Merge pull request #238 from pablomiralles22/fenwick-tree

Fenwick tree

data_structures/fenwick_tree/fenwick_tree.py

@@ -0,0 +1,54 @@
+
+
+# Returns the right most significant bit of an integer.
+# For example, 12 is represented by 1100 in binary, so it's LSB is the third position, 4.
+def LSB(n):
+    return n & -n
+
+
+class FenwickTree:
+    '''
+    A Fenwick Tree allows you to sum a range of elements and update an element in an array in O(log(n)). A segment tree
+    can also achieve this, but it takes twice the memory, making it less memory efficient. On the other hand, a segment tree
+    can compute more functions in a range of elements, like the minimum or maximum.
+    The way it works is that given an index (note that we start with 1 and not 0), the element in the array will be the sum 
+    of the LSB(index) elements below (including index). For example: with index 3, 3 = 11 in binary, and LSB(3) = 1, so this
+    element is equal to the corresponding element in the original array. But 4 = 100 in binary, so LSB(4) = 4, so it is equal
+    to the sum of A[0] + A[1] + A[2] + A[3] (the first 4 elements of the original array).
+    '''
+
+    def __init__(self, array):
+        self.len = len(array)+1
+        # Initialize an array of length n+1 to 0
+        self.arr = [0] * self.len
+        # Update the array to the one passed in the parameters
+        for i in range(0, self.len - 1):
+            self.update(i, array[i])
+
+    def update(self, index, val):
+        j = index+1
+        # Update the value for every element that sums A[index]
+        while j < self.len:
+            self.arr[j] += val
+            j += LSB(j)
+
+    # Get the sum of all elements before index (included)
+    def get_sum(self, index):
+        sum = 0
+        index += 1
+        while index > 0:
+            sum += self.arr[index]
+            index -= LSB(index)
+        return sum
+
+    # Get the sum of all elements in the range [start, end]
+    def get_sum_range(self, start, end):
+        return self.get_sum(end) - self.get_sum(start-1)
+
+
+if __name__ == '__main__':
+    arr = [1, 2, 3, 4, 5, 6, 7, 8]
+    fw = FenwickTree(arr)
+    print(fw.get_sum(3))
+    print(fw.get_sum(5))
+    print(fw.get_sum_range(1, 7))