:
+            list: Normal Array of the Fenwick tree
+
+        >>> a = [i for i in range(128)]
+        >>> f = FenwickTree(a)
+        >>> f.get_array() == a
+        True
+        """
+        arr = deepcopy(self.tree)
+        for i in range(self.size - 1, 0, -1):
+            j = self.next(i)
+            if j < self.size:
+                arr[j] -= arr[i]
+        return arr
+
     @staticmethod
     def next(index: int) -> int:
         return index + (index & (-index))

From fecde440f20076f9a8956f6e4dd927190e350be5 Mon Sep 17 00:00:00 2001
From: AmirMohammad Hosseini Nasab <awmirhn@gmail.com>
Date: Fri, 12 Aug 2022 11:44:24 +0430
Subject: [PATCH 10/14] Add some tests

---
 data_structures/binary_tree/fenwick_tree.py | 65 ++++++++++++++-------
 1 file changed, 43 insertions(+), 22 deletions(-)

diff --git a/data_structures/binary_tree/fenwick_tree.py b/data_structures/binary_tree/fenwick_tree.py
index 849638c79799..3974ee9f9e5d 100644
--- a/data_structures/binary_tree/fenwick_tree.py
+++ b/data_structures/binary_tree/fenwick_tree.py
@@ -7,28 +7,6 @@ class FenwickTree:
     Fenwick Tree
 
     More info: https://en.wikipedia.org/wiki/Fenwick_tree
-
-    >>> f = FenwickTree(size=10)
-    >>> f.query(0, 10)
-    0
-    >>> f.add(9, 10)
-    >>> f.prefix(10)
-    10
-    >>> f.add(9, -10)
-    >>> f.add(1, 20)
-    >>> f.query(0, 1)
-    0
-    >>> f.query(1, 10)
-    20
-    >>> f.query(0, 10)
-    20
-    >>> f.update(2, 10)
-    >>> f.query(0, 2)
-    20
-    >>> f.query(2, 3)
-    10
-    >>> f.query(0, 10)
-    30
     """
 
     def __init__(self, arr: List[int] = None, size: int = None) -> None:
@@ -110,6 +88,15 @@ def add(self, index: int, value: int) -> None:
 
         Returns:
             None
+
+        >>> f = FenwickTree([1, 2, 3, 4, 5])
+        >>> f.add(0, 1)
+        >>> f.add(1, 2)
+        >>> f.add(2, 3)
+        >>> f.add(3, 4)
+        >>> f.add(4, 5)
+        >>> f.get_array()
+        [2, 4, 6, 8, 10]
         """
         if index == 0:
             self.tree[0] += value
@@ -128,6 +115,15 @@ def update(self, index: int, value: int) -> None:
 
         Returns:
             None
+
+        >>> f = FenwickTree([5, 4, 3, 2, 1])
+        >>> f.update(0, 1)
+        >>> f.update(1, 2)
+        >>> f.update(2, 3)
+        >>> f.update(3, 4)
+        >>> f.update(4, 5)
+        >>> f.get_array()
+        [1, 2, 3, 4, 5]
         """
         self.add(index, value - self.get(index))
 
@@ -140,6 +136,14 @@ def prefix(self, right: int) -> int:
 
         Returns:
             int: sum of all elements in [0, right)
+
+        >>> a = [i for i in range(128)]
+        >>> f = FenwickTree(a)
+        >>> res = True
+        >>> for i in range(len(a)):
+        ...     res = res and f.prefix(i) == sum(a[:i])
+        >>> res
+        True
         """
         if right == 0:
             return 0
@@ -160,6 +164,15 @@ def query(self, left: int, right: int) -> int:
 
         Returns:
             int: sum of all elements in [left, right)
+
+        >>> a = [i for i in range(128)]
+        >>> f = FenwickTree(a)
+        >>> res = True
+        >>> for i in range(len(a)):
+        ...     for j in range(i + 1, len(a)):
+        ...         res = res and f.query(i, j) == sum(a[i:j])
+        >>> res
+        True
         """
         return self.prefix(right) - self.prefix(left)
 
@@ -172,6 +185,14 @@ def get(self, index: int) -> int:
 
         Returns:
             int: Value of element at index
+
+        >>> a = [i for i in range(128)]
+        >>> f = FenwickTree(a)
+        >>> res = True
+        >>> for i in range(len(a)):
+        ...     res = res and f.get(i) == a[i]
+        >>> res
+        True
         """
         return self.query(index, index + 1)
 

From 46e9747655e05ddf5b5b300de0af599081ea105a Mon Sep 17 00:00:00 2001
From: AmirMohammad Hosseini Nasab
 <19665344+itsamirhn@users.noreply.github.com>
Date: Sat, 13 Aug 2022 16:12:24 +0430
Subject: [PATCH 11/14] Update data_structures/binary_tree/fenwick_tree.py

Co-authored-by: Christian Clauss <cclauss@me.com>
---
 data_structures/binary_tree/fenwick_tree.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/data_structures/binary_tree/fenwick_tree.py b/data_structures/binary_tree/fenwick_tree.py
index 3974ee9f9e5d..53212cd3a8d1 100644
--- a/data_structures/binary_tree/fenwick_tree.py
+++ b/data_structures/binary_tree/fenwick_tree.py
@@ -63,7 +63,7 @@ def get_array(self) -> List[int]:
         >>> f.get_array() == a
         True
         """
-        arr = deepcopy(self.tree)
+        arr = self.tree[:]
         for i in range(self.size - 1, 0, -1):
             j = self.next(i)
             if j < self.size:

From 769d5b44b71749bc7ea62becc55b2857df450574 Mon Sep 17 00:00:00 2001
From: AmirMohammad Hosseini Nasab
 <19665344+itsamirhn@users.noreply.github.com>
Date: Sat, 13 Aug 2022 16:12:32 +0430
Subject: [PATCH 12/14] Update data_structures/binary_tree/fenwick_tree.py

Co-authored-by: Christian Clauss <cclauss@me.com>
---
 data_structures/binary_tree/fenwick_tree.py | 1 -
 1 file changed, 1 deletion(-)

diff --git a/data_structures/binary_tree/fenwick_tree.py b/data_structures/binary_tree/fenwick_tree.py
index 53212cd3a8d1..c79c087c354e 100644
--- a/data_structures/binary_tree/fenwick_tree.py
+++ b/data_structures/binary_tree/fenwick_tree.py
@@ -1,5 +1,4 @@
 from copy import deepcopy
-from typing import List
 
 
 class FenwickTree:

From d493a580ca0762aa561562e704d4db233be497e3 Mon Sep 17 00:00:00 2001
From: AmirMohammad Hosseini Nasab
 <19665344+itsamirhn@users.noreply.github.com>
Date: Sat, 13 Aug 2022 16:12:39 +0430
Subject: [PATCH 13/14] Update data_structures/binary_tree/fenwick_tree.py

Co-authored-by: Christian Clauss <cclauss@me.com>
---
 data_structures/binary_tree/fenwick_tree.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/data_structures/binary_tree/fenwick_tree.py b/data_structures/binary_tree/fenwick_tree.py
index c79c087c354e..93700b704dc8 100644
--- a/data_structures/binary_tree/fenwick_tree.py
+++ b/data_structures/binary_tree/fenwick_tree.py
@@ -8,7 +8,7 @@ class FenwickTree:
     More info: https://en.wikipedia.org/wiki/Fenwick_tree
     """
 
-    def __init__(self, arr: List[int] = None, size: int = None) -> None:
+    def __init__(self, arr: list[int] = None, size: int = None) -> None:
         """
         Constructor for the Fenwick tree
 

From 66c906ea6f4c5fa88c999b61afcf46e6e594683a Mon Sep 17 00:00:00 2001
From: AmirMohammad Hosseini Nasab <awmirhn@gmail.com>
Date: Sat, 13 Aug 2022 16:16:36 +0430
Subject: [PATCH 14/14] change `List` to `list`

---
 data_structures/binary_tree/fenwick_tree.py | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/data_structures/binary_tree/fenwick_tree.py b/data_structures/binary_tree/fenwick_tree.py
index 93700b704dc8..96020d1427af 100644
--- a/data_structures/binary_tree/fenwick_tree.py
+++ b/data_structures/binary_tree/fenwick_tree.py
@@ -25,7 +25,7 @@ def __init__(self, arr: list[int] = None, size: int = None) -> None:
         else:
             raise ValueError("Either arr or size must be specified")
 
-    def init(self, arr: List[int]) -> None:
+    def init(self, arr: list[int]) -> None:
         """
         Initialize the Fenwick tree with arr in O(N)
 
@@ -50,7 +50,7 @@ def init(self, arr: List[int]) -> None:
             if j < self.size:
                 self.tree[j] += self.tree[i]
 
-    def get_array(self) -> List[int]:
+    def get_array(self) -> list[int]:
         """
         Get the Normal Array of the Fenwick tree in O(N)