Merge pull request #3520 from issac5693/master

adding fenwick data structure

data_structures/Fenwick tree/python/fenwick tree.py

@@ -0,0 +1,66 @@
+# Python implementation of Binary Indexed Tree
+
+# Returns sum of arr[0..index]. This function assumes
+# that the array is preprocessed and partial sums of
+# array elements are stored in BITree[].
+def getsum(BITTree,i):
+	s = 0 #initialize result
+
+	# index in BITree[] is 1 more than the index in arr[]
+	i = i+1
+
+	# Traverse ancestors of BITree[index]
+	while i > 0:
+
+		# Add current element of BITree to sum
+		s += BITTree[i]
+
+		# Move index to parent node in getSum View
+		i -= i & (-i)
+	return s
+
+# Updates a node in Binary Index Tree (BITree) at given index
+# in BITree. The given value 'val' is added to BITree[i] and
+# all of its ancestors in tree.
+def updatebit(BITTree , n , i ,v):
+
+	# index in BITree[] is 1 more than the index in arr[]
+	i += 1
+
+	# Traverse all ancestors and add 'val'
+	while i <= n:
+
+		# Add 'val' to current node of BI Tree
+		BITTree[i] += v
+
+		# Update index to that of parent in update View
+		i += i & (-i)
+
+
+# Constructs and returns a Binary Indexed Tree for given
+# array of size n.
+def construct(arr, n):
+
+	# Create and initialize BITree[] as 0
+	BITTree = [0]*(n+1)
+
+	# Store the actual values in BITree[] using update()
+	for i in range(n):
+		updatebit(BITTree, n, i, arr[i])
+
+	# Uncomment below lines to see contents of BITree[]
+	#for i in range(1,n+1):
+	#	 print BITTree[i],
+	return BITTree
+
+
+# Driver code to test above methods
+freq = [2, 1, 1, 3, 2, 3, 4, 5, 6, 7, 8, 9]
+BITTree = construct(freq,len(freq))
+print("Sum of elements in arr[0..5] is " + str(getsum(BITTree,5)))
+freq[3] += 6
+updatebit(BITTree, len(freq), 3, 6)
+print("Sum of elements in arr[0..5]"+
+					" after update is " + str(getsum(BITTree,5)))
+
+# This code is contributed by Isaac Martin