fenwick-tree

The naive way would be to linearly iterate the range and multiply with each number in the range. Example: Array: {1,2,3,4,5,6,7,8,9,10}; Multiply index 3 to index 8 with 2. Assuming one based index. Result array should be : {1,2,6,8,10,12,14,16,9,10}; I know that Binary indexed tree can be used for the 'sum' part. How can I efficiently multiply a given range with a number? If you want to actually modify the array, you can't do better than the naive linear algorithm: you have to iterate the entire range and modify each index accordingly. If you mean something like, you have update operations

I tried to implement the Fenwick Tree in Java, but I am not getting the desired result. Here is my code: import java.io.*; import java.util.*; import java.math.*; class fenwick1 { public static int N; public static long[] a; public static void main(String[] args)throws IOException { BufferedReader br = new BufferedReader(new InputStreamReader(System.in)); N = Integer.parseInt(br.readLine()); a = new long[N]; String[] str = br.readLine().split(" "); for (int i = 0; i < N; i++) { a[i] = Long.parseLong(str[i]); } increment(2, 10); System.out.println(a[2]); System.out.println(query(4)); } public

Today i listened a lecture about fenwick trees (binary indexed trees) and the teacher says than this tree is a generalization of interval and segment trees, but my implementations of this three data structures are different. Is this afirmation true? and Why? I have never heard binary indexed trees called a generalization of anything. It's certainly not a generalization of interval trees and segment trees . I suggest you follow the links to convince yourself of this. than this tree is a generalization of interval and segment trees If by "this tree" your teacher meant "the binary indexed tree",

Fenwick tree is a data structure which allows two kind of operations (you can augment it with more operations): point update update(index, value) prefix sum query(index) Both of the operations are in O(log(n)) where n is the size of an array. I have no problems understanding how to do both operations and the logic behind them. My question is how can I initialize a Fenwick tree from an array. Clearly I can achieve this in O(nlog(n)) , by calling n times update(i, arr[i]) , but is there a way to initialize it in O(n) . Why am I asking this if wikipedia tells that you can initialize in nlog(n) ?

This question already has an answer here: meaning of (number) & (-number) 3 answers For example: int get(int i) { int res = 0; while (i) { res = (res + tree[i]) % MOD; i -= ( (i) & (-i) ); } return res; } A tree update function: void update(int i, int val) { while (i <= m) { tree[i] = (tree[i] + val) % MOD; i += ( (i) & (-i) ); } } Can you please explain what they do in the code by using ( (i) & (-i) ) ? This two functions are a modified implementation of a Binary index tree (Fenwick tree) data structure. Here is two pictures to supplement MikeCAT's answer showing how i variable updates for