From f16270e735118e303e0ff75d4fb4e707a1336f86 Mon Sep 17 00:00:00 2001
From: Leyang Zou <leyang.zou@student.tdsb.on.ca>
Date: Fri, 2 Oct 2020 19:06:34 -0400
Subject: [PATCH] Add Binary Indexed Tree

---
 Binary Indexed Tree/BinaryIndexedTree.py | 43 ++++++++++++++++++++++++
 1 file changed, 43 insertions(+)
 create mode 100644 Binary Indexed Tree/BinaryIndexedTree.py

diff --git a/Binary Indexed Tree/BinaryIndexedTree.py b/Binary Indexed Tree/BinaryIndexedTree.py
new file mode 100644
index 0000000..12025a8
--- /dev/null
+++ b/Binary Indexed Tree/BinaryIndexedTree.py	
@@ -0,0 +1,43 @@
+class BinaryIndexedTree:
+    def __init__(self, arr):
+        self.len = 1 + len(arr)
+        self.tree = [0] * self.len # stores BIT
+        self.orig = [0] * self.len # stores original array
+        # build tree from values
+        for i in range(len(arr)):
+            self.update(i, arr[i])
+    
+    def update(self, i, diff):
+        """
+        Updates the value at index i by diff.
+        """
+        i += 1 # BIT is one-indexed
+        self.orig[i] += diff # update original
+        # update BIT
+        while i < self.len:
+            self.tree[i] += diff
+            i += i & -i
+
+    def query(self, i):
+        """
+        Returns the sum of arr[0..i], inclusive.
+        """
+        i += 1 # BIT is one-indexed
+        ans = 0
+        while i != 0:
+            ans += self.tree[i]
+            i -= i & -i
+        return ans
+
+    def get(self, i):
+        """
+        Get the element at position i
+        """
+        return self.orig[i + 1]
+
+if __name__ == '__main__':
+    bit = BinaryIndexedTree([4, 8, 4, 5, 6, 3, 2, 2, 8, 1])
+    print('Sum of arr[0..4]:', bit.query(4))
+    bit.update(2, -10) # decrease [2] by 10
+    print('Sum of arr[0..4] after updating arr[2]:', bit.query(4))
+    print('Value of arr[7]:', bit.get(7))