fenwick_tree.py: Add FenwickTree Data Structure

This adds Fenwick Data Structure which can update an element of a list
and query the sum of any range of it in only O(log(N)) time complexity.

Closes NITSkmOS#220

README.md

@@ -36,7 +36,7 @@ This repository contains examples of various algorithms written on different pro
 | [Linear Linked List](https://en.wikipedia.org/wiki/Linked_list)                                 | [:octocat:](linked_list/C)            | [:octocat:](linked_list/Cpp)          |                                       | [:octocat:](linked_list/Python)       |
 | [AVL Tree](https://en.wikipedia.org/wiki/AVL_tree)                                              | [:octocat:](avl_tree/C)               |                                       | [:octocat:](avl_tree/Java)            | [:octocat:](avl_tree/Python)          |
 | [Binary Search Tree](https://en.wikipedia.org/wiki/Binary_search_tree)                          |                                       | [:octocat:](binary_search_tree/Cpp)                                       |                                       |                                       |
-| [Fenwick Tree](https://en.wikipedia.org/wiki/Fenwick_tree)                                      |                                       |                                       | [:octocat:](fenwick_tree/java)        |                                       |
+| [Fenwick Tree](https://en.wikipedia.org/wiki/Fenwick_tree)                                      |                                       |                                       | [:octocat:](fenwick_tree/java)        | [:octocat:](fenwick_tree/Python)      |
 
 
 ## Sample Run

fenwick_tree/Python/fenwick_tree.py

@@ -0,0 +1,90 @@
+def lsb(x):
+    """Returns the Last Significant Bit (LSB) of x"""
+    return x & -x
+
+
+class FenwickTree:
+    """A simple implementation of a Fenwick tree"""
+
+    def __init__(self, size):
+        self.data = [0] * (size + 1)  # Initialise 0-filled data array
+
+    def _cumulative_sum(self, right):
+        """
+        Returns the sum from 0 to right (inclusive)
+
+        :param right: The inclusive right index
+        :return: sum([left; right])
+        """
+        res = 0
+        index = right + 1  # Convert to 1-based index
+        while index > 0:
+            res += self.data[index]
+            index -= lsb(index)
+
+        return res
+
+    def sum(self, left, right):
+        """
+        Returns the sum from left (inclusive) to right (inclusive)
+
+        :param right: The inclusive right index
+        :param left: The inclusive left index
+        :return: sum([left; right])
+        """
+        return self._cumulative_sum(right) - self._cumulative_sum(left - 1)
+
+    def add(self, index, diff):
+        """
+        Add the difference to the data index
+
+        :param index: The index to update
+        :param diff: The amount to add to that index
+        """
+        index += 1  # Convert to 1-based index
+
+        while index < len(self.data):
+            self.data[index] += diff
+            index += lsb(index)
+
+
+def main():
+    tree = FenwickTree(8)
+
+    # Set initial value(by default it's 0)
+    for i in range(8):
+        tree.add(i, i)
+
+    # Now it's 0, 1, 2, 3, 4, 5, 6, 7
+
+    # [0, 1, 2, 3, 4, 5, 6, 7]
+    #  ^--------------------^
+    # 0 + 1 + 2...+ 7 = 28
+    assert tree.sum(0, 7) == 28
+
+    # [0, 1, 2, 3, 4, 5, 6, 7]
+    #  ^-----^
+    #  4 + 5 + 6 = 15
+    assert tree.sum(4, 6) == 15
+
+    # [0, 1, 2, 3, 4, 5, 6, 7]
+    #  ^--------^
+    #  0 + 1 + 2 + 3 = 6
+    assert tree.sum(0, 3) == 6
+
+    # Update the numbers again
+    for i in range(8):
+        tree.add(i, 1 - i)
+        # Initial value i
+        # Added: 1 - i
+        # Res: i + 1 - i = 1
+
+    # [1, 1, 1, 1, 1, 1, 1, 1]
+    #  ^--------------------^
+    # 1 * 8 = 8
+    assert tree.sum(0, 7) == 8
+    print("Tests passed")
+
+
+if __name__ == "__main__":
+    main()