to calculate prefix sum effieciently when there are lot of updates

Author: Arjiit

Fenwick_Tree/fenwickTree.java

@@ -1 +1,82 @@
- 
+/*
+
+Space Complexity - O(n)
+T.C. to create - O(nlogn)
+T.C. to update - O(logn)
+T.C. to get prefix sum - O(logn)
+
+*/
+
+public class fenwickTree {
+
+	/*
+	For updating the value in tree, we start from index + 1 and we keep adding the value for next nodes,
+	till we reach an outside range of trees.
+	*/
+
+	public void updateBinaryIndexedTree(int binaryIndexedTree[], int val, int index) {
+		while (index < binaryIndexedTree.length) {
+			binaryIndexedTree[index] += val; // adding to original value in node
+			index = getIndex(index); // getting next index
+
+		}
+	}
+
+	/*
+	To get sum from (0, index), we start from index + 1 node and keep going up
+	via parent to reach 0.
+	*/
+
+	public int getSum(int binaryIndexedTree[], int index) {
+		index = index + 1;
+		int sum = 0;
+		while (index > 0) {
+			sum = sum + binaryIndexedTree[index];
+			index = getParent(index);
+		} 
+		return sum;
+	}
+
+	/*
+	Creating the Fenwick tree is like updating fenwick tree for every value in the array.
+	*/
+
+	public int[] createTree(int[] input) {
+		int binaryIndexedTree[] = new int[input.length + 1];
+		for (int i=1; i<= input.length; i++) {
+			updateBinaryIndexedTree(binaryIndexedTree, input[i-1], i); // 0th index value of input, will be stored at 1
+		}
+		return binaryIndexedTree;
+	}
+
+	/*
+	To get parent 
+	1) Get 2's complement (Flip all bits and add 1) (minus of index)
+	2) AND it with current INDEX
+	3) SUBTRACT it from the index
+	*/
+
+	public int getParent(int index) {
+		return index - (index & -index);
+	}
+
+	/*
+	To get next
+	1) Get 2's complement (minus of index)
+	2) AND it with current INDEX
+	3) ADD it to the index
+	*/
+
+	public int getNext(int index) {
+		return index + (index & -index);
+	}
+
+	public static void main(String[] args) {
+		int[] input = {1,2,3,4,5,6,7};
+		fenwickTree ft = new fenwickTree();
+		int[] binaryIndexedTree = ft.createTree(input);
+		assert 1 == ft.getSum(binaryIndexedTree, 0);
+		assert 3 == ft.getSum(binaryIndexedTree, 1);
+		assert 6 == ft.getSum(binaryIndexedTree, 2);
+	}
+}