Merge pull request #416 from shakeelsamsu/master

Implemented fenwick tree in python

Author: matthewsamuel95

Data Structures/Fenwick_tree/fenwick.py

@@ -0,0 +1,65 @@
+"""
+@author: shakeelsamsu
+https://gihtub.com/shakeelsamsu
+Oct 7 18 9:42:35 PM
+"""
+
+class fenwick:
+    """Fenwick Tree"""
+    
+    #def __init__(self, list):
+    #    """Initialize BIT with list in O(n*log(n))"""
+    #    self.array = [0] * (len(list) + 1)
+    #    for idx, val in enumerate(list):
+    #        self.update(idx, val)
+
+    def __init__(self, list):
+        """"Initialize BIT with list in O(n)"""
+        self.array = [0] + list
+        for idx in range(1, len(self.array)):
+            idx2 = idx + (idx & -idx)
+            if idx2 < len(self.array):
+                self.array[idx2] += self.array[idx]
+
+    def prefix_query(self, idx):
+        """Computes prefix sum of up to including the idx-th element"""
+        idx += 1
+        result = 0
+        while idx:
+            result += self.array[idx]
+            idx -= idx & -idx
+        return result
+
+    def range_query(self, from_idx, to_idx):
+        """Computes the range sum between two indices (both inclusive)"""
+        return self.prefix_query(to_idx) - self.prefix_query(from_idx - 1)
+
+    def update(self, idx, add):
+        """Add a value to the idx-th element"""
+        idx += 1
+        while idx < len(self.array):
+            self.array[idx] += add
+            idx += idx & -idx
+
+
+if __name__ == '__main__':
+    array = [1, 7, 3, 0, 5, 8, 3, 2, 6, 2, 1, 1, 4, 5]
+    bit = fenwick(array)
+    print('Array: [{}]'.format(', '.join(map(str, array))))
+    print()
+
+    print('Prefix sum of first {} elements: {}'.format(13, bit.prefix_query(12)))
+    print('Prefix sum of first {} elements: {}'.format(7, bit.prefix_query(6)))
+    print('Range sum from pos {} to pos {}: {}'.format(1, 5, bit.range_query(1, 5)))
+    print()
+    
+    bit.update(4, 2)
+    print('Add {} to element at pos {}'.format(2, 4))
+    new_array = [bit.range_query(idx, idx) for idx in range(len(array))]
+    print('Array: [{}]'.format(', '.join(map(str, new_array))))
+    print()
+
+    print('Prefix sum of first {} elements: {}'.format(13, bit.prefix_query(12)))
+    print('Prefix sum of first {} elements: {}'.format(7, bit.prefix_query(6)))
+    print('Range sum from pos {} to pos {}: {}'.format(1, 5, bit.range_query(1, 5)))
+    print()